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Alphabetical Index of Vertex Figure Usages

While facets of uniform polytopes by definition are uniform as well – in fact, the dynkin diagram of a facet of a Wythoffian polytope is derived by omission of just one node (and its incident links) – this does not hold true with respect to vertex figures. On the contrary, most generally the vertex figure of a uniform polytope is not uniform. By means of the concept of lace simplices the vertex figure of Wytoffian polytopes can be derived none the less systematically (as is outlined here).

Accordingly this listing of vertex figure polytopes runs much shorter than that for facets, especially because the following table was generated from the files included in the "incmats" folder. Thus these listings therefore do not aim to be any complete enumeration, they represent only the results from so far in this webspace provided individual polytope files.

Total count of currently listed polytopes, which occur as vertex figures of others: 304


0...9 - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - V - X - Z



Vertex Figure Used in Polytopes

0 ... 9

2doe 2sishi
2firp 2firp
2gad 2fix,   2gashi
2gike 2gahi,   2gax
2gissid 2gaghi
2hehad 2thox
2ike 2ex,   2gishi
2sissid 2gofix,   2gohi
2tet 2gogishi,   2hi,   2pen,   2tes
2thah 2tho
2thahp 2rhohid
2tho 2hehad
2thox 2guhsa
6tet 6tes

B

bad-verf bad
bend-verf bend
bidhin tedjak
bidrap bidhin
brene bifoh
bril haxabrag,   lin,   moarojak
broc bif

C

cabbix-verf cabbix
cadditradid dittady+dox
caddix-verf caddix
chad-verf chad
chon x3o4o3o4o
cid ex+fix,   gishi+gashi
co octet,   x4o4o *b3o,   x8o4o *b3o
cubaope icaf
cube aubautipip,   bauautipip,   bicyte ausodip,   biscpoxic,   bitapna,   bitefa,   chi,   cute,   cyte cubau sodip,   dapabdi poxic,   dox,   eoctaco,   haucope,   hautope,   kitapna,   kitefa,   m3o3m3o,   octaco,   octatricu,   pexic,   pibhaki,   poxic,   radh,   stoc,   tautisdip,   tetacoaoct,   tibbid
cubpy icopy

D

dah kaje
daj nal
dibhid-verf dibhid
did x5o5o *b5/2o
dihin dijak,   hixalrix
dijak Dutour 7D Type A,   gahax
disdi-verf disdi
ditdid dittady
ditti idhi
doe ikhon,   pibhaki,   quidex,   sishi
dot dotet,   hinro,   mo
dudsi paphicki

E

ek vee
ekip rake
enep ru
ex pennit,   phitte,   pitest

F

f v3o ragaghi
f v5o righi
f x3o BAVFfxoo xFofxFVo3xxFxooxo5xooxFfoV&#zx,   DCBAVFfxoo xxxFofxFVo3xoxxFxooxo5ofxooxFfoV&#zx,   FAxoFFxoox3foFFxofoxo oxofofxFof3ooxofxfoFf&#zx,   biscrahi,   oFfoo3ooxxF3Fxoxo3ooffx&#zx,   oct || (x,f)-co || (F,x)-co || (x,x,f)-toe || F-oct || (f,x)-tut || tet,   oct || (x,f)-tut || (F,x)-co || (x,x,f)-toe || F-oct || (f,x)-tut || tet,   ooofxfooo3xoxxoxxox5ofxofoxfo&#xt,   oooxfxooo3xoxoxoxox5ofxfofxfo&#xt,   oxofxfooo3xxxxoxxox5ooxofoxfo&#xt,   srid || ff-ike || f-doe || ff-ike || srid,   xFfxo3xoxoF3fxooo3oofFx&#zx,   xooFxxFfooFoofo3xxFooFxxxFooFxx3ofooFoofFxxFoox&#xt,   xoxFoFxox3oxoooooxo5ooxofoxoo&#xt
f x4o riddoh
f x5/2o raghi
f x5o ripped
f3o3x x5o3o3o3*a
f3o4x x5o3o4o3*a
f3o5x x5o3o5o3*a
fenandoh-verf fenandoh
fidoh-verf fidoh
firp dah
fix x3o3o5o5/2o
fy goh

G

gabdacan-verf gabdacan
gacid gahi+gohi,   gax+gofix
gad fix,   gashi
gafwan-verf gafwan
gahax Dutour 8D Type A
gatopin-verf gatopin
gee axh,   zee
geep rek
geepy zeepy
gicdatrid gidtixhi+dox
gidtid gidtixhi
gike gax,   padiap
gipbin-verf gipbin
gissid gaghi
gissidagike gogishiagax,   gogishiragax
gohi x3o5o5/2o5o
gyepip 2/10-luna of ex,   3/10-luna of ex,   4/10-luna of ex,   biscex,   rotunda of ex,   telex,   xofo3ooox5oxoo&#xt
gyspid zucypit

H

han daj
hax Dutour 7D Type A,   haxt,   jakamo,   laq
he linoh
hehad thox
hesa Dutour 8D Type A,   bay,   hauhocto,   laqalin
hex shitte,   tac,   x4o3o3o4o
hexat hedhon,   thon,   trah
hexip rag,   rixascad,   taccarat
hexpy tacpy
hext x3o3o3o4o3o
hi hi - 120 ikadoes,   o3o3o5o5/2x
hin hint,   jak,   madek
hinnip ranq
hinpy jakpy
hip rath
hit-verf hit
hixadot jakamo
hixalrix hopalril
hixip octatetdip,   roc
hocto bayoh
hopalril ocalroc
hopip rene
howoh-verf 2howoh,   howoh
hudsi paphacki

I

ico chont,   hext
id apech
ike 2/10-luna of ex,   3/10-luna of ex,   4/10-luna of ex,   biscex,   cydadex,   ditusna,   dodeca-diminished rotunda of ex,   eikedpy,   gishi,   icau prissi,   id || f-ike || ike || pt,   ite,   kepisna,   kidisna,   pedhon,   pedisna,   rotunda of ex,   sody,   spohi
irl-verf irl
irohlohn-verf irohlohn

J

jak naq
jakip riffy

K

kafandoh-verf kafandoh
kaje quil

L

laq naquoh

M

m m3o m3m3m3o,   m3o3m3o,   m3o3o3m
m2m3o triddit
mesdi-verf mesdi
mibdi 2/10-luna of ex,   idimex
mo jakoh

N

n-ap n-apt
n-p n-pidpy
nal fib
naq fy
nat-verf nat

O

ocpe reday
oct baudeca,   co || f-oct || oct || pt,   doehon,   haddet,   pex hex,   stico,   tabene
oct+6{3} hex+8oct
octacube icoap,   tessap
octasc hexasc
octatepe hexaf,   rixa
octdip traxh
octete hexete
octpen tro
octpy hexpy
odip bicyte gysrit,   cyte gysrit,   cyted srit
oho datha
ope hexaico,   oxo oxo3oox4ooo&#xt,   rapaspid,   rat
ox4oo&#q 3-squippyp-blend,   ope
oxqxo8ooooo&#qt lt-(o8o4x *b3x)

P

P-ap x4oPo4x
p2p5p gap dual
pap 1/10-luna of ex,   id || srid || F-ike || ti,   ikadoaid,   ikadoe,   twau doaid,   twau sridati
pedip o5o3x3o5o
pedpy ite
pen hitte
penaf hixaf
pendip icoy
penp octa tratet,   ril,   trial tratet
pent o3o3o3o4o3x
peppy ikepy
pinnip han
pip biscrox,   fxoo2ofVx3xxoo5xoof&zx,   icau pretasto,   ikaid,   ike||id||srid||ti,   oofoo3oxoxo5xooox&#xt,   owaudope,   peppia pero,   telex,   twau iddip,   twau sriddip,   twau tipe,   xoxFoFxox3oxoooooxo5ooxofoxoo&#xt,   xoxFofo3oxoofox5ooxooxx&#xt,   xoxxFxxox3oxoxoxoxo5ooxoooxoo&#xt

Q

q x3o arse aurap,   baudeca,   mibdirit,   pactat,   pexrit,   tetatut
q x3o3o rin
q x3o3o3o rax
q x4o octatoe,   rich
q x5o ripech
q3o3x gadtatdic
q3o4x x4o3o4o3*a
q3o5x x4o3o5o3*a
quacant-verf quacant
quil yab

R

raccoth-verf raccoth
rad m3o3m3o,   tabene,   tibbit
radah-verf radah
rag haxh
rap hin,   rapt,   todin
rapesc hinsc
rappip hinanit,   ratasiphin,   rojak
rappy hinpy
rapt hint
rat hinoh
reday hede
rene henne
rhote tibbic
ril hesa
rillip robay
rinah-verf rinah
rix hax
rixasc haxesc
rixip haxabrox,   rojaka hejak,   rolaq
rixpy haxpy
roc hocto
rox hi - 120 ikadoes,   x3o3o *b3o5o

S

scad cyxh
sicdatrid sidtixhi+dox
sidtid sidtixhi
sirco x3o3o4o3*a
sishi o3o5o5/2o5x
sissid gofix
sissidagad gaghi || gofix,   gashia,   sishi || fix
snit cube + n-p honeycomb
spid cypit
spil-verf spil
squaf icates
squahix bro
squahop barn
squap octacube,   spiddish
squapen bersa
squasc octasc
squat octh
squatet brox,   nitarin,   rixasarx
squepe octepe
squete octete
squippy octpy
squippyp hexaico,   traltisdip
squoct brinoh
srid x3o3o5o3*a
staf cyloh
stappy gikepy
stip gikagid,   raggix

T

tac gee,   penth
taccup garag,   rez,   rilastaf
tacpy geepy
teddi FAxoFFxoox3foFFxofoxo oxofofxFof3ooxofxfoFf&#zx,   FAxoFFxxox3foFFxofxxo oxofofxFof3ooxofxfoFf&#zx,   dodeca-diminished rotunda of ex,   icau pretasto,   idimex,   ikadoaid,   telex,   xofo3ooox3oxoo&#xt
tekah bichon,   m3m3m3o
tepasc rixasc
tepe rix,   tessarit
tepepy rixpy
tes icarico,   icot
tet gap dual,   gico,   gogishi,   m3m3o3o,   m3o3o3m,   oqo3ooq&#xt,   quidex,   radh,   tibbic,   tibbid,   tibbit
tet-dim-doe pd{3,5,3}
tetaf hixalrix,   penaf
tetdip he
tete penit
tethex tark
tethix treday
tetoct bragabrox,   sez
tetpen trene
tetrap torfy
tettac tarv
tettepe rolinoh
thah tho
thahp rhohid
that ahach
tho hehad
thox thox
ti aphexah
tibbid bidot
tic o3o4x4o4*b
tid o3o5x5o5*b
tikit bideca,   m3m3m3o,   m3m3o3o
tin-verf tin
tisdip icarit,   nit,   rapasrip
tobcu gytoh
toe ashexah
topax-verf topax
traf bidhin,   dihin,   tetaf
trahex barz,   ragabrag
trahin borfy
trahix brene
trapen broc
trarap branq
trat hihexah
tratac bark
tratepe rolin
tratet bril,   penarappip
tratetpy brilpy
tratrip dottasibrid,   nitasirhin,   ram
triddip dot,   teta ope
triddippy dotpy
trigee brav
trihop breday
trioc breday
trip aurap,   tetripau tuttip,   tript,   turap
triphix ribfoh
trippasc rapesc
trippen buffy
trippy rappy
tript rapt
trittip ramoh
troct brag,   ratanit
turap hosiap
tut ahexah
tutrip turap

V

v f3o 3rasishi,   rasishi
v f5/2o ragashi
v x3o rigogishi
v x5o ragishi
v3o3x gadtaxady
v3x3o sidtaxhi
vee ka

X

x f3o rih
x f5/2o rofix
x q3o coatobcu,   coatoe,   dirico,   oxux3xxoo4oooo&#xt,   pabdirico,   poccont,   pox rico,   wx ox3xx4oo&#zx
x v5o rigfix
x3o4q o3o3o4s4*a
x3v3o dattady
xo oq&#q gybeffip,   tisdip
xo ox&#h deca
xo ox&#k cont
xo ox&#q triddip,   xxo ooo3oxx&#xt
xo xo3ox&#q spix
xo2oq&#q 3-tisdip-blend
xo3/2ox&#q firp
xo3oo&#q tepe,   xxo ooo3oxx&#xt
xo3oo3ox&#q penaspid,   scad
xo3ox&#h batatoh
xo3ox&#q etetaco,   gyspid,   oxx3oox3xxo&#xt,   spid,   tetaco,   tetaco ausrip,   tetacoaoct,   xo3oo3ox&#q
xo4ox&#q spic
xx ox&#q tetaco ausrip
xxo oxx&#q card
xxo&#q cope,   eoctaco,   etetaco,   tobcupe,   tricupe

Z

zee ek
zeep riv


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