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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: 292


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
2gad 2fix,   2gashi
2gike 2gahi,   2gax
2gissid 2gaghi
2ike 2ex,   2gishi
2ike+gad 2ex+fix
2oct+6 2hex+8oct
2sissid 2gofix,   2gohi
2tet 2gogishi,   2hi,   2pen,   2tes
2thah 2tho
2thahp 2rhohid
2tho 2hehad
2trip-blend turap
3tet 3pen
6tet 6tes

B

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

C

cabbix-verf cabbix
cadditradid dittady+dox
caddix-verf caddix
card-verf card
chad-verf chad
cho chopy
chon x3o4o3o4o
cid ex+fix,   gishi+gashi
co o3o3o4x4*a,   octet,   copy,   x4o4o *b3o,   x8o4o *b3o
cope-verf cope,   eoctaco,   etetaco,   tricupe
cube 2ico,   aubautipip,   bauautipip,   bicyte ausodip,   chi,   octaco,   cute,   cubpy,   cytau tes,   cyte cubau sodip,   dapabdi poxic,   dox,   ecubedpy,   ecubpy,   eoctaco,   ico,   m3o3m3o,   tibbid,   pibhaki,   o4x4o4o,   o4o3o8x,   haucope,   tetacoaoct,   octatricu,   biscpoxic,   pabdico,   pexic,   poxic,   radh,   stoc,   tautisdip,   hautope
cubpy cubasc,   icopy

D

day deker,   ux
dibhid-verf dibhid
did didpy
dihin dijak,   hixalrix
dijak Dutour 7D Type A,   gahax
disdi-verf disdi
ditdid dittady
doe pibhaki,   o3o5o10x,   sishi,   x3o5o3o
dot dotpy,   hinro,   mo
dudsi paphicki

E

ek vee
ekip rake
ene day,   enne
enep ru
ex x3o3o3o5o,   x4o3o3o5o,   x5o3o3o5o

F

f v3o ragaghi
f v5o righi
f x3o BAVFfxoo xFofxFVo3xxFxooxo5xooxFfoV&#zx,   DCBAVFfxoo xxxFofxFVo3xoxxFxooxo5ofxooxFfoV&#zx,   FAxoFFxoox3foFFxofoxo oxofofxFof3ooxofxfoFf&#zx,   biscrahi,   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,   oFfoo3ooxxF3Fxoxo3ooffx&#zx,   ooofxfooo3xoxxoxxox5ofxofoxfo&#xt,   oooxfxooo3xoxoxoxox5ofxfofxfo&#xt,   oxofxfooo3xxxxoxxox5ooxofoxfo&#xt,   rahi,   srid || ff-ike || f-doe || ff-ike || srid,   xFfxo3xoxoF3fxooo3oofFx&#zx,   xooFxxFfooFoofo3xxFooFxxxFooFxx3ofooFoofFxxFoox&#xt,   xoxFoFxox3oxoooooxo5ooxofoxoo&#xt
f x4o o4o3x5o
f x5/2o raghi
f x5o o5x3o5o
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,   gadpy,   gashi
gafwan-verf gafwan
gaghi gaghipy
gahax Dutour 8D Type A
gatopin-verf gatopin
gee axh,   tacpy,   zee
geep rek
gicdatrid gidtixhi+dox
gidtid gidtixhi
gidtixhi gidtixhipy
gike gahi,   gax,   gikepy
gipbin-verf gipbin
gissid gaghi
gohi x3o5o5/2o5o
gyepip 2/10-luna of ex,   3/10-luna of ex,   4/10-luna of ex,   xofo3ooox5oxoo&#xt,   telex,   biscex,   dodeca-diminished rotunda of ex,   rotunda of ex
gyspid zucypit

H

hax Dutour 7D Type A,   haxpy,   haxt,   laq
haxpy haxesc
he linoh
hesa bay,   Dutour 8D Type A,   hauhocto,   hesapy
hex Dutour 5D Type A,   hexpy,   o4o3o3o5x,   tac,   test,   x4o3o3o4o
hexasc hexete
hexat x3o6o3o
hexip rag,   taccarat
hexpy hexasc,   tacpy
hi o3o3o5o5/2x
hin dijak,   hinpy,   hint,   jak,   madek
hinnip ranq
hinpy hinsc,   jakpy
hip o3x3o6o
hit-verf hit
hix ax,   hop,   stef
hixalrix hopalril
hixip roc
hocto bayoh
hop hept,   oca
hopalril ocalroc
hopip rene
howoh-verf 2howoh,   howoh
hudsi paphacki

I

ico hext,   icopy,   o3o4o3o4x
id x3o3o *b5o
ike 2/10-luna of ex,   3/10-luna of ex,   4/10-luna of ex,   cydadex,   xofo3ooox5oxoo&#xt,   eikedpy,   eikepy,   ex,   gishi,   icau prissi,   id || f-ike || ike || pt,   it,   ikepy,   o5o3o6x,   telex,   biscex,   dodeca-diminished rotunda of ex,   rotunda of ex,   x4o3o5o,   x5o3o5o
irl-verf irl
irohlohn-verf irohlohn

J

jak jakpy,   naq
jakip riffy

K

kafandoh-verf kafandoh

L

laq naquoh

M

m m3o m3m3m3o,   m3o2m3o,   m3o3m3o,   m3o3o3m
m3m3o m3m3m3o,   m3m3o3o,   dudeca
m3m4o m3m3m3o
mesdi-verf mesdi
mibdi 2/10-luna of ex,   idimex
mo jakoh

N

n/d-py line || perp {n}
n-ap n-appy,   n-apt,   x4oPo4x
naq fy
nat-verf nat
n-p n-pidpy,   n-pipy

O

oca ene,   octo
ocpe reday
oct aurap,   chon,   co || f-oct || oct || pt,   eoctpy,   haddet,   hex,   tabene,   o4o3o5x,   o4o3o6x,   octpy,   pex hex,   stico
oct+6{4} hex+8oct
octacube icoap,   tessap
octasc hexasc,   octete
octatepe hexaf
octdip traxh
octete hexete,   octepe
octpen tro
octpy hexpy,   octasc
octu s3s4o3o4o
oho datha,   ohopy
ope hexaico,   opepy,   rapaspid,   rat
ope-verf ope
oxqxo8ooooo&#qt lt-(o8o4x *b3x)

P

p2p5p gap dual
pap 1/10-luna of ex,   ikadoe,   id || srid || F-ike || ti,   ikadoaid,   pappy,   twau doaid,   twau sridati
pedip o5o3x3o5o
pedpy it
pen hix,   o3o3o3o5x,   pendpy,   pent,   stade
pendip icoy
penp octatratet,   penppy,   rapa penp,   ril,   trial tratet
peppy ikepy,   pesc
pinnip han
pip 2rox,   biscrox,   damibdrox,   didamibdrox,   epipdapy,   epippy,   fxoo2ofVx3xxoo5xoof&zx,   ikaid,   oFxFox5AxFoFx2oxofox5ooxofx&#zx,   oFxxox5Fofxfo oxofox5ooxofx&#zx,   oFxxx5Fofxo oxofx5ooxox&#zx,   oofoo3oxoxo5xooox&#xt,   owaudope,   telex,   pippy,   rox,   twau iddip,   twau sriddip,   twau tipe,   xoxFofo3oxoofox5ooxooxx&#xt,   xoxFoFxox3oxoooooxo5ooxofoxoo&#xt,   ike||id||srid||ti,   xoxxFxxox3oxoxoxoxo5ooxoooxoo&#xt

Q

q x3o arse aurap,   baudeca,   mibdirit,   pactat,   pexrit,   rit,   spix-verf,   tetatut
q x3o3o rin
q x3o3o3o rax
q x4o oct || toe,   rich
q x5o o4x3o5o
q3o3x x4o3o3o3*a
q3o4x x4o3o4o3*a
q3o5x x4o3o5o3*a
quacant-verf quacant

R

raccoth-verf raccoth
rad m3o3m3o,   tabene,   o4m3o3o
radah-verf radah
rag haxh
rap dihin,   hin,   rappy,   rapt
rapesc hinsc,   rapete
rappip ratasiphin,   rojak
rappy hinpy,   rapesc
rapt hint
rat hinoh
reday hede
rene henne
rhote tibbic
ril hesa,   rilpy
rillip robay
rinah-verf rinah
rix hax,   hixadot,   rixpy
rixasc haxesc
rixip rojaka hejak,   rolaq
rixpy rixasc
roc hocto,   rocpy

S

scad cyxh
sicdatrid sidtixhi+dox
sidtid sidtixhi
sidtixhi sidtixhipy
sipstar rappisdi
sirco o3o4x4o4*a,   x3o3o4o3*a
sishi o3o5o5/2o5x,   sishipy
sissid gofix,   gohi,   sissidpy
sissid || gad gaghi || gofix,   sishi || fix
spid cypit,   spidpy
spil-verf spil
spix-verf spix
squaf icates
squahix bro
squahop barn
squap octacube,   squappy,   x4o4o4x
squapen bersa
squasc {4} || fully perp {4},   octasc,   squete
squat x3o4o4o,   x4o4o4o
squatet brox,   nitarin,   rixasarx
squepe octepe
squete octete,   squepe
squippy octpy,   squasc
squippyp hexaico,   traltisdip
squoct brinoh
srid x3o3o5o3*a
srip-verf srip
staf cyloh
stappy gikepy,   stasc
starpedip pt || starpedip
stip gikagid,   raggix,   stippy

T

tac gee,   penth,   tacpy
taccup garag,   rez,   rilastaf
tacpy zeepy,   tacpy
targi rasdi
teddi FAxoFFxoox3foFFxofoxo oxofofxFof3ooxofxfoFf&#zx,   FAxoFFxxox3foFFxofxxo oxofofxFof3ooxofxfoFf&#zx,   ikadoaid,   telex,   dodeca-diminished rotunda of ex,   sadi,   idimex,   xoBo3ofox3xooo&#xt,   xofo3ooox3oxoo&#xt
tepasc rixasc
tepe rix,   tepepy,   tessarit
tepepy rixpy,   tepasc
tes icarico,   icot,   tespy
tet etedpy,   etepy,   gap dual,   gico,   gogishi,   hi,   m3m3o3o,   m3o3o3m,   mix,   tibbid,   o4m3o3o,   tibbic,   oct || f-tet || tet || pt,   pt||tet||co,   pahtex tes,   pen,   radh,   sted,   tete,   tes,   o3o3o6x
tetaf hixalrix
tet-dim-doe pd{3,5,3}
tetdip he
tete pendpy
tethex tark
tethix treday
tetoct bragabrox,   sez
tetpen trene
tetrap torfy
tettac tarv
tettepe rolinoh
tetu sadit
thah tho
thahp rhohid
that s4o3o6o
tho hehad
ti o5o3x3o3*b
tibbid o3o3m3o3o
tic o3o4x4o4*b
tid o3o5x5o5*b
tin-verf tin
tisdip icarit,   nit,   rapasrip
tobcu gytoh
toe o4o3x3o3*b
topax-verf topax
traf dihin,   bidhin,   tetaf
trahex barz,   ragabrag
trahin borfy
trahix brene
trapen broc
trarap branq
trat x4o3o6o
tratac bark
tratepe rolin
tratet bril,   tratetpy
tratetpy brilpy
tratrip ram
triddip dot,   triddippy
triddippy dotpy
trigee brav
trihop breday
trip 2rap,   traf,   aurap,   etripdapy,   etrippy,   o3o4x4o,   tau ope,   rap,   trippy,   tript,   turap,   tetripau tuttip
triphix ribfoh
trippasc rapesc
trippen buffy
trippy rappy,   trippasc
tript rapt
trittip ramoh
troct brag,   ratanit
tut o3o3x3o3*b

V

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

X

x f3o o3x5o3o
x f5/2o rofix
x q3o dirico,   pabdirico,   poccont,   pox rico,   coatobcu,   oxux3xxoo4oooo&#xt,   rico,   coatoe,   wx ox3xx4oo&#zx
x v5o rigfix
x3o4q o3o3o4s4*a
x3v3o dattady
xo oq&#q tisdip
xo ox&#q triddip
xo3oo&#q tepe
xo3oo3ox&#q penaspid,   scad
xo3ox&#q tetaco,   etetaco,   gyspid,   tetacoaoct,   oxx3oox3xxo&#xt,   spid,   xo3oo3ox&#q
xo4ox&#q spic

Z

zee ek,   zeepy
zeep riv


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