Polytope of Type {6,96}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,96}*1152c
Also Known As : {6,96|2}. if this polytope has another name.
Group : SmallGroup(1152,34517)
Rank : 3
Schlafli Type : {6,96}
Number of vertices, edges, etc : 6, 288, 96
Order of s0s1s2 : 96
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,48}*576a
3-fold quotients : {2,96}*384, {6,32}*384
4-fold quotients : {6,24}*288a
6-fold quotients : {2,48}*192, {6,16}*192
8-fold quotients : {6,12}*144a
9-fold quotients : {2,32}*128
12-fold quotients : {2,24}*96, {6,8}*96
16-fold quotients : {6,6}*72a
18-fold quotients : {2,16}*64
24-fold quotients : {2,12}*48, {6,4}*48a
36-fold quotients : {2,8}*32
48-fold quotients : {2,6}*24, {6,2}*24
72-fold quotients : {2,4}*16
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 := ( 1,145)( 2,150)( 3,152)( 4,148)( 5,153)( 6,146)( 7,151)( 8,147)
( 9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)( 16,160)
( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)( 24,164)
( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)( 32,180)
( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)( 40,184)
( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)( 48,197)
( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)( 56,204)
( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)( 64,208)
( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)( 72,212)
( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)( 80,219)
( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)( 88,232)
( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)( 96,236)
( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)(104,252)
(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)(112,256)
(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)(120,269)
(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)(128,276)
(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)(136,280)
(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)(144,284)
(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)(296,435)
(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)(304,448)
(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)(312,452)
(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)(320,468)
(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)(328,472)
(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)(336,485)
(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)(344,492)
(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)(352,496)
(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)(360,500)
(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)(368,507)
(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)(376,520)
(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)(384,524)
(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)(392,540)
(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)(400,544)
(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)(408,557)
(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)(416,564)
(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)(424,568)
(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)(432,572);;
s1 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 11)( 13, 17)( 14, 16)( 15, 18)
( 19, 29)( 20, 28)( 21, 30)( 22, 35)( 23, 34)( 24, 36)( 25, 32)( 26, 31)
( 27, 33)( 37, 56)( 38, 55)( 39, 57)( 40, 62)( 41, 61)( 42, 63)( 43, 59)
( 44, 58)( 45, 60)( 46, 65)( 47, 64)( 48, 66)( 49, 71)( 50, 70)( 51, 72)
( 52, 68)( 53, 67)( 54, 69)( 73,110)( 74,109)( 75,111)( 76,116)( 77,115)
( 78,117)( 79,113)( 80,112)( 81,114)( 82,119)( 83,118)( 84,120)( 85,125)
( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,137)( 92,136)( 93,138)
( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,128)(101,127)
(102,129)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132)(145,146)
(148,152)(149,151)(150,153)(154,155)(157,161)(158,160)(159,162)(163,173)
(164,172)(165,174)(166,179)(167,178)(168,180)(169,176)(170,175)(171,177)
(181,200)(182,199)(183,201)(184,206)(185,205)(186,207)(187,203)(188,202)
(189,204)(190,209)(191,208)(192,210)(193,215)(194,214)(195,216)(196,212)
(197,211)(198,213)(217,254)(218,253)(219,255)(220,260)(221,259)(222,261)
(223,257)(224,256)(225,258)(226,263)(227,262)(228,264)(229,269)(230,268)
(231,270)(232,266)(233,265)(234,267)(235,281)(236,280)(237,282)(238,287)
(239,286)(240,288)(241,284)(242,283)(243,285)(244,272)(245,271)(246,273)
(247,278)(248,277)(249,279)(250,275)(251,274)(252,276)(289,362)(290,361)
(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)(297,366)(298,371)
(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)(305,373)(306,375)
(307,389)(308,388)(309,390)(310,395)(311,394)(312,396)(313,392)(314,391)
(315,393)(316,380)(317,379)(318,381)(319,386)(320,385)(321,387)(322,383)
(323,382)(324,384)(325,416)(326,415)(327,417)(328,422)(329,421)(330,423)
(331,419)(332,418)(333,420)(334,425)(335,424)(336,426)(337,431)(338,430)
(339,432)(340,428)(341,427)(342,429)(343,398)(344,397)(345,399)(346,404)
(347,403)(348,405)(349,401)(350,400)(351,402)(352,407)(353,406)(354,408)
(355,413)(356,412)(357,414)(358,410)(359,409)(360,411)(433,506)(434,505)
(435,507)(436,512)(437,511)(438,513)(439,509)(440,508)(441,510)(442,515)
(443,514)(444,516)(445,521)(446,520)(447,522)(448,518)(449,517)(450,519)
(451,533)(452,532)(453,534)(454,539)(455,538)(456,540)(457,536)(458,535)
(459,537)(460,524)(461,523)(462,525)(463,530)(464,529)(465,531)(466,527)
(467,526)(468,528)(469,560)(470,559)(471,561)(472,566)(473,565)(474,567)
(475,563)(476,562)(477,564)(478,569)(479,568)(480,570)(481,575)(482,574)
(483,576)(484,572)(485,571)(486,573)(487,542)(488,541)(489,543)(490,548)
(491,547)(492,549)(493,545)(494,544)(495,546)(496,551)(497,550)(498,552)
(499,557)(500,556)(501,558)(502,554)(503,553)(504,555);;
s2 := ( 1,433)( 2,440)( 3,438)( 4,439)( 5,437)( 6,435)( 7,436)( 8,434)
( 9,441)( 10,442)( 11,449)( 12,447)( 13,448)( 14,446)( 15,444)( 16,445)
( 17,443)( 18,450)( 19,460)( 20,467)( 21,465)( 22,466)( 23,464)( 24,462)
( 25,463)( 26,461)( 27,468)( 28,451)( 29,458)( 30,456)( 31,457)( 32,455)
( 33,453)( 34,454)( 35,452)( 36,459)( 37,487)( 38,494)( 39,492)( 40,493)
( 41,491)( 42,489)( 43,490)( 44,488)( 45,495)( 46,496)( 47,503)( 48,501)
( 49,502)( 50,500)( 51,498)( 52,499)( 53,497)( 54,504)( 55,469)( 56,476)
( 57,474)( 58,475)( 59,473)( 60,471)( 61,472)( 62,470)( 63,477)( 64,478)
( 65,485)( 66,483)( 67,484)( 68,482)( 69,480)( 70,481)( 71,479)( 72,486)
( 73,541)( 74,548)( 75,546)( 76,547)( 77,545)( 78,543)( 79,544)( 80,542)
( 81,549)( 82,550)( 83,557)( 84,555)( 85,556)( 86,554)( 87,552)( 88,553)
( 89,551)( 90,558)( 91,568)( 92,575)( 93,573)( 94,574)( 95,572)( 96,570)
( 97,571)( 98,569)( 99,576)(100,559)(101,566)(102,564)(103,565)(104,563)
(105,561)(106,562)(107,560)(108,567)(109,505)(110,512)(111,510)(112,511)
(113,509)(114,507)(115,508)(116,506)(117,513)(118,514)(119,521)(120,519)
(121,520)(122,518)(123,516)(124,517)(125,515)(126,522)(127,532)(128,539)
(129,537)(130,538)(131,536)(132,534)(133,535)(134,533)(135,540)(136,523)
(137,530)(138,528)(139,529)(140,527)(141,525)(142,526)(143,524)(144,531)
(145,289)(146,296)(147,294)(148,295)(149,293)(150,291)(151,292)(152,290)
(153,297)(154,298)(155,305)(156,303)(157,304)(158,302)(159,300)(160,301)
(161,299)(162,306)(163,316)(164,323)(165,321)(166,322)(167,320)(168,318)
(169,319)(170,317)(171,324)(172,307)(173,314)(174,312)(175,313)(176,311)
(177,309)(178,310)(179,308)(180,315)(181,343)(182,350)(183,348)(184,349)
(185,347)(186,345)(187,346)(188,344)(189,351)(190,352)(191,359)(192,357)
(193,358)(194,356)(195,354)(196,355)(197,353)(198,360)(199,325)(200,332)
(201,330)(202,331)(203,329)(204,327)(205,328)(206,326)(207,333)(208,334)
(209,341)(210,339)(211,340)(212,338)(213,336)(214,337)(215,335)(216,342)
(217,397)(218,404)(219,402)(220,403)(221,401)(222,399)(223,400)(224,398)
(225,405)(226,406)(227,413)(228,411)(229,412)(230,410)(231,408)(232,409)
(233,407)(234,414)(235,424)(236,431)(237,429)(238,430)(239,428)(240,426)
(241,427)(242,425)(243,432)(244,415)(245,422)(246,420)(247,421)(248,419)
(249,417)(250,418)(251,416)(252,423)(253,361)(254,368)(255,366)(256,367)
