Polytope of Type {88,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {88,6}*1056
Also Known As : {88,6|2}. if this polytope has another name.
Group : SmallGroup(1056,240)
Rank : 3
Schlafli Type : {88,6}
Number of vertices, edges, etc : 88, 264, 6
Order of s₀s₁s₂ : 264
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {44,6}*528a
   3-fold quotients : {88,2}*352
   4-fold quotients : {22,6}*264
   6-fold quotients : {44,2}*176
   11-fold quotients : {8,6}*96
   12-fold quotients : {22,2}*88
   22-fold quotients : {4,6}*48a
   24-fold quotients : {11,2}*44
   33-fold quotients : {8,2}*32
   44-fold quotients : {2,6}*24
   66-fold quotients : {4,2}*16
   88-fold quotients : {2,3}*12
   132-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope