The Variations In Skeletal And DenturePatterns In Excellent Adult Facial Types *SAMUEL GOLDSMAN, D.D.S., M.Sc.D.Niagara Falls, N.Y.The purpose of this research projectwas to investigate the dentoskeletal pat-terns of Caucasian adults having ex-cellent faces. This objective was furtherto be defined by studies of central ten-dency, dispersion, and correlation.Aspects of dentoskeletal pattern to beconsidered included mandibular prom-inence or retrusion, profile convexity,tooth axial inclination, vertical heightproportions, and structural dysplasia inthe anteropostero plane.In addition, the variations were con-trasted according to sex and by com-parisons with previous studies based onsamples characterized by excellence ofocclusion.FACIAL ESTHETICSThe problem of facial harmony andthe intrarelations of the dentofacialcomplex, while consistently occupyingthe attention of dentists and orthodon-tists in particular from the time ofHunter and even before, has alwaysbeen an elusive concept because of theinfinite range of the variations inherentin the morphogenic pattern and thenebulous and indefinite nature of thesubject itself. Yet, the importance ofesthetics as a basic aim of orthodontictherapy needs little elaboration. Infact, Hunter1 in the eighteenth centuryhad suggested that the prime objectiveof this treatment was to beautify theappearance of the mouth.The question must be asked: WhatThesis submitted as partial fu1611menmt ofthe requirements for the degree, Master ofScience, University of Indiana.constitutes an excellent face? Is thereany demonstrable, quantitative criterionfrom which an excellent face can bedefined in terms applicable to the needsof the orthodontic clinician? Stoner'has suggested that each man's con-cept of facial beauty is a function of hisown innermost sensibility and under-standing. Yet, he points out, ". . . theremost certainly is considerable agree-ment among many of us that certainfaces fall well within the definition of. . . . harmony of form." Orthodontistsgenerally share Angle's conviction that"The study of orthodontia is indis-solubly connected with that of art as re-lated to the human face,"3 but doesnot the great universal genius of theKenaissance, Da Vinci, tell us: "Themost admirable faces are those whoseexpression best reveals the passions ofthe SOU^.''^ It is clear that the questionof facial beauty inspires sympatheticconsideration as much by the scientificresearch worker as it does by the sub-jective artist, and that facial beauty isa function of the facial feature inbalance and harmony.The first American to apply the term"dentofacial orthopedics'' was CalvinCase in 1896.5 There are countlessreferences in Case's writings of his pre-occupation with esthetics and his in-terest in the fine arts and their influ-ence on orthodontics.Edward H. Angle admonished theorthodontic profession to have "fixed inour minds the outline of the perfectface . . . ," His intimate concern withthe question of facial esthetics is wellknown to all students of the history of63 64ColdsmanApril, 1959orthodontics. Angle considered that allthe essentials of beauty and perfectionwere to be found in the statue of ApolloBelvedere.Tweed and his followers have beenthe conspicuous leaders of the revivaland reemphasis in recent years of im-provement in facial esthetics as a prac-tical and basic goal of orthodontictherapy. Tweed has placed estheticsfirst in his list of treatment objectives;to achieve this objective he has ad-vocated in many instances the extrac-tion of dental units. Thus, on a basisof clinical experience, he disputesAngle's dictum concerning the necessityfor maintaining a full complement ofteeth in order to gain the ultimate ex-cellence of occlusion and, according toAngle, the ultimate in facial balanceand harmony. Tweed has placed par-ticular emphasis on facial esthetics be-cause he is convinced that good occlu-sion is possible only where there is rea-sonable balance between the variouscomponent parts of the dentofacialcomplex, and ". . . only when normalocclusion accompanies a normal facepattern is the ultimate in balance andharmony of the facial lines possible.GBeauty of facial lines does not de-pend alone on beautifully aligned andideally occluded teeth but upon thesum total of intra-relationships betweenall the structures that enter into theformation of the dentofacial complex.Therefore, the basic etiology of mal-occlusions may lie in the faulty de-velopment or malrelation of these parts.Logically, Angle's major premise ofideal occlusion per se as the primerequisite for the balance and harmonyof facial parts may be faulty, since thebasis for ideal occlusion is the ideallycoordinated development of all thestructures of the face and cranium. Theone rule in the fine arts for the applica-tion of rigid standards to the ideal faceis that there are no rules: every facediffers from every other one to a greateror lesser degree! Yet, there are funda-mental principles in art, the expressionof which signifies beauty - when linesare in balance and harmony, they pos-sess two of the fundamental qualitiecwhich govern the degree of perfectionof the product of the artist. The special-ty of orthodontics revolves around aceaseless pursuit of this.CEPHALOMETRIC METHODS`The most significant advancement inorthodontics in recent years is the wide-spread employment of cephalometricsas an analytical tool and diagnosticaid. With the development of tech-niques for routine appraisal of patients,the cephalometer has been increasinglyaccepted as the most efficient means forstudying therapeutic and prognosticpossibilities and limitations. It is a con-venient procedure for analyzing ab-normalities, localizing and recording thedegree and direction of discrepancy; itcan be applied to functional and to softtissue analysis; it makes possible themore accurate classification of facialtypes; it is used for the study of com-pleted cases; it is a time-linked tech-nique which enables the investigationof problems of growth and developmentthrough the dynamic analysis of serialstudies. Downs has observed : "Cepha-lometrics is to the orthodontist what thedissection room is to the anthropologistand anatomist".' The introduction ofthe cephalometer in the United Statesas an analytical tool in orthodontics iscredited to Broadbent (1931) .'Tweed emphasized the significanceof the Frankfort mandibular planeangle in diagnosis9 He suggested thatthe steeper the plane (the higher theangulation), the poorer the prognosisinsofar as improvement of facial es-thetics is concerned. E. L. Johnson alsoaffirmed this in a later and more com-prehensive study.1 Voi. 29, No. 2Facial Types65Margolis, who had been among thefirst to report on the axial inclinationof the lower incisors", introduced themaxillofacial triangle in 1947l'. He feltthat the character of this triangle wassufficiently narrow so as to establisha basic facial pattern. Tweed introduc-ed a modification of this triangle in1 95413, using more conventional regis-tration points and planes. In a re-analysis of his own treated cases, hecame to the conclusion that the bestcsthetic results were obtained in thosecases having a Frankfort mandibularplane angle of 25", an axial inclinationof mandibular central incisor tooth tomandibular plane of go", and, there-fore, an angulation of 65" of man-dibular central incisor tooth to Frank-fort plane. This latter measurement isconsidered by Tweed to be of para-mount importance.The precise quantitative definition ofmandibular central incisor tooth posi-tioning devised by Tweed was the sub-ject of an article by Wylie14. Wylie, re-analyzing Tweed's sample, came to theconclusion that Tweed oversimplifiedhis treatment concept and the explana-tion of his results, and that the up-righting of the mandibular central in-cisor teeth to a 65" angulation withFrankfort plane was only one element,and not necessarily the most important,in his most successful cases. Wylie sug-gested that the remarkable facialchanges were rather a function ofTweed's extraordinary ability to elicitmandibular growth in the majority ofthese cases.Wylie", in a study of mandibular,nasal, and dental heights, showed thatthese were among the most stable ofdentofacial dimensions. Accepting asvalid the theses of RrodieIG and ofBroadbent" regarding the constancy ofthe proportionality of the facial partsduring growth, he developed as a con-sequence an ascessment of anteropos-tero dysplasia''. Later, Wylie andElsasaer elaborated on this in a studyon the craniofacial morphology of man-dibular retru~ion'~. Wylie and E. L.Johnson studied mandibular and ver-tical dimensions and relationships in anevaluation of facial dysplasia in thevertical planez0.Downs, using a sample of youngadults having excellent occlusion, stud-ied the variations in skeletal and den-ture relationships inherent in thesefacial patterns and pointed out theirimportance in prognosis and in treat-mentZ1. Riedel studied, on a somewhatsimilar sample, the anatomical rela-tionships using the plane from nasionto sella turcica as the principal plane ofreference," instead of Frankfort hori-zontal (as in Downs' method). Riedel,in a later study, applied the analysisof Downs to a sample of better-than-averageJensen and Palling, in a recent sur-vey of the gonia1 angle, showed that,while this angle cannot by itself be re-sponsible for marked facial disharmony,it may well reflect the coordination andproportion between the various partsthat constitute the unity of the face.24The outstanding advantage of ap-plying cephalometric roentgenographicprocedures to craniofacial measure-ments is that they facilitate measure-ments on living subjects which wouldotherwise be impossible. Indeed, ceph-alometrics has progressed to the pointwhere it is no longer the tool of theresearch worker, but is a necessary ad-junct to a complete and well plannedcase analysis from which a diagnosismay be derived. It is not a panacea thatwill supplant all other methods of an-alysis and answer all of the orthodon-tist's diagnostic problems and can nevertake the place of conscientious clinicalobservation. But so long as the scienceof orthodontics remains a problem ofrelations within the dentofacial com- 66 Goldsman April. 1959plex in which, "all we ever find arevariations, endless variations . . . .then cephalometrics will be an invalu-able tool supplementing all other pro-cedures of analysis.METHOD AND MATERIALSA total of one hundred and sixtycases, chosen by perspection as repre-senting better-than-average Caucasianadult faces of no particular ethnicgroup, were photographed full viewand profile view oriented with Frank-fort plane, using the photographic andcephalometric facilities of the IndianaUniversity School of Dentistry.This rather arbitrary sample wasthen subjected to a critical evaluationby an impartial jury of artists fromthe Herron Art Institute of Indian-apolis, Indiana and the Buffalo ArtInstitute, Buffalo, New York. The panelof artists selected those faces, fifty innumber, which could be considered ex-cellent.The artists displayed a startling un-animity in their selection of the casesto be analyzed and, as might be ex-pected, their conception of ideal facialharmony was rather more liberal thanthat of orthodontists. It was felt that abroader sampling would occur ifpeople in the fine arts served as thejury rather than orthodontists, whomight well have preconceived andsomewhat prejudicial ideas of what con-stitutes ideal facial balance and es-thetics.When the fifty cases were submittedto the staff and graduate students of theDepartment of Orthodontia, IndianaUniversity for their critical appraisal,there were some definite areas of dis-agreement: the artists' sample of excel-lent faces included some concave andsome convex types - in other words,a representative sampling of diversefacial types. The orthodontists, on theother hand, tended to prefer thoseY'25faces which fell within the definitionof "flat" or vertical or concave pro-files. The panel of artists, in theircritical appraisal of the photographs,studied the face as a whole, but placedsome emphasis on the profile and, inrather the same manner as the ortho-dontists, stressed that their attentionwas particularly attracted to the lowerface - the area from mouth to chin -as it fitted into the entire face.The fifty cases selected were pro-cured from the files of current patientsof the Indiana University School ofDentistry, from the ranks of stu-dents, and other personnel of theIndiana University Medical Center.The cases were, on the whole, repre-sentative of various economic andsocial levels. There were nineteen malesand thirty-one females of ages rangingfrom fifteen to thirty-six and averagingtwenty-three and one half years.Every one of the fifty cases displayedClass I molar relationships. Except forCase No. 46, the sample consists of un-treated cases. The photographs, ori-entated with the Frankfort plane, ofsome of the cases used in this inves-tigation are shown in Figures 1, 2 and3.WTHODAccurate cephalometric roentgeno-grams, anteropostero and lateral head-plates, were taken in occlusion withthe cephalometer of the Departmentof Orthodontia. These records weremade according to the Rroadbent-Bolton technique for the standardiza-tion of profile x-rays, using a fixed posi-tion of the x-ray tube and a cephalo-stat for positioning of the head witha sixty inch target distance.Since all roentgenograms are en-largements and are subject to x-raydistortion, the question of error incephalometric registrations and theirconsequent effect on measurementsmade therefrom had to be considered. Vol. 29. No. 2Facial Types67Fig. 1 68ColdsmanApril, 1959Pig. 2 Vol. 29, No. 2Facial Types69Fig. 3 Coldsman April, 195970This problem was the subject of a com-prehensive investigation by Adams".Adams reported that this error is with-in acceptable limits of experimental ac-curacy, even though the subjects differin absolute size.Tracings were constructed from theprofile roentgenograms and the mate-rial analyzed according to methods sug-gested by Downs, Tweed, Wylie, E. L.Johnson and Riedel, as well as somemodifications of their techniques whichwill be described as each analyticalmethod is considered. When the meansand acceptable ranges of variationstherefrom were established by deter-mining the standard deviations, poly-gons (after Adams and Vorhies")TABLE IThe Indiana Sample : Summary of Readings nccording to Downs ' Met,hod.CombinedSampleSD. k2.80FACIAL ANGLE M 86.0R 80.0 to 92.0ANGLE OF CONVEXITY M -1.0SD. k5.50R -11.6 to +14.0A B PLANE ANGLE M -4.1SD. k3.10R -10.5 to+4.5?rl!_NEIBULAR. pl.ANr: ANCII,R M 25.4SD k3.83R 16.5 to 36.0SD.+3.74R 56.5 to 70.0SD k4.30Y-AXIS ANGLE M 61.8CANT OF ~CCLUSAL PTANE M 8.6R 2.4 to 39.57 TO Occr.vsi\r, PLANE M 15.6sn k5.69R 5.0 to 30.081) k5.83R -15.0 to tl2.4s1) ,2824R 110.5 to 151.0ST). kl.95it -0.8 to +s.s7 1'0 ~fANDIRIII~AR h\NE M -0.4TO 3 M 136.1'r0 A - P PLANE (in nim.) M3.6Males85.821.94-2.224.47-3.2k2.99-8.3 to +4.580.0 to 89.2-11.6 to +m24.9k3.6216.5 to 32.862.5422.9457.5 t,o 68.07.624.552.4 to 17.014.9225.396.0 to 27.0+n.i4k6.m-11.0 to+11.0137.327.9112n.5 to 1 51 .n3.7 1.980.0 to 4-8.0Females86.2k3.m80.0 to 92.0-0.3k.5.88-4.7k3.12-10.0 to $14.0-3 0.5 to +0.5k3.9017.0 to 36.025.761.38k3.349.23.2 to 19.556.5 to 70.024.091 6.046.0 {to 30.0-0.6525.61-1 5.0 to +12.4135.3k8.7911 0.5 to 148.03.6k1.91-0.8 to +A,(;2.i.78 Vol. 29, No. 2 Facial Types 71were constructed summarizing some ofthe measurements. Correlations wereestablished and tests for reliability andsignificance were also conducted.OBSERVATIONS AND FINDINGS1. The measurements made accord-ing to Downs' technique of analysisare summarized in Table I.2. The measurements observed ac-cording to the analytical method ofRiedel, using S-N (Sella-Nasion) asplane of reference, are summarized inTable 11.3. The measurements derived fromthe evaluation of vertical dysplasia, ac-cording to a technique suggested byWylie, are found in Table 111.TABLE IIThe Indiana Sample : Summary of measure-ments related to S-N plane, according to theanalytical method of Riedel.CombinedSampleSN - POINT AM ........................... 81.22"SD .......................... 2 3.11R ...................... .74.6 to 87.0SN ~ POINT BM ........................... 79.79"SD .......................... + 3.21R ...................... .73.o to 86.0DIFF~ENCESNSNSNM ............................ 1.42"SD .......................... + 2.17R ..................... --?.n-t~ +7.i- GNATHIONM ............................ 80.5"sn .......................... 3.79R ...................... .71.1 to 87.0- MANDIBUIAR PLANEM ............................ 29.3"SD .......................... 25.50R .................... .15.5" to 44.0"-I-!M ........................... 105.0"SD .......................... 26.98R ................... .91.2" to 122.5"4. Data derived from an assessmentof anteropostero dysplasia, according toa method suggested by Wylie, are sum-marized in Table IV.TABLE I11The Indiana Sample: Summary of measure-ments derived from the evaluation of verticaldysplasia.CombinedSampleRAMUS HEIGIIT (mm.)...................... 59.6R .........GONIAL ANGLE ........ .123.8"SD .......................... 26.25R .................. .110.5" to 138.6'M ............................. 79.8 ....................... 24.76R ...................... .70.0 to 90.9M ........................... 121.63SD .............. ....... .+7.41R .................... .106.6 to 137.1M ............................. 55.1SD ......................... .*3.32R ..................... ,493 to 63.5LOWER BORDER OF MANDIBLE (mm.)TOTAL FACE HETGHT (N-GN)UPPER FACE HEIGHT (N-ANS)IAWER FACE HEIGHT (ANS-CN) ......... ......... .66.6SD ......................... .+5.88 54.5 to 78.5innTFH 45.5sn ......................... .+-2.31 ... .a.n to 50.8LFHionTFHM ............................. 54.5SD ......................... .-+2.26RTJFH = Upper Face HeightLFH = Lower Face HeighCTFH = Total Face Height 72Go 1 d s m a nTABLE IVThe Indiana Sample : Summary of measure-ments derived from an assessment. of antero-poster0 dysplasia, according to Wylie 'smet,hod.CombinedSampleLESGTH ~CAXDIELE11 .............. ...... .llG.5PORION-SELLA ...................... 22.8SD ................ ... .*4.10 ........... 12.0 to 29.5ir ............... 168SD ......................... .*2.21R ...................... .12.0 to 21..7M ............................. 20.3sn ............ k4.40PTJI - ER ...................... .ii.o to 30.0.4NS-Pr3rR ............__IJ NIT DYSPLASIA SCUKESD ........................... k.i.20R .................. .--12.0 to t13.0PTJI = Pterygoni:ixillary FissureANS = Anterior Nasal SpineE = 3f:ixill:ir-y 1st Perni:inent. Molar ToothTABLE VThe 1ndi:in:i Sample: Siunin:iry of readingsshowing the axial inclinations of m:ixillar,y:ind m:iiidibular central incisor tecth rehtedto t.he Fxnkfort Iiorizoiitnl.ILRIATRD TO TII E ~'K.\SKFOI;T PLANKMA ?(I I,lri\llY ~ENTK.41. TNCI SOI TOOT~ICo?iih hctlSamplehr .......................... .109.2"SD ................ miR .................. izuo~~.\XDlBLJL.lR CENTRAL INCISOR TOOT11~?M~.4'1'ED TO THE k7R:\SRFOKT PL.\XI?............. .OTi.4"...................Fig. 4 The k'ncial Skeleton Polygon for thecombined samp!e of 50 cases. The polygon iseonstrunted to demonstratc two st:indarddeviations plus and minus from the means,which are ::rrayed along the ceiiter line.Each scale division represents one angulardrgree or one millimrter as the case may bc.5. Axial inclinations of tbe incisorteeth related to the Frankfort hori-zontal are noted in Tablc V.Fig. 4 shows a polyKon for the com-bined sample of fifty cases, constructedfrom the ten measurements used in theoriginal Downs' analysis and also inthis report. In addition, the measure-ment relating the mandibular centralincisor tecth to Frankfort horizontalhas been included because of the in-tcrcst stimulated by the work of Tweed.A range of two standard deviationson either side of the mean is used herein lieu of the range of extremes plotted Vol. 29, No. 2 Facial Types 73in the Indiana Polygon by Adams andVorhiesZ7.The polygon derived from the meas-urements observed in this study will bereferred to, from now on, as the "FacialSkeleton Polygon". Generally speaking,in the polygonic method of illustratingqualitative and quantitative mathe-matical observations for a static ceph-alometric analysis, the readings fallingto the left of the center line, or mean,indicate a Class I1 tendency; those fall-ing to the right a Class I11 trend.COMPARISONS OF THE INDIANA SAMPLE WITH THE ANALYSES OF DOWNS AND RIEDELThc: Facial Angle The mean of theIndiana sample for this angulation is86.0", which is smaller than eitherDowns' reading (87.8') or that ofKiedel (88.6'). The differences of1.8" between the readings for the In-diana sample and the Downs samplehas a t value of 2.239. A t value of thismagnitude could not occur more thanfive times in a hundred on the basis ofchance alone. Since the .05 level ofconfidence is the criterion for sig-nificance used in this report, the dif-ference for facial angle readings be-tween the Indiana sample and Downs'findings is significant at the .05 leveland the null hypothesis rejected. Thedifference of 2.6" between facial anglereadings for the Indiana sample andKiedel's report has a t value of 4.341.A t value of this magnitude would notoccur more than one time in athousand on the basis of chance alone.The null hypothesis is therefore re-jected at the .001 level, and the dif-ference is significant. On the FacialSkeleton Polygon, on which means andvariations to two standard deviations oneither side of the mean of both theDowns and Riedel readings are super-imposed (Fig. 5), the mean of the In-diana sample will be seen to be on theDowns' YEISUR~YLNTI -----RILDEL'S YEAIUILYNII-.-----Fig. 5 hIeaiis aid dispersions (two stand-ard deviations on both sides of the me:ui)of the fiiiditigs of the niialrses of Dowiis andRiedel plot8teil 011 the fncid polygoil for theconibiiied Iiidiaiia sample.retrognathic side as compared with themeans of Downs and Riedel.Angle of Convexity This groupshows the greatest variability of any ofthe measurements of the skeletal pat-tern within the Indiana sample. Themean is -1.O", which is smaller thanthe readings of either Downs (0.0') orRiedel (+l.6'), but neither of thedifferences are significant. The dif-ference between the Indiana sampleand that of Downs (1.0') has a t valueof 1.164, which does not reject the nullhypothesis at the .05 level. The dif-ference of 2.6" between the Indianagroup and that of Kiedel has a t valueof 0.716, which also does not reject the ColdsmanApril, 1959null hypothesis at the .05 level.The A-B Plane Angle The mean ofthe Indiana sample for this angulationis -4.3". The difference of 0.5" be-tween the readings for the Indianasample and the Downs sample has aI value of 1.164. A t value of this mag-nitude does not reject the null hy-pothesis at the .05 level, therefore thedifference is not considered significant.Riedel did not report the necessarydata for this measurement to perfoma test of significance. The standard de-viation for the Indiana sample is 23.10,compared with 23.67 for Downs. Thereadings for the Indiana sample rangefrom -10.5" to +4.5", compared withDowns' ranges : -9.0" to 0.0".Frankfort Alandibular Plane AngleThe mean of the Indiana sample forthis angulation is 25.4", compared withDowns' reading of 21.9" and Riedel's26.2". The difference of 3.5" betweenthe readings for the Indiana group andDowns' reading has a t value of 0.967;the difference of 0.8" between the In-diana sample and that of Riedel has at value of 0.598. In neither instance isthe null hypothesis rejected at the .05level of confidence, and the differencesare therefore not considered significant.The standard deviation for the In-diana sample is k3.83, for theDowns' sample 23.24, and for Riedel's25.95Y-Axis Angle The mean of the In-diana sample for this measurement is61.8", compared with readings forDowns of 59.4" and for Riedel 60.7".The difference of 2.4" between the In-diana sample and that of Downs has a tvalue of 2.408. A t value of this magni-tude could not occur more than twotimes in a hundred on the basis ofchance alone. The null hypothesis istherefore rejected within the acceptedcriterion for significance, and the dif-ference is significant at the .02 level.The difference between the Indianasample and that of Riedel for this meas-urement, a difference of 1.1", has a tvalue of 1.524. A t value of this mag-nitude does not reject the null hy-pothesis at the accepted level of con-fidence (.05) and the difference istherefore not significant. On the FacialSkeleton Polygon (Fig. 5), on whichmeans and ranges of measurements fromthe Indiana sample are plotted, it willbe seen that the mean of the Indianasample for the Y-axis angle is disposedsomewhat retrognathically in com-parison with Downs' reading.The Cant of the Occlusal PlaneThe mean of the Indiana sample for theocclusal plane angle is 8.6", comparedto readings of 9.3" for Downs' sampleand 8.5" for Riedel's. The differenceof 0.7" between the readings for theIndiana group and Downs' has at value of 0.637. The null hypothesisis not rejected at the .05 level. Themean difference is not significant.Riedel did not report the necessarydata to perform a significance test forthis measurement. The standard devia-tion for the Indiana sample is 24.30,compared with Downs' k3.83. Withinthe Indiana sample, the mean differencebetween male and female readings is1.6". The t value is 0.261. The nullhypothesis is not rejected at the ac-cepted level of confidence, and the dif-ference is not significant.The cant of the occlusal plane, re-lating the slope of the occlusion toFrankfort horizontal, is conventionallyplaced in the list of dental measure-ments of the Downs' analysis. A care-ful examination of the measure-ments of this analysis for the fifty casesof the Indiana sample indicated thatactually the occlusal plane angle tendedto behave more in accordance with theactivity of the skeletal structures thanwith the dental. To prove or disprovethis impression, accordingly, a study ofthe correlations of the occlusal plane Vol. 29. No. 2 Facial Types 75angle was undertaken, in which thisangle was correlated with every otherdimension of the Indiana sampleanalysis according to the method ofDowns. This study showed that thecant of the occlusal plane was moreclosely correlated with the skeletalmeasurements than with the dentalreading. A significant correlation at the.001 level was obtained between the oc-clusal plane angle and the facial angle,mandibular plane angle, and the Yaxis. Between this angle and the axialinclination of the lower incisor with theFrankfort plane a significant correla-tion at the .01 level was found andone at the .05 level with the inclinationof the mandibular incisor to the oc-clusal plane.Angulation of the Long Axes ofMaxillary and Mandibular Central In-cisors The mean for the Indiana sam-ple is 136.1' Downs' reading is 135.4'.Riedel's is 131.0". The difference of0.7 between the readings of the In-diana sample and that of Downs has at value of 0.349. The null hypothesisis not rejected at the accepted level ofconfidence, and the difference is notsignificant. The difference of 5.1 ' be-tween the readings of the Indiana sam-ple and that of Riedel has a t value of2.889. A t value of this magnitude couldnot occur more than one time in a hun-dred on a basis of chance alone. Ac-cordingly, the null hypothesis is rejectedand the difference is significant at the.01 level of confidence. The FacialSkeleton Polygon (Fig. 5) illustrateshow the Riedel mean is disposed retrog-nathically as compared with the mean ofthe Indiana group. The standard devia-tion of the Indiana sample is 28.34,compared with Downs' 45.76 andRiedel's 29.24.Maxillary and Mandibular CentralIncisor Teeth Axial Inclinations Re-lated to the Frankfort Horizontal Themeasurements of central incisor teethaxial inclinations to Frankfort plane arenot strictly within the realm of theanalysis according to Downs' method.Since the landmarks of Downs are used,and also because of the intereststimulated by Tweed regarding the posi-tioning of the mandibular incisor toothin relation to Frankfort plane, it wasdeemed reasonable to include thesemeasurements. The necessary data toperform significance tests was reportedneither by Downs nor by Riedel forthe positioning of the mandibular cen-tral incisor tooth.For the angulation of the long axisof mandibular central incisor tooth tothe Frankfort plane, the mean of theIndiana sample is 65.4", with a stan-dard deviation of k5.79. Downs re-ported a mean of 66.7'. Riedel's read-ing is 61.0'. Within the Indiana sample,the mean difference between male andfemales is 1.2". The t value is 0.169.'The null hypothesis is not rejected atthe .05 level, and the difference is notsignificant.For the angulation of the long axisof the maxillary central incisor toothwith the Frankfort plane, the mean ofthe Indiana sample is 109.2", with astandard deviation of k6.01. Riedel re-ports a mean of 111.0", with a standarddeviation of 25.70. Downs' reading is111.3'; he did not report the datanecessary to perform a significance test.The difference of 1.8' between themeans of the Indiana sample andRiedel's study has a t value of 1.544.The null hypothesis is not rejected at the.05 level, and the difference is not sig-nificant.The Angulation of the Long Axisof the Mandibular Central Incisor Re-lated to the Occlusal Plane. For thismeasurement the reading of the In-diana sample is 15.6', compared withDowns' reading of 14.5' and Riedel's20.6'. The difference of 1.1' betweenthe Indiana group and Downs' has a 76 Coldsman April, 1959t value of 0.802. The null hypothesis isnot rejected at the .05 level, and thedifference is not significant. The dif-ference of 5.0" between the Indianasample and Riedel's has a t value of4.108. A t value of this magnitude couldnot occur more than one time in athousand on the basis of chance alone.The null hypothesis is rejected and thedifference is significant at the .001level.The Angulation of the MandibularCentral Incisor to the Frankfort Man-dibular Plane The mean of the In-diana sample for this measurement is-0.4". Downs' reading is + 1.4" ;Riedel's is $3.1". The difference of1.8" between the means of the Indianasample and Downs' has a t value of1.308. The null hypothesis is not rejectedat the .05 level and the difference isnot significant. The difference of 3.5"betwt en the readings of the Indianasample and Riedel has a t value of2 7fi2. A t valiic of thi5 magnitudc couldnot occur more than one time in ahundred on the basis of chance alone.The null hypothesis is rejected and thedifference is significant at the .01 level.The Facial Skeleton Polygon (Fig. 5)shows the retrognathic disposition ofIliedel's mean in relation to that of theIndiana sample. The standard devia-tion for the Indiana group is 25.83,for Downs' study 53.48, and forRiedel's 56.78.The impression is that, in those casesexhibiting excellent occlusion and/orgood facial patterns, the mandibularcentral incisor teeth will tend to bemore or less upright with respect to theFrankfort mandibular plane. The find-ings of the Indiana sample confirm thisKenera1 impression, but further suggestthat there is a wide range of variabilityto be found, as indicated by the stand-ard deviation of 25.83" and the read-ingq which range from -15.0" to$12.4".The Distaiice from the Incisal Edgeof the Maxillary Central Incisor to theAF Plane The reading for the Indiana:ample is 3.6 mm., compared withDowns' reading of 2.7 mm., andRiedel's 5.5 mm. The difference of 0.9mm. between the means of the Indianasample and Downs' study has a t valueof 1.789. Since this could occur morethan five times in one hundred on thebasis of chance alone, the null hy-pothesis is not rejected and the dif-ference is not significant at the level ofconfidence used as the acceptedcriterion of significance (.05) . The dif-ference of 1.9 mm. between the meansof the Indiana sample and Riedel's hasa t value of 3.654. A t value of thismagnitude could not occur more thanone time in a thousand on the basisof chance alone. Accordingly, the nullhypothesis is rejected and the differenceis significant at the .001 level of con-fidence. Fig. 5 shows the retrognathicdisposition of Riedel's reading in com-parison with that of the Indianasample. This particular dimension hasthe smallest standard deviation, thesmallest range of variation of anymeasurement considered in this report.The standard deviation of the Indianasample is k1.95; that of Downs' studyis 21.80, and Riedel's *3.15.CORRELATIONS WITHIN THE INDIANASAMPLE BETWEEN VARIOUS SKELETALAND DENTURE MEASUREMENTS USEDIN DOWNS ANALYTICAL METHODAn examination of polygons for thecases of the Indiana sample shows atendency for certain of the dimensionsto function in a compensatory or bal-ancing manner in opposition to themovements of other dimensions. Thatis to say, where one measurement was,for example, to the right or prognathicside of the mean as seen on the polygon.- especially if the divergence wererelatively great - it would be balanced.. Vol. 29, No. 2 Facial Types 77by an equivalent discrepancy perhapsin the opposite direction of at least oneother dimension.To evaluate this tendency which hadbeen observed by general perspection,it was deemed advisable to correlatethose dimensions which most frequent-ly seemed to function in the compen-satory manner suggested.( 1) Between the facial angle and theY-axis angle, there exists an inversecorrelation of -0.500. The t value is3.50. The null hypothesis is rejectedand the correlation is significant at .01level. The polygon is so constructed thatthe facial angle increases to the rightor prognathic side of the mean line;the Y-axis angle decreases in that direc-t'lon. This negative correlation suggests,therefore, that so far as the polygon-picture is concerned, the two angles willvery often move in the same direction,although not necessarily the same de-gree.(2) A coefficient of correlation of-0.909 exists between the facial angleand the Frankfort mandibular planeangle. The t value is 6.36. The nullhypothesis is rejected and the correla-tion is significant at the .001 level ofconfidence, On the polygon, the Frank-fort mandibular plane angle decreasesto the right of the mean. The inversecorrelation suggests that, as seen onthe polygon, the two dimensions willvery often move in the same directionwith respect to the mean, again notnecessarily' the same degree.(3) Between the Frankfort man-dibular plane angle and the Y-axis, thecoefficient of correlation is positive:+0.619. The t value is 4.33. The nullhypothesis is rejected and the correla-tion is significant at the .001 level. Onthe polygon, both dimensions will beseen to increase in the same directionwith respect to the mean. Since a sig-nificant positive correlation is presentbetween these two measurements, it issuggested that they will often vary inthc same direction.(4) Between the angle of convexityand the A-B plane angle, a negativecoefficient of correlation exists: -0.330.The t value is 2.30. The null hypothesisis rejected and the correlation is sig-nificant at the .05 level. Since the twomeasurements, as constructed on thepolygon, increase in opposite directionsfrom the mean, the significant inversecorrelation indicates that the two di-mensions will often vary in the samedirection.(5) The coefficient of correlation be-tween the angle of convexity and thelinear measurement of the maxillarycentral incisor tooth to the plane fromPoint A to pogonion is +0.279. The tvalue is 1.953. The null hypothesis isnot rejected.(6) Between the facial angle and thelinear measurement of the lower borderof the mandible (gonion to pogonion,which is not a landmark used in Downs'analysis), the coefficient of correlationis +0.344. The t value is 2.41. The nullhypothesis is rejected and the correla-tion is significant at the .05 level ofconfidence. This significant positivecorrelation suggest that often, as thefacial angle increases - as the profiletends to become flatter or more con-cave, the lower border of the mandiblewill increase in absolute size.COMPARISON WITH RIEDEL'S ANALYSIS OF LANDMARKS RELATED TO THE SELLA-NASION PLANE TheIndiana sample mean is 81.22'. Themean reported by Riedel is 82.01'. Thedifference between the means of 0.79'has a t value of 1.12. The null hy-pothesis is not rejected at the .05 leveland the difference is not significant.Riedel's findings show a greater disper-sion. The standard deviation reportedby Riedel is 23.89, compared with theSella-Nasion Plane to Point A 78 Coldsman April, 1959Indiana sample's 23.1 1. TheIndiana sample mean is 79.79". Themean reported by Riedel is 79.97". Themean difference of 0.18" has a t valueof 0.26. For this value of t, the nullhypothesis is not rejected and the dif-ference is not significant at the .05 levelof confidence.Difference Tests of significance,comparing the Indiana sample withRiedel's, can not be performed sinceRiedel did not report the necessary data.For the Indiana sample, the discrep-ancy or difference between the meas-urements of the sella-nasion plane withPoint A and Point B is 1.42". Riedelreports a reading of 2.04". For the In-diana group, the standard deviation isk2.17. The readings range from 4.0"to +7.1".Sella-Nasion Plane Related to theMaxillary Central Incisor For thismeasurement the mean for the Indianareading of 104.0". The value of t forthe mean difference of 1.0" is 0.78. Thisvalue of t does not reject the null hy-pothesis and the difference is not sig-nificant at the .05 level. The standarddeviation for the Indiana sample ise6.98; for Riedel's sample, e5.75.Sella-Nasion Plane Relatad to Gnath-ion The mean for the Indiana sampleis 80.5"; for Kiedel's sample, the meanis 79.3'. The difference between themeans of 1.2" has a t value of 5.284.The null hypothesis is rejected and thedifference is significant at the .001 levelof confidence. The Riedel reading isdisposed retrognathically with relationto that of the Indiana sample. The In-diana sample shows greater dispersion:the standard deviation for the In-diana sample is e3.79, compared withRiedel's reading of 3.39.Sella-Nasion Plane Related to Frank-fort Mandibutar Plane For the In-diana sample, the reading is 29.3'; forSda-Nasion Plane to Point B.samp!e i5 !05.0". Riede! reprts aRiedel's sample, the reading is 3 1.7 ".The mean difference of 2.4" has a tvalue of 2.27. The null hypothesis is re-jected and the difference is significantat the .05 level of confidence. The dis-persion is greater for the Indiana sam-ple. The Indiana sample has a standarddeviation of 25.50 compared withk5.19 for Riedel's sample.EVALUATION OF VERTICAL DYSPLASIALinear Measurements. Table VI, Bsummary of the findings of the Indianasample and those of Wylie and John-son, shows that all readings of the In-diana sample, both linear and angular,are more widely dispersed than those ofWylie and Johnson.Proportion of Total Face Heightwhich is Upper Face Height. The meandifference of 1.7% has a t value of 3.66.The null hypothesis is rejected, and thedifference is significant at the .001 level.The Indiana sample shows wider dis-persion.Gonia1 Angle. This angle is an ana-tomical entity whose dimension is de-fined relatively early in life and neednot be expected to change appreci-ably with increase of age. The meandifference is not significant at the ac-cepted level.The Frankfort mandibular planeangle was correlated with certain den-ture and skeletal dimensions used inthe vertical displacement study ofWylie and Johnson and in the Downs'analysis. The results of this study con-firm the previous findings of Wylie andJohnson, with one exception which willbe noted.(a) As the Frankfort mandibularplane angle becomes steeper (increasesin angulation), the total face height in-creases. The correlation is significant atthe .02 level of confidence.(b) As the mandibular plane anglebecomes steeper, the percentage of low-er face height to the total face height Vol. 29, No. 2 Facial Types 79TABLE VIMandibular and ventical height measurements used in the evaluation of vertical dysplasia:The findings of the Indiana sample and the study of Wylie and Johnson. With the exceptionof the gonia1 angle and the facial height proportions, all measurements are linear andreported in millimeters. Wylie and Johnson did nata report ranges. Their study was under-taken on 47 children between the ages of 11 - 13 years, who were by subjective observationregarded as having good looking faces.Measurcrnent Mean S.D. RangeRAMUS I ......................... 59.6 k5.88 48.2 to 73.1HEIGHT .................... 54.8 23.80ANGLE WJ ....................... 122.5 k4.80LOWER BORDER I ...... 79.8 - +4.76 70.0 to 90.9TOTAL I ......................... 121.63 27.41 106.6 to 137.1FACE HT. WJ .............. 24.55UPPER I ......................... 55.1 23.32 49.3 to 63.5FACE IIT. WJ . . ............. 50.7 k2.58LOWER I ......................... 66.6 25.88 54.5 to 78.5 I ......................... 45.5 22.34 40.0 to 50.8.........................GONIAL I 123.8 26.25 110.5 to 138.6MANDIBLE 23.09FACE HT. WJ ....................... 62.4UFHTFHLFHT FHloo WJ ....................... 43.8 22.18I ......................... 51.5 22.26 49.2 to 60.0WJ ....................... 56.2increases. The correlation is significantat the .01 level.(c) Mandibular plane angle variesinversely with the ramus height. Thenegative correlation is significant at the.001 level of confidence.(d) The mandibular plane anglevaries inversely with the angulation ofthe mandibular central incisor tooth tothe mandibular plane. The negativecorrelation is significant at the .02level. This shows, in other words, thetendency of the lower central incisortooth to become more "upright" with anincrease in Frankfort mandibular planeangulation.(e) The Frankfort mandibularplane angle varies inversely with thefacial angle. The negative correlationis significant at the .001 level.(f) The mandibular plane anglevaries directly with the Y-axis angle.The correlation is significant at the.001 level of confidence.(9) The mandibular plane anglevaries directly with the cant of the oc-clusal plane. The correlation is sig-nificant at the .001 level.(h) The coefficient of correlationbetween the mandibular plane angleand the linear measurement of thelower border of the mandible (gonionto pogonion) is +0.021. The value oft is 0.15. The null hypothesis is not re-jected at the .05 level of confidence,and the correlation is not consideredsignificant. This does not confirm theobservation of Wylie and Johnson whoreported an inverse relationship.THE ASSESSMENT OF ANTEROPOSTERO DYSPLASIATests of significance comparing thefindings of the Indiana sample withthose of Wylie's study can not be per-formed since Wylie reported no data ColdsmanApril, 1959 TABLE VI1A summary of measurements listing the means observed in the assessinent of nnteroposterodysplasia, and compared with the standards of Wylie.Wylie's original analysis was reported from a sample consisting of 45 boys, 11.5 years ofxge, and 48 girls, averaging 11.3 years of age. These mere Class I malocclusions in the latemixed dentition stages.Len th Porion- Sella- Ptm- Ptm- Unit St.Maniible Sella Ptm IL ANS Score Dev. Range1h'I)lANASAMPLE :Male . . . . . , . . 117.0 24.7 lti.4 21.3Peiiiafe . . . . . . 114.G 21.7 17.1 18.7Combined . . . . 116.3 22.8 lti.8 20.3WPLIESANPLE:Male . . . . . . . . 103.0 18.0 18.0 15.0Female . . . . . . 101.0 17.0 17.0 16.0except the means. Wylie stressed, as amatter of clinical experience, that onlya clear-cut, obvious discrepancy fromhis standards had clinical importance.From this point of view, the findings ofthe Indiana sample may be regardedas acceptable deviations from the Wyliemale standard of 0.0 and the femaleare concerned; but all readings havewide ranges of dispersion.Table VI1 compares the findings ob-served in the Indiana sample with thestandards established by Wylie. Theunit score readings for the males isorthognathic: -2.5. The standard de-viation is 24.95. The standard errorof the mean is 1.16. The range is fromThe unit score reading for the fe-males is prognathic: +1.2. The stand-ard deviation is 24.18. The standarderror of the mean is 0.77. The rangeis from -6.5 to $9.5.The unit score reading for the com-bined sample is -0.85, which isorthognathic. The standard deviationis 25.20. The standard error of theSt?r?d?K! cf --I$, 2s far as the means---12.0 to $13.0.tiU.0 -I) I.( 7 24.95 -12.0 to +13.u57.0 $1.2 24.18 4.5.tU +Y.557.4 -0.83 25.20 -12.0 to +13.052.0 0.052.0 -1.0mean is 0.74. The range is from -12.0to $-13.0. THE INDIANA SAMPLE:DISCUSSION OF SOME SPECIFIC CASESAn opportunity is afforded for com-paring a set of monozygotic femaletwins, seventeen years, nine monthso!d, cases 2 and 3 (Fig, 6); None ofthe dimensions differ appreciably be-tween these two cases, neither in theeleven measurements plotted on thepolygons, the assessment of antero-poster0 dysplasia, the analysis againstthe sella-nasion plane, nor the verticalheight studies. The greatest differentiation occursin the absolute linear measurements forcertain dimensions of the mandible -the gonia1 angle, the lower border ofthe mandible (gonion to pogonion, andthe absolute mandibular length) asmeasured for the anteropostero dis-placement analysis - and the total faceheight. But none of these differencescan be considered conspicuous.The mandibular length for Case 2is 114.0 mm.; the lower border of theFig. 6 Above and center, photographs of monozygotic twins, cases 2 and 3. Below, case 22.This is :in example of similar skeletal and denture readings with other cases in an altogether(Iifferent type of face. The twins' faces are mesognathic while case 22 is more convex. Vol. 29, No. 2Facial Types81 82 Coldsman, April, I959mandible measures 75.0 mm. For Case3 these values are 109.5 mm. and 70.4mm., well within the wide range of ex-pected variability. At the same time,the Frankfort mandibular plane angleand the facial angle remain substantial-ly the same. The gonia1 angle of Case2 is greater than that of Case 3 : 116.2'to 113.6", but the standard deviation isk6.25 for the entire sample andk6.03 for the females. The total facialheight for Case 2 is 109.8 mm., com-pared with 106.6 mm. for Case 3, adifference principally due to a slightlygreater proportion of upper face height.But the small increase in absolute sizeof Case 2's dimensions is not conspicu-Case 22 is a male, twenty-four years,two months of age (Fig. 6). This in-dividual, whose facial contours seem, onsubjective appraisal, to be slightly onthe convex or retrognathic side as com-pared with the straight or mesognathicprofiles of the twins, displays startlinglysimilar readings in comparison with thetwins, of all of the measurements sum-marized by the polygons (Fig. 7).The greatest discrepancy, which mayhave some bearing on the profile con-tour, is to be found in the dimensionrelating the maxillary central incisortooth to the plane from point A topogonion, which is 5.5 mm., comparedwith the twins' readings of 3 mm. and2 mm. But even this difference is withintwo standard deviations. The standarddeviation for this reading is 21.95.As might be expected, the absolutelinear size of anatomical structures isgreater in the male (Case 22) than forthe twins. However, the facial heightproportions are not greatly at variance.In case 22, the percentage of lower faceheight to total face height is 55.4 percent, compared with the twins' readings:50.8 per cent and 51.2 per cent. Themean for this reading is 54.5 per cent;standard deviation is 22.26. Thus, theous.Fig. 7 Facial polygoiis of the twins incomparison with case 22.face in Case 22 is disposed slightlymore vertically, principally due to thegreater lower face height, as comparedwith the twins.Of all the measurements, the greatestdiscrepancy occurs in the assessment ofanteropostero dysplasia. For the twins,the unit scores are f4.3 and f4.6;the score for Case 22 is -11.0.This difference occurs because of therelative positioning of the head of thecondyle and, more particularly, themaxillary first molar. The distance ofthese reference points from sella turcicaand the pterygomaxillary fissure, respec-tively, is much greater in Case 22, wherethe high orthognathic unit score is buta reflection of the linear measurements.The compensatory mechanism re- Vol. 29. No. 2Facial Types83sponsible for the overall excellence ofthe profile balance and proportion func-tions in two ways. The Y-axis angleand the facial angle are slightly prog-nathic (in relation to the mean valuesfor these dimensions), thus placingpogonion in a relatively good relation-ship with respect to the facial plane.This, in conjunction with the prog-nathic (in relation to the mean) Frank-fort mandibular plane angulation of18" overcomes the orthognathic dis-placement in the anteropostero planeof space. At the same time, all polygonreadings are well within the polygonlimits (Fig. 7). The tendency of theskeletal measurements, including theocclusal plane angle, to be on the prog-nathic side of the mean is balanced byan equivalent tendency for the denturereadings to be on the retrognathic side.The resulting facial patterns are in ex-cellent overall balance.Cases 9 and 43 illustrate an interest-Fig. 8Two examples of mesognathic faces, 84 Coldsman April, 1959ing contrast in dimensions within thestraight or mesognathic facial typeFig. 8.Case 9, a female nineteen years,eleven months of age is the personwhose facial measurements most closelyapproximate the mean of every rela-tionship investigated. This is true notonly for the polygon measurements, butfor all other dimensions considered(Fig. 9).The mesognathic face of Case 43, amale thirty-six years, four months ofage displays some interesting tendenciesin comparison with Case 9. While thedenture readings are well within thepolygon limits, they are uniformly tothe right (towards the Class I11 side)C SC 43---.- CISL *-------Fig. 9 Facial polygons for two cases hav-ing mesognathic faces compared with eachother and with the means for the combinedsample.of the corresponding Case 9 readings.The denture measurements of Case 43unmistakably imitate and parallel thoseof Case 9, but the contrasts between thedimensions are more marked, moreexaggerated, as shown in Figure 9.With regard to the skeletal readings,this imitative or parallel tendency isbest illustrated on the polygon. Themost conspicuous skeletal discrepancy isobserved between the Frankfort man-dibular plane readings: 29.2" for Case43, and 26.0" for Case 9. The steeperFrankfort mandibular plane angle isaccompanied by the corresponding in-crease in total facial height (which isnot unexpected for the male), especiallyof the lower face. This is consistent withthe previously noted positive and sig-nificant correlation between Frankfortmandibular plane angle and the per-centage of lower to total facial height.It would be expected that, in view ofthe negative correlation between theFrankfort mandibular plane angle andiiie laciai angle, iht: sieepeI rriardibukirplane angle would be accompanied bya corresponding decrease in the facialangle. That this is usually true is attestedby the coefficient of correlation of-0.909. In Case 43, however, the facialangle is 89.5", as compared with themean of the combined sample of 86.0"and the Case 9'reading of 87.0". Sincethe standard deviation for this dimen-sion is e2.80, this difference takes onspecial importance. It would seem,therefore, that the facial angle in con-junction with the Y-axis angle andthe readings for the angle of con-vexity and A-B plane, functions as acompensatory mechanism against themandibular plane, so that, althoughthe mesognathic face displays indices ofprofile contour to the right of the meanvertical line of the polygons, it remainsin excellent general balance withoutshowing tendencies toward concavity.The unit score of anteropostero dis- Vol. 29, No. 2Facial Types85Fig. 10Above, case 23, R cnnvex fare. Below, rase 46, n rnnrnve fare.placement for Case 43 is +2.0 whichfrom the point of view of clinical ex-perience does not represent an im-portant prognathic departure from themean. This is another measurement,within the mesognathic facial type, withan ever-so-slight tendency toward theprognathic. The unit score for Case 9is 0.0.Cases 46 and 23, both females, affordan interesting contrast in two excellentfaces subjectively rated as concave andconvex, respectively, Fig. 10.Case 23, the convex facial type, istwenty years, six months of age. Herskeletal and denture dimensions tendto fall to the left of the mean, asshown on the polygon (Fig. 11). Rut allreadings are well within the polygoniclimits. The score for anteropostero dis-placement is also well within the ac-ceptable ranges, but shows a slight ten- 86 Coldsman April, 1959dency towards the orthognathic. Thereading is -2.5, which is not a sig-nificant variation from the mean.Case 46, the concave facial type, isfifteen years of age. This is the only per-son of the sample who is undergoingcurrent orthodontic treatment. Themalocclusion was of the Class I11 type;thc orthodontic problem was primarilyconfined to the maxillary arch due toa relative lack of growth in the anteriorxegment of the maxilla with a con-sequent displacement of anterior dentalunits, particularly the upper cuspids.Here, a steep Frankfort mandibularplane angle is compensated by relative-ly high readings of the angle of con-vexity and the A-B plane angle towardthe Class I11 side of the polygon. Atthe same time, the facial angle alsofalls on the Class I11 side of the mean,as does the Y-axis angle (Fig. 11).'The concave tendency of this facial pat-tern is undoubtedly a result of the lackof development of the anterior portionof the maxilla, since a faciai angie of88" is reasonably close to the mean.Jt would be expected that if the Frank-fort mandibular plane angle were notso steep, but more in accordance withthe general tendencies of the otherdimensions - toward the Class I11 sideof the polygon, the facial appearancewould be markedly prognathic. Thisdisposition of dimensions should becorrelated with the unit score foranteropostero dysplasia, which is + 1.5,a score which suggests again thc im-portance of an overall comparison ofthe anatomical structures in order tounderstand the definition of the facialpattern. The displacement of parts insuch a slightly prognathic relation -the mean for females is +1.2 - isanother indication of the effect of thecompensatory mechanism functioningbetween the various parts (especially inview of the Frankfort mandibular planereading of 30") which often results inVARIATIONS OF SKELETAL AND DENTURE PATTERNS %dCllt 4s C.SE 2,----Fig. 11 Polygons of two cases showing con-trast in remlings between n concave (case46) and n convex (case 23) type face.an excellent facial pattern in spite ofextreme discrepancies in individualdimensions.The total facial heights of the twofaces are similar: 120.0 mm. for Case46 and 123.0 mm. for Case 23. The per-centages of lower face height to totalface height are also not at appreciablevariance: 55.9 per cent for Case 46;54.8 per cent for Case 23. This in-dicates how, in two different facial typesexhibiting excellent overall balance andharmony, the profile proportions maybe reasonably comparable even thoughconsiderable variation may be displayedwith other dimensions.With the exception of the measure-ment for maxillary central incisor tooth Vol. 29, No. 2 Facial Types 87to the A.P. plane which varies only.3 mm. from the mean, all the denturedimensions of Case 46 vary directly andin opposite direction (towards the ClassI11 side) from those of Case 23. Theirsupport of the general concave patternis to be expected, as is, by contrast, thelarger angulation, the less "upright-ness", of the dentition of Case 23 in aconvex face.The obvious corollary to these ob-servations is the general assumption thatit is entirely conceivable and, indeed,logical that all three profile types -the concave, the convex, and themesognathic or straight can and do oc-cur in nature as ideal patterns with ex-cellent balance and harmony.Cases 31 and 38 (Fig. 12) have in-teresting and provocative characteristicsin common for which a certain amountof speculation is justified.Fig. 12 Two individuals whose readings tend to be similar. The skeletal readings arcuniformly excellent, being close to the mean line. Although these faces appear to be inexcellent artistic balance, all denture readings, without exception, are very extreme, beingon the Class I1 side of the polygon. Case 38, above; case 31, below. 88 Coldsman April, 1959Fig. 13 Fnrinl polygon for cnsc! 38 coni-Imred with riisr 31.An examination of the polygons(Fig. 13) shows that the skeletal read-ings for both cases are close to the meanor well within the limits of acceptabledeviations therefrom. The Case 38skeletal readings are closer to the mean,but the difference is of no special im-portance; those of Case 31 tend toparallel these readings, with the great-est discrepancy showing in the Y-axisangulation. The occlusal plane angula-tion of both cases parallels the activityof the skeletal structures.The curious features of these casesare in the denture patterns. Althoughboth faces are in excellent generalbalance and all skeletal readings wellwithin the acceptable ranges of varia-tions, the denture patterns for bothcases are extreme. This discrepancy ispronounced; except for the occlusalplane angle, all denture readings forCase 38 are beyond the limits of thepolygon, on the left or Class I1 side;those of Case 31 either touch or areextremely close to the left or Class I1limit of the polygon.It must be mentioned here that theuse of the term "denture readings" doesnot include, for purposes of interpreta-tion, the measurement of the cant ofthe occlusal plane, whose curious ten-dency to function so often in a mannerparallel with the direction of theskeletal measurements has already beennoted.Cases 38 and 31 illustrate the fol-lowing maxim : the overall facial pat-tern may conceivably be excellent, pro-vided the skeletal relationships are inexcellent balance and proportion, evenwhen the denture readings exhibit awide scatter or dispersion. Thus, anexcellent facial pattern may be definedwith an astonishing degree of in-dependence from the denture patternor the disposition of the teeth.A tendency for certain structures inthe dentofacial complex to balance orcompensate extremes in other dimen-sions to produce an overall balance andharmony in the general facial propor-tions has been previously noted. Thiscompensatory property is illustrated inCases 1, 15, 49, and 46, whose skel-etal and denture polygons arc shownin Figure 14.It has been shown that there arehigh negative correlations between theFrankfort mandibular plane angle andthe facial angle, and between the facialangle and the Y-axis angle. A studyof the polygons will show the tendencyof facial angle to decrease as the man-dibular plane becomes steeper. At thesame time, the Y-axis angle tends toincrease. The compensatory mechanismis cvidenccd in those cases where, with Vol. 29, No. 2 Facial Types 89a high Frankfort mandibular planeangle, the facial angle and Y-axis angleremain close to the mean, or even tothe right of the mean vertical line. Thealternative compensation is for the A-Bplane angle and the angle convexity todeploy to the right (or Class I11 side)of the mean.For these individuals it has been sug-gested that the compensatory propertyacted through a reversal or minimizingof the correlations between the facial,Y-axis, and mandibular plane angles, inaddition to the disposition of the angleof convexity and A-B plane angle to theright of the mean. With these cases,the denture readings, except for Case1, generally are to the right of the mean,with the angulation of the mandibularcentral incisor tooth related to man-dibular plane being extreme for Case46 - on the Class I11 side of thepolygon. In Case 46, the occlusal planereading functions in an opposite direc-tion from the mandibular plane angula-tion, reversing, in this case, the correla-tion. In Cases 1, 15, and 49, the oc-clusal plane readings, while not cor-relating exactly with the positive co-eaicient, remain, along with the Frank-fort mandibular plane values, on theleft of the mean vertical line.SUMMAR\* AND CONCLUSIONS1. An attempt has been made toevaluate, from lateral cephalometricroentgenograms, a sample of fifty ex-cellent Caucasian faces, selected by apanel of artists because of the harmonyof the facial balance and proportion.The opinions of the artists were re-markably uniform and included repre-sentative facial types ranging from theconcave or prognathic, through thestraight or mesognathic, to the convexor retrognathic.2. A quantitative analysis was made,according to standardized ,cepha-lometric techniques, of the facial andCASE ,5----- CIIL .r-------Fig. 14Facial polygons : cases 1, 15, 49,46.denture patterns. Measures of centraltendency and tests of confidence wereestablished, as well as studies of disper-sion in terms of the standard deviation,for each of the angular and linear meas-urements of the diverse anatomicaldimensions.3. The objective was further definedby studies of correlations and tests ofsignificance of differences betweenmales and females within the Indianasample, and by comparisons with pre-vious studies.4. Means and ranges of variabilityto two standard deviations for the tenmeasurements used in the Downs'analysis and for the measurement re-lating the long axis of the mandibularcentral incisor tooth to the Frankfort 90 Goldsman April, 1959horizontal were plotted on the FacialSkeleton Polygons, constructed for thecombined sample of fifty cases, thenineteen males, and the thirty-one fe-males. The polygons are a convenientyardstick for comparison with othercases.5. There were no significant dif-ferences between the males and the fe-males in any of the measurements.6. The males tended to be slightlymore concave in skeletal pattern due tothe more prognathic readings of theangle of convexity and the A-B planeangle; on the other hand, this was com-pensated by the higher facial angula-tion and smaller Y-axis of the females.7. In both skeletal and denture pat-terns, the dispersion of the femalereadings was either almost identical ordefinitely broader than that of themales.8. In the assessment of anteroposterodysplasia, the male unit-score was ll~llLly lllWl Ir VI C"YS.." .... " -A.I--the female, but the difference was notstatistically or clinically significant, andthe ranges of variability were wide.9. In the analysis according to themethod introduced by Downs, themeasurements of the Indiana samplewere similar to those of Downs withthe exception of the facial angle andthe Y-axis angle where significant dif-ferences do exist. The range of extremeof all measurements of the Indianasample is wider than that of Downs;all of Downs' denture measurements,as well as the Frankfort mandibularplane angle and the angle of convexity,have smaller standard deviations thanthose of the Indiana group.10. The facial angle and the Y-axisangle of the Indiana sample were dis-posed slightly toward the retrognathicor Class I1 side of Downs' findings.11. In the analysis according to thetechnique suggested by Downs, thefindings of the Indiana sample were sig--1:-l- l-- ---- nrthnmnQth;r than that 01nificantly different from those of Riedelin the facial angle, and in all readingsof the denture pattern, with the ex-ception of the measurement relating themaxillary central incisor tooth tothe Frankfort horizontal. Riedel re-ported a wider dispersion in terms ofstandard deviation than those of theIndiana sample in all measurementswith the exception of the angle of con-vexity, the Y-axis angle, and the rela-tionship of the maxillary central incisortooth to Frankfort horizontal.12. As compared with the findingsof Riedel, the facial angle of the Indi-ana sample was disposed retrognathical-ly, while those denture readings sig-nificantly at variance with those ofRiedel were disposed prognathically.13. A study of the correlations be-tween the occlusal plane angle andother measurements of skeletal anddenture patterns shows that the oc-clusal planc angle is more closely cor-related with the measurements of theskeletal pattern, rather than with thoseof the denture pattern, thus tending inmost cases to imitate the activity of theskeletal pattern.14. The role of the teeth in estheticsis difficult to define or assess as shownby the wide variability displayed byall denture readings. The broad dis-persion of measurements of the denturepattern, as compared with those ofthe skeletal pattern, suggests that anexcellent face is less dependent uponthe denture, or that the denture pat-tern, in itself, is too variable anddiversified an entity to be labelled ofparamount importance in the main-tenance of excellent facial pattern inuntreated cases.15. The hypotheses of Tweed and hisfollowers regarding mandibular incisorpositioning as index of facial estheticscannot be substantiated in this sampleof untreated cases in view of the liberaldispersion and variability of the read- Vol. 29, No. ZI- acial.- . ' Types91ings, i.e., while the mean of the In-diana sample for the angulation ofthe mandibular central incisor tooth toFrankfort plane was 65.4" (which com-pares favorably with Tweed's findingof 65.0') the standard deviation was25.79, with readings ranging from52.4" to 75.0".16. In the appraisal of landmarksmeasured against the sella-nasion plane(S-N), the findings of the Indianasample differed significantly from thoseof Riedel's analysis in two measure-ments: S-N to gnathion and S-N tomandibular plane. In comparison withthe findings of the Indiana sample,Riedel's measurements were disposedretrognathically. The dispersion waswider for the Indiana sample in allmeasurements except S-N to Point Aand S-N to Point B.17. Significant coefficients of correla-tion derived from the Frankfort man-dibular plane angle and various skeletaland denture measurements used in theevaluation of vertical dysplasia accord-ing to the technique devised by Wylieand Johnson show that, as this anglebecomes steeper (increases), the facialangle becomes smaller, the Y-iLyisangle increases, the gonia1 angle be-comes larger, the ramus height de-creases, the total face height - espe-cially the lower face - increases, andthe angulation of the mandibular cen-tral incisor teeth to the Frankfort man-dibular plane decreases. This confirmsthe previous report of Wylie and John-son.18. There is some indication that acompensatory mechanism or balancingproperty functions within the dento-facial complex. This property exists inorder to preserve the overall harmonyand proportions of the facial pattern.Where one dimension shows an ob-vious discrepancy, one or more of theothers will compensate by varying insuch a way as to minimize the expectedpattern of activity suggested by sig-nificant correlations with the dimensiondisplaying the obvious deviation fromthe mean.19. The sample used in this projectis of special interest because of thevaried facial types represented - akaleidoscope of Caucasian facial typesand of variations in measurements andrelationships. Since the cases are, withone exception, untreated, they may beconsidered as being essentially ana-tomically stable, as compared with anequivalent number of treated cases. Yet,tremendous variation is demonstratedhere.304 Hancock Bldg.REFERENCES1. Hunter, John. The Natural History ofthe Human Teeth. London, J. Jolt~uon,1803.3. Stoner, Morris M. A Photoinetric Analy-sis of the b'acial Profile. Am. J. Ortk.3. Angle, Edward H. Malocclusion of llicTeeth, ed. 7. Philadelphia, 8. S. WhitcCo., 1907.4. Leollnrdo dn Vinci, a film. New York,l%(: Pictura E'ilms Corporation, 1952.5. Case, Calvin S. Facial and Oral Deforni-ities. Chicago, C. S. Case and Go., 189ti.ti. Tweed, Oharles H. Evolutionary Trendsin Orthodontics, Past, Present, and Fu-ture. Am. J. Orrh. 39:81-108, 1953. 1).108.7. Downs, William B. The Role of Csphal-ometrics in Orthodontic Case Analvsis41: 433-469, 1955.and Diagnosis. Am. J. Orf78. 38:162-i82,1952. p. 166.8. Broadbent, B. H. A New X-ray Tech-nique and its An-lication to orthodontia.Angle Ortho. 1:2, 45-66, 1931.9. Tweed, Charles H. The Frankfort Man-dibular Plane Angle. Ani. J. Orth. andOral Surg., 32 :175-230, 1946.0. Johnson. E. L. The Frankforb Mandibu-lar Plaie Angle and the Facial Pattern.Am. J. Orth. 36:516-533, 1950.1. Margolis, Herbeat. The Axial Inclinationof the Mandibular Incisors. Am. J. Orth.and Oral Surg. 29:571-593, 1943.2. A Basic Facial Pattern and its Applica-tion in Clinical Orthodontics. Am. J.Orth. and Oral Surg. 33 :631-641 1947. 92 Goldsman April, 195913. Tweed, Charles H. The Frankfort Man-dibu1:ir Incisal Angle. Angle Ortho. 24 (3) :121-169, 1954.14. Wylie, W. L. The Mandibular Incisor - Its Role in Facial Esthetics. AngleOrtlio. 25(1) :32-41, 1955.13. Wylie, W. L. The Relationship Between 1t:imuu Height, Dental Height, and Over- bite. ATII. J. Ortk. ant1 Oral Surg. 32:16. 13rotlie, All;m G. On the Growth Pat- tern of the Human Head from the ThirdMonth to the Eighth Year of Life. Am.J. Anat. 74:39-60, 1941.17. Broadben t, B. H. The Face of the Nor- nial Child. Angle Ortho. 7 : 183-208, 193718. Wylie, W. L. The Assessment of Antero-postero Dysplasia. Angle Ortho. 17 :97-109, 1947.57-G7, 194G.19. Wylie, W. L. and Elsasser, W. A. TheCraniofacial Morphology of Mandibular Retrusion. Am. J. Phys. Anthrop. 6:4G1-474, 1948.20. Wylie, W. L. and Johnson, E. L. RapidEvalua.tion of Facial Dysplasia in ,the Vertical Plane. Angle Ortlko. 22 : 165- 182, 1952.21. DON~S, William B. Variations in FacialRelationships: Their Significance inTreatment and Prognosis. Am. J. Orth.22. Riedel, Richard A. Esthetics and ItsRelation to Orthodontic Therapy. Angle23. Riedel, Hiellard A. Relations of Maxil-lary Structures to Cranium in Malm#- elusion and in Normal Occlusion. AngleOrtho. 22 :142-145, 1952.24. Jenseii, Elli and Pallings, Mogens. TheGonia1 Angle: A Survey. Am. J. Orth.25. Simon, Paul W. Fundamental Principles of a Systematic Diagnosis of DentalAnomalies. The Stratford CO., Boston, 1926.26. Adanis, J. William. Correction of Errorin Cephalometric Roentgenograms. AngleOrtho. 10:3-13, 1940.27. Adams, J. William and Vorhies, Jack.Polygonic Interpretation of Cephalomet- ric Findings. Angle Ortho. 21 (4) : 194- 197, 1951.34:812-840, 1948.OI'tllo. 20 :1G8-178, 1950.40 : 120-133, 1954.