Polytope of Type {6,92}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,92}*1104a
Also Known As : {6,92|2}. if this polytope has another name.
Group : SmallGroup(1104,108)
Rank : 3
Schlafli Type : {6,92}
Number of vertices, edges, etc : 6, 276, 92
Order of s₀s₁s₂ : 276
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) :
   2-fold quotients : {6,46}*552
   3-fold quotients : {2,92}*368
   6-fold quotients : {2,46}*184
   12-fold quotients : {2,23}*92
   23-fold quotients : {6,4}*48a
   46-fold quotients : {6,2}*24
   69-fold quotients : {2,4}*16
   92-fold quotients : {3,2}*12
   138-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope