Polytope of Type {6,94}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,94}*1128
Also Known As : {6,94|2}. if this polytope has another name.
Group : SmallGroup(1128,34)
Rank : 3
Schlafli Type : {6,94}
Number of vertices, edges, etc : 6, 282, 94
Order of s₀s₁s₂ : 282
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) :
   3-fold quotients : {2,94}*376
   6-fold quotients : {2,47}*188
   47-fold quotients : {6,2}*24
   94-fold quotients : {3,2}*12
   141-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 48, 95)( 49, 96)( 50, 97)( 51, 98)( 52, 99)( 53,100)( 54,101)( 55,102)
( 56,103)( 57,104)( 58,105)( 59,106)( 60,107)( 61,108)( 62,109)( 63,110)
( 64,111)( 65,112)( 66,113)( 67,114)( 68,115)( 69,116)( 70,117)( 71,118)
( 72,119)( 73,120)( 74,121)( 75,122)( 76,123)( 77,124)( 78,125)( 79,126)
( 80,127)( 81,128)( 82,129)( 83,130)( 84,131)( 85,132)( 86,133)( 87,134)
( 88,135)( 89,136)( 90,137)( 91,138)( 92,139)( 93,140)( 94,141)(189,236)
(190,237)(191,238)(192,239)(193,240)(194,241)(195,242)(196,243)(197,244)
(198,245)(199,246)(200,247)(201,248)(202,249)(203,250)(204,251)(205,252)
(206,253)(207,254)(208,255)(209,256)(210,257)(211,258)(212,259)(213,260)
(214,261)(215,262)(216,263)(217,264)(218,265)(219,266)(220,267)(221,268)
(222,269)(223,270)(224,271)(225,272)(226,273)(227,274)(228,275)(229,276)
(230,277)(231,278)(232,279)(233,280)(234,281)(235,282);;
s1 := (  1, 48)(  2, 94)(  3, 93)(  4, 92)(  5, 91)(  6, 90)(  7, 89)(  8, 88)
(  9, 87)( 10, 86)( 11, 85)( 12, 84)( 13, 83)( 14, 82)( 15, 81)( 16, 80)
( 17, 79)( 18, 78)( 19, 77)( 20, 76)( 21, 75)( 22, 74)( 23, 73)( 24, 72)
( 25, 71)( 26, 70)( 27, 69)( 28, 68)( 29, 67)( 30, 66)( 31, 65)( 32, 64)
( 33, 63)( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 58)( 39, 57)( 40, 56)
( 41, 55)( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)( 96,141)
( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)(104,133)
(105,132)(106,131)(107,130)(108,129)(109,128)(110,127)(111,126)(112,125)
(113,124)(114,123)(115,122)(116,121)(117,120)(118,119)(142,189)(143,235)
(144,234)(145,233)(146,232)(147,231)(148,230)(149,229)(150,228)(151,227)
(152,226)(153,225)(154,224)(155,223)(156,222)(157,221)(158,220)(159,219)
(160,218)(161,217)(162,216)(163,215)(164,214)(165,213)(166,212)(167,211)
(168,210)(169,209)(170,208)(171,207)(172,206)(173,205)(174,204)(175,203)
(176,202)(177,201)(178,200)(179,199)(180,198)(181,197)(182,196)(183,195)
(184,194)(185,193)(186,192)(187,191)(188,190)(237,282)(238,281)(239,280)
(240,279)(241,278)(242,277)(243,276)(244,275)(245,274)(246,273)(247,272)
(248,271)(249,270)(250,269)(251,268)(252,267)(253,266)(254,265)(255,264)
(256,263)(257,262)(258,261)(259,260);;
s2 := (  1,143)(  2,142)(  3,188)(  4,187)(  5,186)(  6,185)(  7,184)(  8,183)
(  9,182)( 10,181)( 11,180)( 12,179)( 13,178)( 14,177)( 15,176)( 16,175)
( 17,174)( 18,173)( 19,172)( 20,171)( 21,170)( 22,169)( 23,168)( 24,167)
( 25,166)( 26,165)( 27,164)( 28,163)( 29,162)( 30,161)( 31,160)( 32,159)
( 33,158)( 34,157)( 35,156)( 36,155)( 37,154)( 38,153)( 39,152)( 40,151)
( 41,150)( 42,149)( 43,148)( 44,147)( 45,146)( 46,145)( 47,144)( 48,190)
( 49,189)( 50,235)( 51,234)( 52,233)( 53,232)( 54,231)( 55,230)( 56,229)
( 57,228)( 58,227)( 59,226)( 60,225)( 61,224)( 62,223)( 63,222)( 64,221)
( 65,220)( 66,219)( 67,218)( 68,217)( 69,216)( 70,215)( 71,214)( 72,213)
( 73,212)( 74,211)( 75,210)( 76,209)( 77,208)( 78,207)( 79,206)( 80,205)
( 81,204)( 82,203)( 83,202)( 84,201)( 85,200)( 86,199)( 87,198)( 88,197)
( 89,196)( 90,195)( 91,194)( 92,193)( 93,192)( 94,191)( 95,237)( 96,236)
( 97,282)( 98,281)( 99,280)(100,279)(101,278)(102,277)(103,276)(104,275)
(105,274)(106,273)(107,272)(108,271)(109,270)(110,269)(111,268)(112,267)
(113,266)(114,265)(115,264)(116,263)(117,262)(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);;
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, 
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*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(282)!( 48, 95)( 49, 96)( 50, 97)( 51, 98)( 52, 99)( 53,100)( 54,101)
( 55,102)( 56,103)( 57,104)( 58,105)( 59,106)( 60,107)( 61,108)( 62,109)
( 63,110)( 64,111)( 65,112)( 66,113)( 67,114)( 68,115)( 69,116)( 70,117)
( 71,118)( 72,119)( 73,120)( 74,121)( 75,122)( 76,123)( 77,124)( 78,125)
( 79,126)( 80,127)( 81,128)( 82,129)( 83,130)( 84,131)( 85,132)( 86,133)
( 87,134)( 88,135)( 89,136)( 90,137)( 91,138)( 92,139)( 93,140)( 94,141)
(189,236)(190,237)(191,238)(192,239)(193,240)(194,241)(195,242)(196,243)
(197,244)(198,245)(199,246)(200,247)(201,248)(202,249)(203,250)(204,251)
(205,252)(206,253)(207,254)(208,255)(209,256)(210,257)(211,258)(212,259)
(213,260)(214,261)(215,262)(216,263)(217,264)(218,265)(219,266)(220,267)
(221,268)(222,269)(223,270)(224,271)(225,272)(226,273)(227,274)(228,275)
(229,276)(230,277)(231,278)(232,279)(233,280)(234,281)(235,282);
s1 := Sym(282)!(  1, 48)(  2, 94)(  3, 93)(  4, 92)(  5, 91)(  6, 90)(  7, 89)
(  8, 88)(  9, 87)( 10, 86)( 11, 85)( 12, 84)( 13, 83)( 14, 82)( 15, 81)
( 16, 80)( 17, 79)( 18, 78)( 19, 77)( 20, 76)( 21, 75)( 22, 74)( 23, 73)
( 24, 72)( 25, 71)( 26, 70)( 27, 69)( 28, 68)( 29, 67)( 30, 66)( 31, 65)
( 32, 64)( 33, 63)( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 58)( 39, 57)
( 40, 56)( 41, 55)( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)
( 96,141)( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,135)(103,134)
(104,133)(105,132)(106,131)(107,130)(108,129)(109,128)(110,127)(111,126)
(112,125)(113,124)(114,123)(115,122)(116,121)(117,120)(118,119)(142,189)
(143,235)(144,234)(145,233)(146,232)(147,231)(148,230)(149,229)(150,228)
(151,227)(152,226)(153,225)(154,224)(155,223)(156,222)(157,221)(158,220)
(159,219)(160,218)(161,217)(162,216)(163,215)(164,214)(165,213)(166,212)
(167,211)(168,210)(169,209)(170,208)(171,207)(172,206)(173,205)(174,204)
(175,203)(176,202)(177,201)(178,200)(179,199)(180,198)(181,197)(182,196)
(183,195)(184,194)(185,193)(186,192)(187,191)(188,190)(237,282)(238,281)
(239,280)(240,279)(241,278)(242,277)(243,276)(244,275)(245,274)(246,273)
(247,272)(248,271)(249,270)(250,269)(251,268)(252,267)(253,266)(254,265)
(255,264)(256,263)(257,262)(258,261)(259,260);
s2 := Sym(282)!(  1,143)(  2,142)(  3,188)(  4,187)(  5,186)(  6,185)(  7,184)
(  8,183)(  9,182)( 10,181)( 11,180)( 12,179)( 13,178)( 14,177)( 15,176)
( 16,175)( 17,174)( 18,173)( 19,172)( 20,171)( 21,170)( 22,169)( 23,168)
( 24,167)( 25,166)( 26,165)( 27,164)( 28,163)( 29,162)( 30,161)( 31,160)
( 32,159)( 33,158)( 34,157)( 35,156)( 36,155)( 37,154)( 38,153)( 39,152)
( 40,151)( 41,150)( 42,149)( 43,148)( 44,147)( 45,146)( 46,145)( 47,144)
( 48,190)( 49,189)( 50,235)( 51,234)( 52,233)( 53,232)( 54,231)( 55,230)
( 56,229)( 57,228)( 58,227)( 59,226)( 60,225)( 61,224)( 62,223)( 63,222)
( 64,221)( 65,220)( 66,219)( 67,218)( 68,217)( 69,216)( 70,215)( 71,214)
( 72,213)( 73,212)( 74,211)( 75,210)( 76,209)( 77,208)( 78,207)( 79,206)
( 80,205)( 81,204)( 82,203)( 83,202)( 84,201)( 85,200)( 86,199)( 87,198)
( 88,197)( 89,196)( 90,195)( 91,194)( 92,193)( 93,192)( 94,191)( 95,237)
( 96,236)( 97,282)( 98,281)( 99,280)(100,279)(101,278)(102,277)(103,276)
(104,275)(105,274)(106,273)(107,272)(108,271)(109,270)(110,269)(111,268)
(112,267)(113,266)(114,265)(115,264)(116,263)(117,262)(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);
poly := sub<Sym(282)|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, 
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*s1*s2 >;

References : None.
to this polytope