Polytope of Type {234,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {234,2}*936
if this polytope has a name.
Group : SmallGroup(936,70)
Rank : 3
Schlafli Type : {234,2}
Number of vertices, edges, etc : 234, 234, 2
Order of s₀s₁s₂ : 234
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {234,2,2} of size 1872
Vertex Figure Of :
   {2,234,2} of size 1872
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {117,2}*468
   3-fold quotients : {78,2}*312
   6-fold quotients : {39,2}*156
   9-fold quotients : {26,2}*104
   13-fold quotients : {18,2}*72
   18-fold quotients : {13,2}*52
   26-fold quotients : {9,2}*36
   39-fold quotients : {6,2}*24
   78-fold quotients : {3,2}*12
   117-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {468,2}*1872, {234,4}*1872a
Permutation Representation (GAP) :

s0 := (  2,  3)(  4, 37)(  5, 39)(  6, 38)(  7, 34)(  8, 36)(  9, 35)( 10, 31)
( 11, 33)( 12, 32)( 13, 28)( 14, 30)( 15, 29)( 16, 25)( 17, 27)( 18, 26)
( 19, 22)( 20, 24)( 21, 23)( 40, 80)( 41, 79)( 42, 81)( 43,116)( 44,115)
( 45,117)( 46,113)( 47,112)( 48,114)( 49,110)( 50,109)( 51,111)( 52,107)
( 53,106)( 54,108)( 55,104)( 56,103)( 57,105)( 58,101)( 59,100)( 60,102)
( 61, 98)( 62, 97)( 63, 99)( 64, 95)( 65, 94)( 66, 96)( 67, 92)( 68, 91)
( 69, 93)( 70, 89)( 71, 88)( 72, 90)( 73, 86)( 74, 85)( 75, 87)( 76, 83)
( 77, 82)( 78, 84)(119,120)(121,154)(122,156)(123,155)(124,151)(125,153)
(126,152)(127,148)(128,150)(129,149)(130,145)(131,147)(132,146)(133,142)
(134,144)(135,143)(136,139)(137,141)(138,140)(157,197)(158,196)(159,198)
(160,233)(161,232)(162,234)(163,230)(164,229)(165,231)(166,227)(167,226)
(168,228)(169,224)(170,223)(171,225)(172,221)(173,220)(174,222)(175,218)
(176,217)(177,219)(178,215)(179,214)(180,216)(181,212)(182,211)(183,213)
(184,209)(185,208)(186,210)(187,206)(188,205)(189,207)(190,203)(191,202)
(192,204)(193,200)(194,199)(195,201);;
s1 := (  1,160)(  2,162)(  3,161)(  4,157)(  5,159)(  6,158)(  7,193)(  8,195)
(  9,194)( 10,190)( 11,192)( 12,191)( 13,187)( 14,189)( 15,188)( 16,184)
( 17,186)( 18,185)( 19,181)( 20,183)( 21,182)( 22,178)( 23,180)( 24,179)
( 25,175)( 26,177)( 27,176)( 28,172)( 29,174)( 30,173)( 31,169)( 32,171)
( 33,170)( 34,166)( 35,168)( 36,167)( 37,163)( 38,165)( 39,164)( 40,121)
( 41,123)( 42,122)( 43,118)( 44,120)( 45,119)( 46,154)( 47,156)( 48,155)
( 49,151)( 50,153)( 51,152)( 52,148)( 53,150)( 54,149)( 55,145)( 56,147)
( 57,146)( 58,142)( 59,144)( 60,143)( 61,139)( 62,141)( 63,140)( 64,136)
( 65,138)( 66,137)( 67,133)( 68,135)( 69,134)( 70,130)( 71,132)( 72,131)
( 73,127)( 74,129)( 75,128)( 76,124)( 77,126)( 78,125)( 79,200)( 80,199)
( 81,201)( 82,197)( 83,196)( 84,198)( 85,233)( 86,232)( 87,234)( 88,230)
( 89,229)( 90,231)( 91,227)( 92,226)( 93,228)( 94,224)( 95,223)( 96,225)
( 97,221)( 98,220)( 99,222)(100,218)(101,217)(102,219)(103,215)(104,214)
(105,216)(106,212)(107,211)(108,213)(109,209)(110,208)(111,210)(112,206)
(113,205)(114,207)(115,203)(116,202)(117,204);;
s2 := (235,236);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(236)!(  2,  3)(  4, 37)(  5, 39)(  6, 38)(  7, 34)(  8, 36)(  9, 35)
( 10, 31)( 11, 33)( 12, 32)( 13, 28)( 14, 30)( 15, 29)( 16, 25)( 17, 27)
( 18, 26)( 19, 22)( 20, 24)( 21, 23)( 40, 80)( 41, 79)( 42, 81)( 43,116)
( 44,115)( 45,117)( 46,113)( 47,112)( 48,114)( 49,110)( 50,109)( 51,111)
( 52,107)( 53,106)( 54,108)( 55,104)( 56,103)( 57,105)( 58,101)( 59,100)
( 60,102)( 61, 98)( 62, 97)( 63, 99)( 64, 95)( 65, 94)( 66, 96)( 67, 92)
( 68, 91)( 69, 93)( 70, 89)( 71, 88)( 72, 90)( 73, 86)( 74, 85)( 75, 87)
( 76, 83)( 77, 82)( 78, 84)(119,120)(121,154)(122,156)(123,155)(124,151)
(125,153)(126,152)(127,148)(128,150)(129,149)(130,145)(131,147)(132,146)
(133,142)(134,144)(135,143)(136,139)(137,141)(138,140)(157,197)(158,196)
(159,198)(160,233)(161,232)(162,234)(163,230)(164,229)(165,231)(166,227)
(167,226)(168,228)(169,224)(170,223)(171,225)(172,221)(173,220)(174,222)
(175,218)(176,217)(177,219)(178,215)(179,214)(180,216)(181,212)(182,211)
(183,213)(184,209)(185,208)(186,210)(187,206)(188,205)(189,207)(190,203)
(191,202)(192,204)(193,200)(194,199)(195,201);
s1 := Sym(236)!(  1,160)(  2,162)(  3,161)(  4,157)(  5,159)(  6,158)(  7,193)
(  8,195)(  9,194)( 10,190)( 11,192)( 12,191)( 13,187)( 14,189)( 15,188)
( 16,184)( 17,186)( 18,185)( 19,181)( 20,183)( 21,182)( 22,178)( 23,180)
( 24,179)( 25,175)( 26,177)( 27,176)( 28,172)( 29,174)( 30,173)( 31,169)
( 32,171)( 33,170)( 34,166)( 35,168)( 36,167)( 37,163)( 38,165)( 39,164)
( 40,121)( 41,123)( 42,122)( 43,118)( 44,120)( 45,119)( 46,154)( 47,156)
( 48,155)( 49,151)( 50,153)( 51,152)( 52,148)( 53,150)( 54,149)( 55,145)
( 56,147)( 57,146)( 58,142)( 59,144)( 60,143)( 61,139)( 62,141)( 63,140)
( 64,136)( 65,138)( 66,137)( 67,133)( 68,135)( 69,134)( 70,130)( 71,132)
( 72,131)( 73,127)( 74,129)( 75,128)( 76,124)( 77,126)( 78,125)( 79,200)
( 80,199)( 81,201)( 82,197)( 83,196)( 84,198)( 85,233)( 86,232)( 87,234)
( 88,230)( 89,229)( 90,231)( 91,227)( 92,226)( 93,228)( 94,224)( 95,223)
( 96,225)( 97,221)( 98,220)( 99,222)(100,218)(101,217)(102,219)(103,215)
(104,214)(105,216)(106,212)(107,211)(108,213)(109,209)(110,208)(111,210)
(112,206)(113,205)(114,207)(115,203)(116,202)(117,204);
s2 := Sym(236)!(235,236);
poly := sub<Sym(236)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope