Polytope of Type {6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*1152j
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 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual
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}*576c
16-fold quotients : {6,6}*72a
48-fold quotients : {2,6}*24, {6,2}*24
96-fold quotients : {2,3}*12, {3,2}*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)( 2,146)( 3,154)( 4,158)( 5,149)( 6,145)( 7,153)( 8,157)
( 9,151)( 10,147)( 11,155)( 12,159)( 13,152)( 14,148)( 15,156)( 16,160)
( 17,166)( 18,162)( 19,170)( 20,174)( 21,165)( 22,161)( 23,169)( 24,173)
( 25,167)( 26,163)( 27,171)( 28,175)( 29,168)( 30,164)( 31,172)( 32,176)
( 33,182)( 34,178)( 35,186)( 36,190)( 37,181)( 38,177)( 39,185)( 40,189)
( 41,183)( 42,179)( 43,187)( 44,191)( 45,184)( 46,180)( 47,188)( 48,192)
( 49,278)( 50,274)( 51,282)( 52,286)( 53,277)( 54,273)( 55,281)( 56,285)
( 57,279)( 58,275)( 59,283)( 60,287)( 61,280)( 62,276)( 63,284)( 64,288)
( 65,246)( 66,242)( 67,250)( 68,254)( 69,245)( 70,241)( 71,249)( 72,253)
( 73,247)( 74,243)( 75,251)( 76,255)( 77,248)( 78,244)( 79,252)( 80,256)
( 81,262)( 82,258)( 83,266)( 84,270)( 85,261)( 86,257)( 87,265)( 88,269)
( 89,263)( 90,259)( 91,267)( 92,271)( 93,264)( 94,260)( 95,268)( 96,272)
( 97,214)( 98,210)( 99,218)(100,222)(101,213)(102,209)(103,217)(104,221)
(105,215)(106,211)(107,219)(108,223)(109,216)(110,212)(111,220)(112,224)
(113,230)(114,226)(115,234)(116,238)(117,229)(118,225)(119,233)(120,237)
(121,231)(122,227)(123,235)(124,239)(125,232)(126,228)(127,236)(128,240)
(129,198)(130,194)(131,202)(132,206)(133,197)(134,193)(135,201)(136,205)
(137,199)(138,195)(139,203)(140,207)(141,200)(142,196)(143,204)(144,208);;
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,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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)( 2,146)( 3,154)( 4,158)( 5,149)( 6,145)( 7,153)
( 8,157)( 9,151)( 10,147)( 11,155)( 12,159)( 13,152)( 14,148)( 15,156)
( 16,160)( 17,166)( 18,162)( 19,170)( 20,174)( 21,165)( 22,161)( 23,169)
( 24,173)( 25,167)( 26,163)( 27,171)( 28,175)( 29,168)( 30,164)( 31,172)
( 32,176)( 33,182)( 34,178)( 35,186)( 36,190)( 37,181)( 38,177)( 39,185)
( 40,189)( 41,183)( 42,179)( 43,187)( 44,191)( 45,184)( 46,180)( 47,188)
( 48,192)( 49,278)( 50,274)( 51,282)( 52,286)( 53,277)( 54,273)( 55,281)
( 56,285)( 57,279)( 58,275)( 59,283)( 60,287)( 61,280)( 62,276)( 63,284)
( 64,288)( 65,246)( 66,242)( 67,250)( 68,254)( 69,245)( 70,241)( 71,249)
( 72,253)( 73,247)( 74,243)( 75,251)( 76,255)( 77,248)( 78,244)( 79,252)
( 80,256)( 81,262)( 82,258)( 83,266)( 84,270)( 85,261)( 86,257)( 87,265)
( 88,269)( 89,263)( 90,259)( 91,267)( 92,271)( 93,264)( 94,260)( 95,268)
( 96,272)( 97,214)( 98,210)( 99,218)(100,222)(101,213)(102,209)(103,217)
(104,221)(105,215)(106,211)(107,219)(108,223)(109,216)(110,212)(111,220)
(112,224)(113,230)(114,226)(115,234)(116,238)(117,229)(118,225)(119,233)
(120,237)(121,231)(122,227)(123,235)(124,239)(125,232)(126,228)(127,236)
(128,240)(129,198)(130,194)(131,202)(132,206)(133,197)(134,193)(135,201)
(136,205)(137,199)(138,195)(139,203)(140,207)(141,200)(142,196)(143,204)
(144,208);
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,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References : None.
to this polytope