Polytope of Type {6,87}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope