Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155485)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 96, 288, 96
Order of s₀s₁s₂ : 24
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 : {6,3}*576
   3-fold quotients : {6,6}*384d
   4-fold quotients : {6,6}*288a
   6-fold quotients : {6,3}*192
   8-fold quotients : {6,3}*144
   12-fold quotients : {6,6}*96
   16-fold quotients : {6,6}*72b
   24-fold quotients : {3,6}*48, {6,3}*48
   32-fold quotients : {6,3}*36
   48-fold quotients : {3,3}*24, {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 := (  3,  4)(  5,  6)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)( 21, 22)
( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 37, 38)( 41, 45)( 42, 46)
( 43, 48)( 44, 47)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,102)( 54,101)
( 55,103)( 56,104)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)
( 63,108)( 64,107)( 65,113)( 66,114)( 67,116)( 68,115)( 69,118)( 70,117)
( 71,119)( 72,120)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)
( 79,124)( 80,123)( 81,129)( 82,130)( 83,132)( 84,131)( 85,134)( 86,133)
( 87,135)( 88,136)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)( 94,138)
( 95,140)( 96,139)(147,148)(149,150)(153,157)(154,158)(155,160)(156,159)
(163,164)(165,166)(169,173)(170,174)(171,176)(172,175)(179,180)(181,182)
(185,189)(186,190)(187,192)(188,191)(193,241)(194,242)(195,244)(196,243)
(197,246)(198,245)(199,247)(200,248)(201,253)(202,254)(203,256)(204,255)
(205,249)(206,250)(207,252)(208,251)(209,257)(210,258)(211,260)(212,259)
(213,262)(214,261)(215,263)(216,264)(217,269)(218,270)(219,272)(220,271)
(221,265)(222,266)(223,268)(224,267)(225,273)(226,274)(227,276)(228,275)
(229,278)(230,277)(231,279)(232,280)(233,285)(234,286)(235,288)(236,287)
(237,281)(238,282)(239,284)(240,283);;
s1 := (  1, 49)(  2, 52)(  3, 51)(  4, 50)(  5, 63)(  6, 62)(  7, 61)(  8, 64)
(  9, 59)( 10, 58)( 11, 57)( 12, 60)( 13, 55)( 14, 54)( 15, 53)( 16, 56)
( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 95)( 22, 94)( 23, 93)( 24, 96)
( 25, 91)( 26, 90)( 27, 89)( 28, 92)( 29, 87)( 30, 86)( 31, 85)( 32, 88)
( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 79)( 38, 78)( 39, 77)( 40, 80)
( 41, 75)( 42, 74)( 43, 73)( 44, 76)( 45, 71)( 46, 70)( 47, 69)( 48, 72)
( 98,100)(101,111)(102,110)(103,109)(104,112)(105,107)(113,129)(114,132)
(115,131)(116,130)(117,143)(118,142)(119,141)(120,144)(121,139)(122,138)
(123,137)(124,140)(125,135)(126,134)(127,133)(128,136)(145,193)(146,196)
(147,195)(148,194)(149,207)(150,206)(151,205)(152,208)(153,203)(154,202)
(155,201)(156,204)(157,199)(158,198)(159,197)(160,200)(161,225)(162,228)
(163,227)(164,226)(165,239)(166,238)(167,237)(168,240)(169,235)(170,234)
(171,233)(172,236)(173,231)(174,230)(175,229)(176,232)(177,209)(178,212)
(179,211)(180,210)(181,223)(182,222)(183,221)(184,224)(185,219)(186,218)
(187,217)(188,220)(189,215)(190,214)(191,213)(192,216)(242,244)(245,255)
(246,254)(247,253)(248,256)(249,251)(257,273)(258,276)(259,275)(260,274)
(261,287)(262,286)(263,285)(264,288)(265,283)(266,282)(267,281)(268,284)
(269,279)(270,278)(271,277)(272,280);;
s2 := (  1,167)(  2,168)(  3,166)(  4,165)(  5,164)(  6,163)(  7,161)(  8,162)
(  9,169)( 10,170)( 11,172)( 12,171)( 13,173)( 14,174)( 15,176)( 16,175)
( 17,151)( 18,152)( 19,150)( 20,149)( 21,148)( 22,147)( 23,145)( 24,146)
( 25,153)( 26,154)( 27,156)( 28,155)( 29,157)( 30,158)( 31,160)( 32,159)
( 33,183)( 34,184)( 35,182)( 36,181)( 37,180)( 38,179)( 39,177)( 40,178)
( 41,185)( 42,186)( 43,188)( 44,187)( 45,189)( 46,190)( 47,192)( 48,191)
( 49,263)( 50,264)( 51,262)( 52,261)( 53,260)( 54,259)( 55,257)( 56,258)
( 57,265)( 58,266)( 59,268)( 60,267)( 61,269)( 62,270)( 63,272)( 64,271)
( 65,247)( 66,248)( 67,246)( 68,245)( 69,244)( 70,243)( 71,241)( 72,242)
( 73,249)( 74,250)( 75,252)( 76,251)( 77,253)( 78,254)( 79,256)( 80,255)
( 81,279)( 82,280)( 83,278)( 84,277)( 85,276)( 86,275)( 87,273)( 88,274)
( 89,281)( 90,282)( 91,284)( 92,283)( 93,285)( 94,286)( 95,288)( 96,287)
( 97,215)( 98,216)( 99,214)(100,213)(101,212)(102,211)(103,209)(104,210)
(105,217)(106,218)(107,220)(108,219)(109,221)(110,222)(111,224)(112,223)
(113,199)(114,200)(115,198)(116,197)(117,196)(118,195)(119,193)(120,194)
(121,201)(122,202)(123,204)(124,203)(125,205)(126,206)(127,208)(128,207)
(129,231)(130,232)(131,230)(132,229)(133,228)(134,227)(135,225)(136,226)
(137,233)(138,234)(139,236)(140,235)(141,237)(142,238)(143,240)(144,239);;
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, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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)!(  3,  4)(  5,  6)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)
( 21, 22)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 37, 38)( 41, 45)
( 42, 46)( 43, 48)( 44, 47)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,102)
( 54,101)( 55,103)( 56,104)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)
( 62,106)( 63,108)( 64,107)( 65,113)( 66,114)( 67,116)( 68,115)( 69,118)
( 70,117)( 71,119)( 72,120)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)
( 78,122)( 79,124)( 80,123)( 81,129)( 82,130)( 83,132)( 84,131)( 85,134)
( 86,133)( 87,135)( 88,136)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)
( 94,138)( 95,140)( 96,139)(147,148)(149,150)(153,157)(154,158)(155,160)
(156,159)(163,164)(165,166)(169,173)(170,174)(171,176)(172,175)(179,180)
(181,182)(185,189)(186,190)(187,192)(188,191)(193,241)(194,242)(195,244)
(196,243)(197,246)(198,245)(199,247)(200,248)(201,253)(202,254)(203,256)
(204,255)(205,249)(206,250)(207,252)(208,251)(209,257)(210,258)(211,260)
(212,259)(213,262)(214,261)(215,263)(216,264)(217,269)(218,270)(219,272)
(220,271)(221,265)(222,266)(223,268)(224,267)(225,273)(226,274)(227,276)
(228,275)(229,278)(230,277)(231,279)(232,280)(233,285)(234,286)(235,288)
(236,287)(237,281)(238,282)(239,284)(240,283);
s1 := Sym(288)!(  1, 49)(  2, 52)(  3, 51)(  4, 50)(  5, 63)(  6, 62)(  7, 61)
(  8, 64)(  9, 59)( 10, 58)( 11, 57)( 12, 60)( 13, 55)( 14, 54)( 15, 53)
( 16, 56)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 95)( 22, 94)( 23, 93)
( 24, 96)( 25, 91)( 26, 90)( 27, 89)( 28, 92)( 29, 87)( 30, 86)( 31, 85)
( 32, 88)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 79)( 38, 78)( 39, 77)
( 40, 80)( 41, 75)( 42, 74)( 43, 73)( 44, 76)( 45, 71)( 46, 70)( 47, 69)
( 48, 72)( 98,100)(101,111)(102,110)(103,109)(104,112)(105,107)(113,129)
(114,132)(115,131)(116,130)(117,143)(118,142)(119,141)(120,144)(121,139)
(122,138)(123,137)(124,140)(125,135)(126,134)(127,133)(128,136)(145,193)
(146,196)(147,195)(148,194)(149,207)(150,206)(151,205)(152,208)(153,203)
(154,202)(155,201)(156,204)(157,199)(158,198)(159,197)(160,200)(161,225)
(162,228)(163,227)(164,226)(165,239)(166,238)(167,237)(168,240)(169,235)
(170,234)(171,233)(172,236)(173,231)(174,230)(175,229)(176,232)(177,209)
(178,212)(179,211)(180,210)(181,223)(182,222)(183,221)(184,224)(185,219)
(186,218)(187,217)(188,220)(189,215)(190,214)(191,213)(192,216)(242,244)
(245,255)(246,254)(247,253)(248,256)(249,251)(257,273)(258,276)(259,275)
(260,274)(261,287)(262,286)(263,285)(264,288)(265,283)(266,282)(267,281)
(268,284)(269,279)(270,278)(271,277)(272,280);
s2 := Sym(288)!(  1,167)(  2,168)(  3,166)(  4,165)(  5,164)(  6,163)(  7,161)
(  8,162)(  9,169)( 10,170)( 11,172)( 12,171)( 13,173)( 14,174)( 15,176)
( 16,175)( 17,151)( 18,152)( 19,150)( 20,149)( 21,148)( 22,147)( 23,145)
( 24,146)( 25,153)( 26,154)( 27,156)( 28,155)( 29,157)( 30,158)( 31,160)
( 32,159)( 33,183)( 34,184)( 35,182)( 36,181)( 37,180)( 38,179)( 39,177)
( 40,178)( 41,185)( 42,186)( 43,188)( 44,187)( 45,189)( 46,190)( 47,192)
( 48,191)( 49,263)( 50,264)( 51,262)( 52,261)( 53,260)( 54,259)( 55,257)
( 56,258)( 57,265)( 58,266)( 59,268)( 60,267)( 61,269)( 62,270)( 63,272)
( 64,271)( 65,247)( 66,248)( 67,246)( 68,245)( 69,244)( 70,243)( 71,241)
( 72,242)( 73,249)( 74,250)( 75,252)( 76,251)( 77,253)( 78,254)( 79,256)
( 80,255)( 81,279)( 82,280)( 83,278)( 84,277)( 85,276)( 86,275)( 87,273)
( 88,274)( 89,281)( 90,282)( 91,284)( 92,283)( 93,285)( 94,286)( 95,288)
( 96,287)( 97,215)( 98,216)( 99,214)(100,213)(101,212)(102,211)(103,209)
(104,210)(105,217)(106,218)(107,220)(108,219)(109,221)(110,222)(111,224)
(112,223)(113,199)(114,200)(115,198)(116,197)(117,196)(118,195)(119,193)
(120,194)(121,201)(122,202)(123,204)(124,203)(125,205)(126,206)(127,208)
(128,207)(129,231)(130,232)(131,230)(132,229)(133,228)(134,227)(135,225)
(136,226)(137,233)(138,234)(139,236)(140,235)(141,237)(142,238)(143,240)
(144,239);
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, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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