Polytope of Type {6,93}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope