Polytope of Type {272,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {272,2}*1088
if this polytope has a name.
Group : SmallGroup(1088,970)
Rank : 3
Schlafli Type : {272,2}
Number of vertices, edges, etc : 272, 272, 2
Order of s₀s₁s₂ : 272
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 :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {136,2}*544
   4-fold quotients : {68,2}*272
   8-fold quotients : {34,2}*136
   16-fold quotients : {17,2}*68
   17-fold quotients : {16,2}*64
   34-fold quotients : {8,2}*32
   68-fold quotients : {4,2}*16
   136-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)
( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)( 26, 27)
( 35, 52)( 36, 68)( 37, 67)( 38, 66)( 39, 65)( 40, 64)( 41, 63)( 42, 62)
( 43, 61)( 44, 60)( 45, 59)( 46, 58)( 47, 57)( 48, 56)( 49, 55)( 50, 54)
( 51, 53)( 69,103)( 70,119)( 71,118)( 72,117)( 73,116)( 74,115)( 75,114)
( 76,113)( 77,112)( 78,111)( 79,110)( 80,109)( 81,108)( 82,107)( 83,106)
( 84,105)( 85,104)( 86,120)( 87,136)( 88,135)( 89,134)( 90,133)( 91,132)
( 92,131)( 93,130)( 94,129)( 95,128)( 96,127)( 97,126)( 98,125)( 99,124)
(100,123)(101,122)(102,121)(137,205)(138,221)(139,220)(140,219)(141,218)
(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)(148,211)(149,210)
(150,209)(151,208)(152,207)(153,206)(154,222)(155,238)(156,237)(157,236)
(158,235)(159,234)(160,233)(161,232)(162,231)(163,230)(164,229)(165,228)
(166,227)(167,226)(168,225)(169,224)(170,223)(171,256)(172,272)(173,271)
(174,270)(175,269)(176,268)(177,267)(178,266)(179,265)(180,264)(181,263)
(182,262)(183,261)(184,260)(185,259)(186,258)(187,257)(188,239)(189,255)
(190,254)(191,253)(192,252)(193,251)(194,250)(195,249)(196,248)(197,247)
(198,246)(199,245)(200,244)(201,243)(202,242)(203,241)(204,240);;
s1 := (  1,138)(  2,137)(  3,153)(  4,152)(  5,151)(  6,150)(  7,149)(  8,148)
(  9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,141)( 16,140)
( 17,139)( 18,155)( 19,154)( 20,170)( 21,169)( 22,168)( 23,167)( 24,166)
( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)( 32,158)
( 33,157)( 34,156)( 35,189)( 36,188)( 37,204)( 38,203)( 39,202)( 40,201)
( 41,200)( 42,199)( 43,198)( 44,197)( 45,196)( 46,195)( 47,194)( 48,193)
( 49,192)( 50,191)( 51,190)( 52,172)( 53,171)( 54,187)( 55,186)( 56,185)
( 57,184)( 58,183)( 59,182)( 60,181)( 61,180)( 62,179)( 63,178)( 64,177)
( 65,176)( 66,175)( 67,174)( 68,173)( 69,240)( 70,239)( 71,255)( 72,254)
( 73,253)( 74,252)( 75,251)( 76,250)( 77,249)( 78,248)( 79,247)( 80,246)
( 81,245)( 82,244)( 83,243)( 84,242)( 85,241)( 86,257)( 87,256)( 88,272)
( 89,271)( 90,270)( 91,269)( 92,268)( 93,267)( 94,266)( 95,265)( 96,264)
( 97,263)( 98,262)( 99,261)(100,260)(101,259)(102,258)(103,206)(104,205)
(105,221)(106,220)(107,219)(108,218)(109,217)(110,216)(111,215)(112,214)
(113,213)(114,212)(115,211)(116,210)(117,209)(118,208)(119,207)(120,223)
(121,222)(122,238)(123,237)(124,236)(125,235)(126,234)(127,233)(128,232)
(129,231)(130,230)(131,229)(132,228)(133,227)(134,226)(135,225)(136,224);;
s2 := (273,274);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(274)!(  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)
(  9, 10)( 19, 34)( 20, 33)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 25, 28)
( 26, 27)( 35, 52)( 36, 68)( 37, 67)( 38, 66)( 39, 65)( 40, 64)( 41, 63)
( 42, 62)( 43, 61)( 44, 60)( 45, 59)( 46, 58)( 47, 57)( 48, 56)( 49, 55)
( 50, 54)( 51, 53)( 69,103)( 70,119)( 71,118)( 72,117)( 73,116)( 74,115)
( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)( 80,109)( 81,108)( 82,107)
( 83,106)( 84,105)( 85,104)( 86,120)( 87,136)( 88,135)( 89,134)( 90,133)
( 91,132)( 92,131)( 93,130)( 94,129)( 95,128)( 96,127)( 97,126)( 98,125)
( 99,124)(100,123)(101,122)(102,121)(137,205)(138,221)(139,220)(140,219)
(141,218)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)(148,211)
(149,210)(150,209)(151,208)(152,207)(153,206)(154,222)(155,238)(156,237)
(157,236)(158,235)(159,234)(160,233)(161,232)(162,231)(163,230)(164,229)
(165,228)(166,227)(167,226)(168,225)(169,224)(170,223)(171,256)(172,272)
(173,271)(174,270)(175,269)(176,268)(177,267)(178,266)(179,265)(180,264)
(181,263)(182,262)(183,261)(184,260)(185,259)(186,258)(187,257)(188,239)
(189,255)(190,254)(191,253)(192,252)(193,251)(194,250)(195,249)(196,248)
(197,247)(198,246)(199,245)(200,244)(201,243)(202,242)(203,241)(204,240);
s1 := Sym(274)!(  1,138)(  2,137)(  3,153)(  4,152)(  5,151)(  6,150)(  7,149)
(  8,148)(  9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,141)
( 16,140)( 17,139)( 18,155)( 19,154)( 20,170)( 21,169)( 22,168)( 23,167)
( 24,166)( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)
( 32,158)( 33,157)( 34,156)( 35,189)( 36,188)( 37,204)( 38,203)( 39,202)
( 40,201)( 41,200)( 42,199)( 43,198)( 44,197)( 45,196)( 46,195)( 47,194)
( 48,193)( 49,192)( 50,191)( 51,190)( 52,172)( 53,171)( 54,187)( 55,186)
( 56,185)( 57,184)( 58,183)( 59,182)( 60,181)( 61,180)( 62,179)( 63,178)
( 64,177)( 65,176)( 66,175)( 67,174)( 68,173)( 69,240)( 70,239)( 71,255)
( 72,254)( 73,253)( 74,252)( 75,251)( 76,250)( 77,249)( 78,248)( 79,247)
( 80,246)( 81,245)( 82,244)( 83,243)( 84,242)( 85,241)( 86,257)( 87,256)
( 88,272)( 89,271)( 90,270)( 91,269)( 92,268)( 93,267)( 94,266)( 95,265)
( 96,264)( 97,263)( 98,262)( 99,261)(100,260)(101,259)(102,258)(103,206)
(104,205)(105,221)(106,220)(107,219)(108,218)(109,217)(110,216)(111,215)
(112,214)(113,213)(114,212)(115,211)(116,210)(117,209)(118,208)(119,207)
(120,223)(121,222)(122,238)(123,237)(124,236)(125,235)(126,234)(127,233)
(128,232)(129,231)(130,230)(131,229)(132,228)(133,227)(134,226)(135,225)
(136,224);
s2 := Sym(274)!(273,274);
poly := sub<Sym(274)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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