Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*1152i
if this polytope has a name.
Group : SmallGroup(1152,157852)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 96, 288, 96
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*576e
   16-fold quotients : {6,6}*72c
   32-fold quotients : {3,6}*36
   48-fold quotients : {6,2}*24
   96-fold quotients : {3,2}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  3,  4)(  7,  8)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)
( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49, 97)( 50, 98)
( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,109)( 58,110)
( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,129)( 66,130)
( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)( 73,141)( 74,142)
( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,113)( 82,114)
( 83,116)( 84,115)( 85,117)( 86,118)( 87,120)( 88,119)( 89,125)( 90,126)
( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)(147,148)(151,152)
(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)
(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)
(173,185)(174,186)(175,188)(176,187)(193,241)(194,242)(195,244)(196,243)
(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)(204,255)
(205,249)(206,250)(207,252)(208,251)(209,273)(210,274)(211,276)(212,275)
(213,277)(214,278)(215,280)(216,279)(217,285)(218,286)(219,288)(220,287)
(221,281)(222,282)(223,284)(224,283)(225,257)(226,258)(227,260)(228,259)
(229,261)(230,262)(231,264)(232,263)(233,269)(234,270)(235,272)(236,271)
(237,265)(238,266)(239,268)(240,267);;
s1 := (  1,194)(  2,193)(  3,195)(  4,196)(  5,206)(  6,205)(  7,207)(  8,208)
(  9,202)( 10,201)( 11,203)( 12,204)( 13,198)( 14,197)( 15,199)( 16,200)
( 17,226)( 18,225)( 19,227)( 20,228)( 21,238)( 22,237)( 23,239)( 24,240)
( 25,234)( 26,233)( 27,235)( 28,236)( 29,230)( 30,229)( 31,231)( 32,232)
( 33,210)( 34,209)( 35,211)( 36,212)( 37,222)( 38,221)( 39,223)( 40,224)
( 41,218)( 42,217)( 43,219)( 44,220)( 45,214)( 46,213)( 47,215)( 48,216)
( 49,146)( 50,145)( 51,147)( 52,148)( 53,158)( 54,157)( 55,159)( 56,160)
( 57,154)( 58,153)( 59,155)( 60,156)( 61,150)( 62,149)( 63,151)( 64,152)
( 65,178)( 66,177)( 67,179)( 68,180)( 69,190)( 70,189)( 71,191)( 72,192)
( 73,186)( 74,185)( 75,187)( 76,188)( 77,182)( 78,181)( 79,183)( 80,184)
( 81,162)( 82,161)( 83,163)( 84,164)( 85,174)( 86,173)( 87,175)( 88,176)
( 89,170)( 90,169)( 91,171)( 92,172)( 93,166)( 94,165)( 95,167)( 96,168)
( 97,242)( 98,241)( 99,243)(100,244)(101,254)(102,253)(103,255)(104,256)
(105,250)(106,249)(107,251)(108,252)(109,246)(110,245)(111,247)(112,248)
(113,274)(114,273)(115,275)(116,276)(117,286)(118,285)(119,287)(120,288)
(121,282)(122,281)(123,283)(124,284)(125,278)(126,277)(127,279)(128,280)
(129,258)(130,257)(131,259)(132,260)(133,270)(134,269)(135,271)(136,272)
(137,266)(138,265)(139,267)(140,268)(141,262)(142,261)(143,263)(144,264);;
s2 := (  2,  5)(  3,  9)(  4, 13)(  7, 10)(  8, 14)( 12, 15)( 17, 33)( 18, 37)
( 19, 41)( 20, 45)( 21, 34)( 22, 38)( 23, 42)( 24, 46)( 25, 35)( 26, 39)
( 27, 43)( 28, 47)( 29, 36)( 30, 40)( 31, 44)( 32, 48)( 49, 65)( 50, 69)
( 51, 73)( 52, 77)( 53, 66)( 54, 70)( 55, 74)( 56, 78)( 57, 67)( 58, 71)
( 59, 75)( 60, 79)( 61, 68)( 62, 72)( 63, 76)( 64, 80)( 82, 85)( 83, 89)
( 84, 93)( 87, 90)( 88, 94)( 92, 95)( 97,129)( 98,133)( 99,137)(100,141)
(101,130)(102,134)(103,138)(104,142)(105,131)(106,135)(107,139)(108,143)
(109,132)(110,136)(111,140)(112,144)(114,117)(115,121)(116,125)(119,122)
(120,126)(124,127)(146,149)(147,153)(148,157)(151,154)(152,158)(156,159)
(161,177)(162,181)(163,185)(164,189)(165,178)(166,182)(167,186)(168,190)
(169,179)(170,183)(171,187)(172,191)(173,180)(174,184)(175,188)(176,192)
(193,209)(194,213)(195,217)(196,221)(197,210)(198,214)(199,218)(200,222)
(201,211)(202,215)(203,219)(204,223)(205,212)(206,216)(207,220)(208,224)
(226,229)(227,233)(228,237)(231,234)(232,238)(236,239)(241,273)(242,277)
(243,281)(244,285)(245,274)(246,278)(247,282)(248,286)(249,275)(250,279)
(251,283)(252,287)(253,276)(254,280)(255,284)(256,288)(258,261)(259,265)
(260,269)(263,266)(264,270)(268,271);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(288)!(  3,  4)(  7,  8)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)
( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49, 97)
( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,109)
( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,129)
( 66,130)( 67,132)( 68,131)( 69,133)( 70,134)( 71,136)( 72,135)( 73,141)
( 74,142)( 75,144)( 76,143)( 77,137)( 78,138)( 79,140)( 80,139)( 81,113)
( 82,114)( 83,116)( 84,115)( 85,117)( 86,118)( 87,120)( 88,119)( 89,125)
( 90,126)( 91,128)( 92,127)( 93,121)( 94,122)( 95,124)( 96,123)(147,148)
(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)
(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)
(172,191)(173,185)(174,186)(175,188)(176,187)(193,241)(194,242)(195,244)
(196,243)(197,245)(198,246)(199,248)(200,247)(201,253)(202,254)(203,256)
(204,255)(205,249)(206,250)(207,252)(208,251)(209,273)(210,274)(211,276)
(212,275)(213,277)(214,278)(215,280)(216,279)(217,285)(218,286)(219,288)
(220,287)(221,281)(222,282)(223,284)(224,283)(225,257)(226,258)(227,260)
(228,259)(229,261)(230,262)(231,264)(232,263)(233,269)(234,270)(235,272)
(236,271)(237,265)(238,266)(239,268)(240,267);
s1 := Sym(288)!(  1,194)(  2,193)(  3,195)(  4,196)(  5,206)(  6,205)(  7,207)
(  8,208)(  9,202)( 10,201)( 11,203)( 12,204)( 13,198)( 14,197)( 15,199)
( 16,200)( 17,226)( 18,225)( 19,227)( 20,228)( 21,238)( 22,237)( 23,239)
( 24,240)( 25,234)( 26,233)( 27,235)( 28,236)( 29,230)( 30,229)( 31,231)
( 32,232)( 33,210)( 34,209)( 35,211)( 36,212)( 37,222)( 38,221)( 39,223)
( 40,224)( 41,218)( 42,217)( 43,219)( 44,220)( 45,214)( 46,213)( 47,215)
( 48,216)( 49,146)( 50,145)( 51,147)( 52,148)( 53,158)( 54,157)( 55,159)
( 56,160)( 57,154)( 58,153)( 59,155)( 60,156)( 61,150)( 62,149)( 63,151)
( 64,152)( 65,178)( 66,177)( 67,179)( 68,180)( 69,190)( 70,189)( 71,191)
( 72,192)( 73,186)( 74,185)( 75,187)( 76,188)( 77,182)( 78,181)( 79,183)
( 80,184)( 81,162)( 82,161)( 83,163)( 84,164)( 85,174)( 86,173)( 87,175)
( 88,176)( 89,170)( 90,169)( 91,171)( 92,172)( 93,166)( 94,165)( 95,167)
( 96,168)( 97,242)( 98,241)( 99,243)(100,244)(101,254)(102,253)(103,255)
(104,256)(105,250)(106,249)(107,251)(108,252)(109,246)(110,245)(111,247)
(112,248)(113,274)(114,273)(115,275)(116,276)(117,286)(118,285)(119,287)
(120,288)(121,282)(122,281)(123,283)(124,284)(125,278)(126,277)(127,279)
(128,280)(129,258)(130,257)(131,259)(132,260)(133,270)(134,269)(135,271)
(136,272)(137,266)(138,265)(139,267)(140,268)(141,262)(142,261)(143,263)
(144,264);
s2 := Sym(288)!(  2,  5)(  3,  9)(  4, 13)(  7, 10)(  8, 14)( 12, 15)( 17, 33)
( 18, 37)( 19, 41)( 20, 45)( 21, 34)( 22, 38)( 23, 42)( 24, 46)( 25, 35)
( 26, 39)( 27, 43)( 28, 47)( 29, 36)( 30, 40)( 31, 44)( 32, 48)( 49, 65)
( 50, 69)( 51, 73)( 52, 77)( 53, 66)( 54, 70)( 55, 74)( 56, 78)( 57, 67)
( 58, 71)( 59, 75)( 60, 79)( 61, 68)( 62, 72)( 63, 76)( 64, 80)( 82, 85)
( 83, 89)( 84, 93)( 87, 90)( 88, 94)( 92, 95)( 97,129)( 98,133)( 99,137)
(100,141)(101,130)(102,134)(103,138)(104,142)(105,131)(106,135)(107,139)
(108,143)(109,132)(110,136)(111,140)(112,144)(114,117)(115,121)(116,125)
(119,122)(120,126)(124,127)(146,149)(147,153)(148,157)(151,154)(152,158)
(156,159)(161,177)(162,181)(163,185)(164,189)(165,178)(166,182)(167,186)
(168,190)(169,179)(170,183)(171,187)(172,191)(173,180)(174,184)(175,188)
(176,192)(193,209)(194,213)(195,217)(196,221)(197,210)(198,214)(199,218)
(200,222)(201,211)(202,215)(203,219)(204,223)(205,212)(206,216)(207,220)
(208,224)(226,229)(227,233)(228,237)(231,234)(232,238)(236,239)(241,273)
(242,277)(243,281)(244,285)(245,274)(246,278)(247,282)(248,286)(249,275)
(250,279)(251,283)(252,287)(253,276)(254,280)(255,284)(256,288)(258,261)
(259,265)(260,269)(263,266)(264,270)(268,271);
poly := sub<Sym(288)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;

References : None.
to this polytope