(257,365)(258,363)(259,364)(260,362)(261,369)(262,370)(263,377)(264,375)
(265,376)(266,374)(267,372)(268,373)(269,371)(270,378)(271,388)(272,395)
(273,393)(274,394)(275,392)(276,390)(277,391)(278,389)(279,396)(280,379)
(281,386)(282,384)(283,385)(284,383)(285,381)(286,382)(287,380)(288,387);;
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*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,145)( 2,150)( 3,152)( 4,148)( 5,153)( 6,146)( 7,151)
( 8,147)( 9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)
( 16,160)( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)
( 24,164)( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)
( 32,180)( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)
( 40,184)( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)
( 48,197)( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)
( 56,204)( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)
( 64,208)( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)
( 72,212)( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)
( 80,219)( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)
( 88,232)( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)
( 96,236)( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)
(104,252)(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)
(112,256)(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)
(120,269)(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)
(128,276)(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)
(136,280)(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)
(144,284)(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)
(296,435)(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)
(304,448)(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)
(312,452)(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)
(320,468)(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)
(328,472)(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)
(336,485)(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)
(344,492)(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)
(352,496)(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)
(360,500)(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)
(368,507)(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)
(376,520)(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)
(384,524)(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)
(392,540)(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)
(400,544)(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)
(408,557)(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)
(416,564)(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)
(424,568)(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)
(432,572);
s1 := Sym(576)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 11)( 13, 17)( 14, 16)
( 15, 18)( 19, 29)( 20, 28)( 21, 30)( 22, 35)( 23, 34)( 24, 36)( 25, 32)
( 26, 31)( 27, 33)( 37, 56)( 38, 55)( 39, 57)( 40, 62)( 41, 61)( 42, 63)
( 43, 59)( 44, 58)( 45, 60)( 46, 65)( 47, 64)( 48, 66)( 49, 71)( 50, 70)
( 51, 72)( 52, 68)( 53, 67)( 54, 69)( 73,110)( 74,109)( 75,111)( 76,116)
( 77,115)( 78,117)( 79,113)( 80,112)( 81,114)( 82,119)( 83,118)( 84,120)
( 85,125)( 86,124)( 87,126)( 88,122)( 89,121)( 90,123)( 91,137)( 92,136)
( 93,138)( 94,143)( 95,142)( 96,144)( 97,140)( 98,139)( 99,141)(100,128)
(101,127)(102,129)(103,134)(104,133)(105,135)(106,131)(107,130)(108,132)
(145,146)(148,152)(149,151)(150,153)(154,155)(157,161)(158,160)(159,162)
(163,173)(164,172)(165,174)(166,179)(167,178)(168,180)(169,176)(170,175)
(171,177)(181,200)(182,199)(183,201)(184,206)(185,205)(186,207)(187,203)
(188,202)(189,204)(190,209)(191,208)(192,210)(193,215)(194,214)(195,216)
(196,212)(197,211)(198,213)(217,254)(218,253)(219,255)(220,260)(221,259)
(222,261)(223,257)(224,256)(225,258)(226,263)(227,262)(228,264)(229,269)
(230,268)(231,270)(232,266)(233,265)(234,267)(235,281)(236,280)(237,282)
(238,287)(239,286)(240,288)(241,284)(242,283)(243,285)(244,272)(245,271)
(246,273)(247,278)(248,277)(249,279)(250,275)(251,274)(252,276)(289,362)
