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Polytope of Type {6,6}

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