Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*1152k
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
   Self-Petrie
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}*576d
   16-fold quotients : {6,6}*72b
   32-fold quotients : {6,3}*36
   48-fold quotients : {2,6}*24
   96-fold quotients : {2,3}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope