Polytope of Type {87,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {87,6}*1044
if this polytope has a name.
Group : SmallGroup(1044,28)
Rank : 3
Schlafli Type : {87,6}
Number of vertices, edges, etc : 87, 261, 6
Order of s₀s₁s₂ : 174
Order of s₀s₁s₂s₁ : 6
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) :
   3-fold quotients : {87,2}*348
   9-fold quotients : {29,2}*116
   29-fold quotients : {3,6}*36
   87-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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