(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)(297,366)
(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)(305,373)
(306,375)(307,389)(308,388)(309,390)(310,395)(311,394)(312,396)(313,392)
(314,391)(315,393)(316,380)(317,379)(318,381)(319,386)(320,385)(321,387)
(322,383)(323,382)(324,384)(325,416)(326,415)(327,417)(328,422)(329,421)
(330,423)(331,419)(332,418)(333,420)(334,425)(335,424)(336,426)(337,431)
(338,430)(339,432)(340,428)(341,427)(342,429)(343,398)(344,397)(345,399)
(346,404)(347,403)(348,405)(349,401)(350,400)(351,402)(352,407)(353,406)
(354,408)(355,413)(356,412)(357,414)(358,410)(359,409)(360,411)(433,506)
(434,505)(435,507)(436,512)(437,511)(438,513)(439,509)(440,508)(441,510)
(442,515)(443,514)(444,516)(445,521)(446,520)(447,522)(448,518)(449,517)
(450,519)(451,533)(452,532)(453,534)(454,539)(455,538)(456,540)(457,536)
(458,535)(459,537)(460,524)(461,523)(462,525)(463,530)(464,529)(465,531)
(466,527)(467,526)(468,528)(469,560)(470,559)(471,561)(472,566)(473,565)
(474,567)(475,563)(476,562)(477,564)(478,569)(479,568)(480,570)(481,575)
(482,574)(483,576)(484,572)(485,571)(486,573)(487,542)(488,541)(489,543)
(490,548)(491,547)(492,549)(493,545)(494,544)(495,546)(496,551)(497,550)
(498,552)(499,557)(500,556)(501,558)(502,554)(503,553)(504,555);
s2 := Sym(576)!( 1,433)( 2,440)( 3,438)( 4,439)( 5,437)( 6,435)( 7,436)
( 8,434)( 9,441)( 10,442)( 11,449)( 12,447)( 13,448)( 14,446)( 15,444)
( 16,445)( 17,443)( 18,450)( 19,460)( 20,467)( 21,465)( 22,466)( 23,464)
( 24,462)( 25,463)( 26,461)( 27,468)( 28,451)( 29,458)( 30,456)( 31,457)
( 32,455)( 33,453)( 34,454)( 35,452)( 36,459)( 37,487)( 38,494)( 39,492)
( 40,493)( 41,491)( 42,489)( 43,490)( 44,488)( 45,495)( 46,496)( 47,503)
( 48,501)( 49,502)( 50,500)( 51,498)( 52,499)( 53,497)( 54,504)( 55,469)
( 56,476)( 57,474)( 58,475)( 59,473)( 60,471)( 61,472)( 62,470)( 63,477)
( 64,478)( 65,485)( 66,483)( 67,484)( 68,482)( 69,480)( 70,481)( 71,479)
( 72,486)( 73,541)( 74,548)( 75,546)( 76,547)( 77,545)( 78,543)( 79,544)
( 80,542)( 81,549)( 82,550)( 83,557)( 84,555)( 85,556)( 86,554)( 87,552)
( 88,553)( 89,551)( 90,558)( 91,568)( 92,575)( 93,573)( 94,574)( 95,572)
( 96,570)( 97,571)( 98,569)( 99,576)(100,559)(101,566)(102,564)(103,565)
(104,563)(105,561)(106,562)(107,560)(108,567)(109,505)(110,512)(111,510)
(112,511)(113,509)(114,507)(115,508)(116,506)(117,513)(118,514)(119,521)
(120,519)(121,520)(122,518)(123,516)(124,517)(125,515)(126,522)(127,532)
(128,539)(129,537)(130,538)(131,536)(132,534)(133,535)(134,533)(135,540)
(136,523)(137,530)(138,528)(139,529)(140,527)(141,525)(142,526)(143,524)
(144,531)(145,289)(146,296)(147,294)(148,295)(149,293)(150,291)(151,292)
(152,290)(153,297)(154,298)(155,305)(156,303)(157,304)(158,302)(159,300)
(160,301)(161,299)(162,306)(163,316)(164,323)(165,321)(166,322)(167,320)
(168,318)(169,319)(170,317)(171,324)(172,307)(173,314)(174,312)(175,313)
(176,311)(177,309)(178,310)(179,308)(180,315)(181,343)(182,350)(183,348)
(184,349)(185,347)(186,345)(187,346)(188,344)(189,351)(190,352)(191,359)
(192,357)(193,358)(194,356)(195,354)(196,355)(197,353)(198,360)(199,325)
(200,332)(201,330)(202,331)(203,329)(204,327)(205,328)(206,326)(207,333)
(208,334)(209,341)(210,339)(211,340)(212,338)(213,336)(214,337)(215,335)
(216,342)(217,397)(218,404)(219,402)(220,403)(221,401)(222,399)(223,400)
(224,398)(225,405)(226,406)(227,413)(228,411)(229,412)(230,410)(231,408)
(232,409)(233,407)(234,414)(235,424)(236,431)(237,429)(238,430)(239,428)
(240,426)(241,427)(242,425)(243,432)(244,415)(245,422)(246,420)(247,421)
(248,419)(249,417)(250,418)(251,416)(252,423)(253,361)(254,368)(255,366)
(256,367)(257,365)(258,363)(259,364)(260,362)(261,369)(262,370)(263,377)
(264,375)(265,376)(266,374)(267,372)(268,373)(269,371)(270,378)(271,388)
(272,395)(273,393)(274,394)(275,392)(276,390)(277,391)(278,389)(279,396)
(280,379)(281,386)(282,384)(283,385)(284,383)(285,381)(286,382)(287,380)
(288,387);
poly := sub<Sym(576)|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*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope