Polytope of Type {93,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {93,6}*1116
if this polytope has a name.
Group : SmallGroup(1116,36)
Rank : 3
Schlafli Type : {93,6}
Number of vertices, edges, etc : 93, 279, 6
Order of s₀s₁s₂ : 186
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 : {93,2}*372
   9-fold quotients : {31,2}*124
   31-fold quotients : {3,6}*36
   93-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 31)(  3, 30)(  4, 29)(  5, 28)(  6, 27)(  7, 26)(  8, 25)(  9, 24)
( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)( 32, 63)
( 33, 93)( 34, 92)( 35, 91)( 36, 90)( 37, 89)( 38, 88)( 39, 87)( 40, 86)
( 41, 85)( 42, 84)( 43, 83)( 44, 82)( 45, 81)( 46, 80)( 47, 79)( 48, 78)
( 49, 77)( 50, 76)( 51, 75)( 52, 74)( 53, 73)( 54, 72)( 55, 71)( 56, 70)
( 57, 69)( 58, 68)( 59, 67)( 60, 66)( 61, 65)( 62, 64)( 94,187)( 95,217)
( 96,216)( 97,215)( 98,214)( 99,213)(100,212)(101,211)(102,210)(103,209)
(104,208)(105,207)(106,206)(107,205)(108,204)(109,203)(110,202)(111,201)
(112,200)(113,199)(114,198)(115,197)(116,196)(117,195)(118,194)(119,193)
(120,192)(121,191)(122,190)(123,189)(124,188)(125,249)(126,279)(127,278)
(128,277)(129,276)(130,275)(131,274)(132,273)(133,272)(134,271)(135,270)
(136,269)(137,268)(138,267)(139,266)(140,265)(141,264)(142,263)(143,262)
(144,261)(145,260)(146,259)(147,258)(148,257)(149,256)(150,255)(151,254)
(152,253)(153,252)(154,251)(155,250)(156,218)(157,248)(158,247)(159,246)
(160,245)(161,244)(162,243)(163,242)(164,241)(165,240)(166,239)(167,238)
(168,237)(169,236)(170,235)(171,234)(172,233)(173,232)(174,231)(175,230)
(176,229)(177,228)(178,227)(179,226)(180,225)(181,224)(182,223)(183,222)
(184,221)(185,220)(186,219);;
s1 := (  1,126)(  2,125)(  3,155)(  4,154)(  5,153)(  6,152)(  7,151)(  8,150)
(  9,149)( 10,148)( 11,147)( 12,146)( 13,145)( 14,144)( 15,143)( 16,142)
( 17,141)( 18,140)( 19,139)( 20,138)( 21,137)( 22,136)( 23,135)( 24,134)
( 25,133)( 26,132)( 27,131)( 28,130)( 29,129)( 30,128)( 31,127)( 32, 95)
( 33, 94)( 34,124)( 35,123)( 36,122)( 37,121)( 38,120)( 39,119)( 40,118)
( 41,117)( 42,116)( 43,115)( 44,114)( 45,113)( 46,112)( 47,111)( 48,110)
( 49,109)( 50,108)( 51,107)( 52,106)( 53,105)( 54,104)( 55,103)( 56,102)
( 57,101)( 58,100)( 59, 99)( 60, 98)( 61, 97)( 62, 96)( 63,157)( 64,156)
( 65,186)( 66,185)( 67,184)( 68,183)( 69,182)( 70,181)( 71,180)( 72,179)
( 73,178)( 74,177)( 75,176)( 76,175)( 77,174)( 78,173)( 79,172)( 80,171)
( 81,170)( 82,169)( 83,168)( 84,167)( 85,166)( 86,165)( 87,164)( 88,163)
( 89,162)( 90,161)( 91,160)( 92,159)( 93,158)(187,219)(188,218)(189,248)
(190,247)(191,246)(192,245)(193,244)(194,243)(195,242)(196,241)(197,240)
(198,239)(199,238)(200,237)(201,236)(202,235)(203,234)(204,233)(205,232)
(206,231)(207,230)(208,229)(209,228)(210,227)(211,226)(212,225)(213,224)
(214,223)(215,222)(216,221)(217,220)(249,250)(251,279)(252,278)(253,277)
(254,276)(255,275)(256,274)(257,273)(258,272)(259,271)(260,270)(261,269)
(262,268)(263,267)(264,266);;
s2 := ( 32, 63)( 33, 64)( 34, 65)( 35, 66)( 36, 67)( 37, 68)( 38, 69)( 39, 70)
( 40, 71)( 41, 72)( 42, 73)( 43, 74)( 44, 75)( 45, 76)( 46, 77)( 47, 78)
( 48, 79)( 49, 80)( 50, 81)( 51, 82)( 52, 83)( 53, 84)( 54, 85)( 55, 86)
( 56, 87)( 57, 88)( 58, 89)( 59, 90)( 60, 91)( 61, 92)( 62, 93)(125,156)
(126,157)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)
(134,165)(135,166)(136,167)(137,168)(138,169)(139,170)(140,171)(141,172)
(142,173)(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)(149,180)
(150,181)(151,182)(152,183)(153,184)(154,185)(155,186)(218,249)(219,250)
(220,251)(221,252)(222,253)(223,254)(224,255)(225,256)(226,257)(227,258)
(228,259)(229,260)(230,261)(231,262)(232,263)(233,264)(234,265)(235,266)
(236,267)(237,268)(238,269)(239,270)(240,271)(241,272)(242,273)(243,274)
(244,275)(245,276)(246,277)(247,278)(248,279);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(279)!(  2, 31)(  3, 30)(  4, 29)(  5, 28)(  6, 27)(  7, 26)(  8, 25)
(  9, 24)( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)
( 32, 63)( 33, 93)( 34, 92)( 35, 91)( 36, 90)( 37, 89)( 38, 88)( 39, 87)
( 40, 86)( 41, 85)( 42, 84)( 43, 83)( 44, 82)( 45, 81)( 46, 80)( 47, 79)
( 48, 78)( 49, 77)( 50, 76)( 51, 75)( 52, 74)( 53, 73)( 54, 72)( 55, 71)
( 56, 70)( 57, 69)( 58, 68)( 59, 67)( 60, 66)( 61, 65)( 62, 64)( 94,187)
( 95,217)( 96,216)( 97,215)( 98,214)( 99,213)(100,212)(101,211)(102,210)
(103,209)(104,208)(105,207)(106,206)(107,205)(108,204)(109,203)(110,202)
(111,201)(112,200)(113,199)(114,198)(115,197)(116,196)(117,195)(118,194)
(119,193)(120,192)(121,191)(122,190)(123,189)(124,188)(125,249)(126,279)
(127,278)(128,277)(129,276)(130,275)(131,274)(132,273)(133,272)(134,271)
(135,270)(136,269)(137,268)(138,267)(139,266)(140,265)(141,264)(142,263)
(143,262)(144,261)(145,260)(146,259)(147,258)(148,257)(149,256)(150,255)
(151,254)(152,253)(153,252)(154,251)(155,250)(156,218)(157,248)(158,247)
(159,246)(160,245)(161,244)(162,243)(163,242)(164,241)(165,240)(166,239)
(167,238)(168,237)(169,236)(170,235)(171,234)(172,233)(173,232)(174,231)
(175,230)(176,229)(177,228)(178,227)(179,226)(180,225)(181,224)(182,223)
(183,222)(184,221)(185,220)(186,219);
s1 := Sym(279)!(  1,126)(  2,125)(  3,155)(  4,154)(  5,153)(  6,152)(  7,151)
(  8,150)(  9,149)( 10,148)( 11,147)( 12,146)( 13,145)( 14,144)( 15,143)
( 16,142)( 17,141)( 18,140)( 19,139)( 20,138)( 21,137)( 22,136)( 23,135)
( 24,134)( 25,133)( 26,132)( 27,131)( 28,130)( 29,129)( 30,128)( 31,127)
( 32, 95)( 33, 94)( 34,124)( 35,123)( 36,122)( 37,121)( 38,120)( 39,119)
( 40,118)( 41,117)( 42,116)( 43,115)( 44,114)( 45,113)( 46,112)( 47,111)
( 48,110)( 49,109)( 50,108)( 51,107)( 52,106)( 53,105)( 54,104)( 55,103)
( 56,102)( 57,101)( 58,100)( 59, 99)( 60, 98)( 61, 97)( 62, 96)( 63,157)
( 64,156)( 65,186)( 66,185)( 67,184)( 68,183)( 69,182)( 70,181)( 71,180)
( 72,179)( 73,178)( 74,177)( 75,176)( 76,175)( 77,174)( 78,173)( 79,172)
( 80,171)( 81,170)( 82,169)( 83,168)( 84,167)( 85,166)( 86,165)( 87,164)
( 88,163)( 89,162)( 90,161)( 91,160)( 92,159)( 93,158)(187,219)(188,218)
(189,248)(190,247)(191,246)(192,245)(193,244)(194,243)(195,242)(196,241)
(197,240)(198,239)(199,238)(200,237)(201,236)(202,235)(203,234)(204,233)
(205,232)(206,231)(207,230)(208,229)(209,228)(210,227)(211,226)(212,225)
(213,224)(214,223)(215,222)(216,221)(217,220)(249,250)(251,279)(252,278)
(253,277)(254,276)(255,275)(256,274)(257,273)(258,272)(259,271)(260,270)
(261,269)(262,268)(263,267)(264,266);
s2 := Sym(279)!( 32, 63)( 33, 64)( 34, 65)( 35, 66)( 36, 67)( 37, 68)( 38, 69)
( 39, 70)( 40, 71)( 41, 72)( 42, 73)( 43, 74)( 44, 75)( 45, 76)( 46, 77)
( 47, 78)( 48, 79)( 49, 80)( 50, 81)( 51, 82)( 52, 83)( 53, 84)( 54, 85)
( 55, 86)( 56, 87)( 57, 88)( 58, 89)( 59, 90)( 60, 91)( 61, 92)( 62, 93)
(125,156)(126,157)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)
(133,164)(134,165)(135,166)(136,167)(137,168)(138,169)(139,170)(140,171)
(141,172)(142,173)(143,174)(144,175)(145,176)(146,177)(147,178)(148,179)
(149,180)(150,181)(151,182)(152,183)(153,184)(154,185)(155,186)(218,249)
(219,250)(220,251)(221,252)(222,253)(223,254)(224,255)(225,256)(226,257)
(227,258)(228,259)(229,260)(230,261)(231,262)(232,263)(233,264)(234,265)
(235,266)(236,267)(237,268)(238,269)(239,270)(240,271)(241,272)(242,273)
(243,274)(244,275)(245,276)(246,277)(247,278)(248,279);
poly := sub<Sym(279)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope