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Polytope of Type {12,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,8}*1152c
if this polytope has a name.
Group : SmallGroup(1152,119757)
Rank : 4
Schlafli Type : {12,6,8}
Number of vertices, edges, etc : 12, 36, 24, 8
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   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 : {12,6,4}*576b, {6,6,8}*576c
   3-fold quotients : {12,2,8}*384
   4-fold quotients : {3,6,8}*288, {12,6,2}*288b, {6,6,4}*288c
   6-fold quotients : {12,2,4}*192, {6,2,8}*192
   8-fold quotients : {3,6,4}*144, {6,6,2}*144c
   9-fold quotients : {4,2,8}*128
   12-fold quotients : {3,2,8}*96, {12,2,2}*96, {6,2,4}*96
   16-fold quotients : {3,6,2}*72
   18-fold quotients : {4,2,4}*64, {2,2,8}*64
   24-fold quotients : {3,2,4}*48, {6,2,2}*48
   36-fold quotients : {2,2,4}*32, {4,2,2}*32
   48-fold quotients : {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,145)(  2,147)(  3,146)(  4,151)(  5,153)(  6,152)(  7,148)(  8,150)
(  9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)( 16,157)
( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)( 24,170)
( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)( 32,180)
( 33,179)( 34,175)( 35,177)( 36,176)( 37,181)( 38,183)( 39,182)( 40,187)
( 41,189)( 42,188)( 43,184)( 44,186)( 45,185)( 46,190)( 47,192)( 48,191)
( 49,196)( 50,198)( 51,197)( 52,193)( 53,195)( 54,194)( 55,199)( 56,201)
( 57,200)( 58,205)( 59,207)( 60,206)( 61,202)( 62,204)( 63,203)( 64,208)
( 65,210)( 66,209)( 67,214)( 68,216)( 69,215)( 70,211)( 71,213)( 72,212)
( 73,217)( 74,219)( 75,218)( 76,223)( 77,225)( 78,224)( 79,220)( 80,222)
( 81,221)( 82,226)( 83,228)( 84,227)( 85,232)( 86,234)( 87,233)( 88,229)
( 89,231)( 90,230)( 91,235)( 92,237)( 93,236)( 94,241)( 95,243)( 96,242)
( 97,238)( 98,240)( 99,239)(100,244)(101,246)(102,245)(103,250)(104,252)
(105,251)(106,247)(107,249)(108,248)(109,253)(110,255)(111,254)(112,259)
(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)(120,263)
(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)(128,273)
(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)(136,280)
(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)(144,284)
(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)(296,438)
(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)(304,445)
(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)(312,458)
(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)(320,468)
(321,467)(322,463)(323,465)(324,464)(325,469)(326,471)(327,470)(328,475)
(329,477)(330,476)(331,472)(332,474)(333,473)(334,478)(335,480)(336,479)
(337,484)(338,486)(339,485)(340,481)(341,483)(342,482)(343,487)(344,489)
(345,488)(346,493)(347,495)(348,494)(349,490)(350,492)(351,491)(352,496)
(353,498)(354,497)(355,502)(356,504)(357,503)(358,499)(359,501)(360,500)
(361,505)(362,507)(363,506)(364,511)(365,513)(366,512)(367,508)(368,510)
(369,509)(370,514)(371,516)(372,515)(373,520)(374,522)(375,521)(376,517)
(377,519)(378,518)(379,523)(380,525)(381,524)(382,529)(383,531)(384,530)
(385,526)(386,528)(387,527)(388,532)(389,534)(390,533)(391,538)(392,540)
(393,539)(394,535)(395,537)(396,536)(397,541)(398,543)(399,542)(400,547)
(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)(408,551)
(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)(416,561)
(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)(424,568)
(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)(432,572);;
s1 := (  1,110)(  2,109)(  3,111)(  4,116)(  5,115)(  6,117)(  7,113)(  8,112)
(  9,114)( 10,119)( 11,118)( 12,120)( 13,125)( 14,124)( 15,126)( 16,122)
( 17,121)( 18,123)( 19,128)( 20,127)( 21,129)( 22,134)( 23,133)( 24,135)
( 25,131)( 26,130)( 27,132)( 28,137)( 29,136)( 30,138)( 31,143)( 32,142)
( 33,144)( 34,140)( 35,139)( 36,141)( 37, 83)( 38, 82)( 39, 84)( 40, 89)
( 41, 88)( 42, 90)( 43, 86)( 44, 85)( 45, 87)( 46, 74)( 47, 73)( 48, 75)
( 49, 80)( 50, 79)( 51, 81)( 52, 77)( 53, 76)( 54, 78)( 55,101)( 56,100)
( 57,102)( 58,107)( 59,106)( 60,108)( 61,104)( 62,103)( 63,105)( 64, 92)
( 65, 91)( 66, 93)( 67, 98)( 68, 97)( 69, 99)( 70, 95)( 71, 94)( 72, 96)
(145,272)(146,271)(147,273)(148,278)(149,277)(150,279)(151,275)(152,274)
(153,276)(154,281)(155,280)(156,282)(157,287)(158,286)(159,288)(160,284)
(161,283)(162,285)(163,254)(164,253)(165,255)(166,260)(167,259)(168,261)
(169,257)(170,256)(171,258)(172,263)(173,262)(174,264)(175,269)(176,268)
(177,270)(178,266)(179,265)(180,267)(181,245)(182,244)(183,246)(184,251)
(185,250)(186,252)(187,248)(188,247)(189,249)(190,236)(191,235)(192,237)
(193,242)(194,241)(195,243)(196,239)(197,238)(198,240)(199,227)(200,226)
(201,228)(202,233)(203,232)(204,234)(205,230)(206,229)(207,231)(208,218)
(209,217)(210,219)(211,224)(212,223)(213,225)(214,221)(215,220)(216,222)
(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)(307,380)(308,379)(309,381)(310,386)(311,385)(312,387)
(313,383)(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)(320,394)
(321,396)(322,392)(323,391)(324,393)(325,398)(326,397)(327,399)(328,404)
(329,403)(330,405)(331,401)(332,400)(333,402)(334,407)(335,406)(336,408)
(337,413)(338,412)(339,414)(340,410)(341,409)(342,411)(343,416)(344,415)
(345,417)(346,422)(347,421)(348,423)(349,419)(350,418)(351,420)(352,425)
(353,424)(354,426)(355,431)(356,430)(357,432)(358,428)(359,427)(360,429)
(433,524)(434,523)(435,525)(436,530)(437,529)(438,531)(439,527)(440,526)
(441,528)(442,533)(443,532)(444,534)(445,539)(446,538)(447,540)(448,536)
(449,535)(450,537)(451,506)(452,505)(453,507)(454,512)(455,511)(456,513)
(457,509)(458,508)(459,510)(460,515)(461,514)(462,516)(463,521)(464,520)
(465,522)(466,518)(467,517)(468,519)(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, 73)(  2, 78)(  3, 80)(  4, 76)(  5, 81)(  6, 74)(  7, 79)(  8, 75)
(  9, 77)( 10, 82)( 11, 87)( 12, 89)( 13, 85)( 14, 90)( 15, 83)( 16, 88)
( 17, 84)( 18, 86)( 19, 91)( 20, 96)( 21, 98)( 22, 94)( 23, 99)( 24, 92)
( 25, 97)( 26, 93)( 27, 95)( 28,100)( 29,105)( 30,107)( 31,103)( 32,108)
( 33,101)( 34,106)( 35,102)( 36,104)( 37,118)( 38,123)( 39,125)( 40,121)
( 41,126)( 42,119)( 43,124)( 44,120)( 45,122)( 46,109)( 47,114)( 48,116)
( 49,112)( 50,117)( 51,110)( 52,115)( 53,111)( 54,113)( 55,136)( 56,141)
( 57,143)( 58,139)( 59,144)( 60,137)( 61,142)( 62,138)( 63,140)( 64,127)
( 65,132)( 66,134)( 67,130)( 68,135)( 69,128)( 70,133)( 71,129)( 72,131)
(145,217)(146,222)(147,224)(148,220)(149,225)(150,218)(151,223)(152,219)
(153,221)(154,226)(155,231)(156,233)(157,229)(158,234)(159,227)(160,232)
(161,228)(162,230)(163,235)(164,240)(165,242)(166,238)(167,243)(168,236)
(169,241)(170,237)(171,239)(172,244)(173,249)(174,251)(175,247)(176,252)
(177,245)(178,250)(179,246)(180,248)(181,262)(182,267)(183,269)(184,265)
(185,270)(186,263)(187,268)(188,264)(189,266)(190,253)(191,258)(192,260)
(193,256)(194,261)(195,254)(196,259)(197,255)(198,257)(199,280)(200,285)
(201,287)(202,283)(203,288)(204,281)(205,286)(206,282)(207,284)(208,271)
(209,276)(210,278)(211,274)(212,279)(213,272)(214,277)(215,273)(216,275)
(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)(295,367)(296,363)
(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)(303,371)(304,376)
(305,372)(306,374)(307,379)(308,384)(309,386)(310,382)(311,387)(312,380)
(313,385)(314,381)(315,383)(316,388)(317,393)(318,395)(319,391)(320,396)
(321,389)(322,394)(323,390)(324,392)(325,406)(326,411)(327,413)(328,409)
(329,414)(330,407)(331,412)(332,408)(333,410)(334,397)(335,402)(336,404)
(337,400)(338,405)(339,398)(340,403)(341,399)(342,401)(343,424)(344,429)
(345,431)(346,427)(347,432)(348,425)(349,430)(350,426)(351,428)(352,415)
(353,420)(354,422)(355,418)(356,423)(357,416)(358,421)(359,417)(360,419)
(433,505)(434,510)(435,512)(436,508)(437,513)(438,506)(439,511)(440,507)
(441,509)(442,514)(443,519)(444,521)(445,517)(446,522)(447,515)(448,520)
(449,516)(450,518)(451,523)(452,528)(453,530)(454,526)(455,531)(456,524)
(457,529)(458,525)(459,527)(460,532)(461,537)(462,539)(463,535)(464,540)
(465,533)(466,538)(467,534)(468,536)(469,550)(470,555)(471,557)(472,553)
(473,558)(474,551)(475,556)(476,552)(477,554)(478,541)(479,546)(480,548)
(481,544)(482,549)(483,542)(484,547)(485,543)(486,545)(487,568)(488,573)
(489,575)(490,571)(491,576)(492,569)(493,574)(494,570)(495,572)(496,559)
(497,564)(498,566)(499,562)(500,567)(501,560)(502,565)(503,561)(504,563);;
s3 := (  1,289)(  2,290)(  3,291)(  4,292)(  5,293)(  6,294)(  7,295)(  8,296)
(  9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)
( 17,305)( 18,306)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)( 24,312)
( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)
( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)( 40,337)
( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)
( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,352)( 56,353)
( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)( 64,343)
( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)( 72,351)
( 73,397)( 74,398)( 75,399)( 76,400)( 77,401)( 78,402)( 79,403)( 80,404)
( 81,405)( 82,406)( 83,407)( 84,408)( 85,409)( 86,410)( 87,411)( 88,412)
( 89,413)( 90,414)( 91,415)( 92,416)( 93,417)( 94,418)( 95,419)( 96,420)
( 97,421)( 98,422)( 99,423)(100,424)(101,425)(102,426)(103,427)(104,428)
(105,429)(106,430)(107,431)(108,432)(109,361)(110,362)(111,363)(112,364)
(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)(120,372)
(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,379)(128,380)
(129,381)(130,382)(131,383)(132,384)(133,385)(134,386)(135,387)(136,388)
(137,389)(138,390)(139,391)(140,392)(141,393)(142,394)(143,395)(144,396)
(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)
(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)
(161,449)(162,450)(163,451)(164,452)(165,453)(166,454)(167,455)(168,456)
(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)(176,464)
(177,465)(178,466)(179,467)(180,468)(181,478)(182,479)(183,480)(184,481)
(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)(192,471)
(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,496)(200,497)
(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)(208,487)
(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)
(217,541)(218,542)(219,543)(220,544)(221,545)(222,546)(223,547)(224,548)
(225,549)(226,550)(227,551)(228,552)(229,553)(230,554)(231,555)(232,556)
(233,557)(234,558)(235,559)(236,560)(237,561)(238,562)(239,563)(240,564)
(241,565)(242,566)(243,567)(244,568)(245,569)(246,570)(247,571)(248,572)
(249,573)(250,574)(251,575)(252,576)(253,505)(254,506)(255,507)(256,508)
(257,509)(258,510)(259,511)(260,512)(261,513)(262,514)(263,515)(264,516)
(265,517)(266,518)(267,519)(268,520)(269,521)(270,522)(271,523)(272,524)
(273,525)(274,526)(275,527)(276,528)(277,529)(278,530)(279,531)(280,532)
(281,533)(282,534)(283,535)(284,536)(285,537)(286,538)(287,539)(288,540);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,145)(  2,147)(  3,146)(  4,151)(  5,153)(  6,152)(  7,148)
(  8,150)(  9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)
( 16,157)( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)
( 24,170)( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)
( 32,180)( 33,179)( 34,175)( 35,177)( 36,176)( 37,181)( 38,183)( 39,182)
( 40,187)( 41,189)( 42,188)( 43,184)( 44,186)( 45,185)( 46,190)( 47,192)
( 48,191)( 49,196)( 50,198)( 51,197)( 52,193)( 53,195)( 54,194)( 55,199)
( 56,201)( 57,200)( 58,205)( 59,207)( 60,206)( 61,202)( 62,204)( 63,203)
( 64,208)( 65,210)( 66,209)( 67,214)( 68,216)( 69,215)( 70,211)( 71,213)
( 72,212)( 73,217)( 74,219)( 75,218)( 76,223)( 77,225)( 78,224)( 79,220)
( 80,222)( 81,221)( 82,226)( 83,228)( 84,227)( 85,232)( 86,234)( 87,233)
( 88,229)( 89,231)( 90,230)( 91,235)( 92,237)( 93,236)( 94,241)( 95,243)
( 96,242)( 97,238)( 98,240)( 99,239)(100,244)(101,246)(102,245)(103,250)
(104,252)(105,251)(106,247)(107,249)(108,248)(109,253)(110,255)(111,254)
(112,259)(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)
(120,263)(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)
(128,273)(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)
(136,280)(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)
(144,284)(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)
(296,438)(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)
(304,445)(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)
(312,458)(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)
(320,468)(321,467)(322,463)(323,465)(324,464)(325,469)(326,471)(327,470)
(328,475)(329,477)(330,476)(331,472)(332,474)(333,473)(334,478)(335,480)
(336,479)(337,484)(338,486)(339,485)(340,481)(341,483)(342,482)(343,487)
(344,489)(345,488)(346,493)(347,495)(348,494)(349,490)(350,492)(351,491)
(352,496)(353,498)(354,497)(355,502)(356,504)(357,503)(358,499)(359,501)
(360,500)(361,505)(362,507)(363,506)(364,511)(365,513)(366,512)(367,508)
(368,510)(369,509)(370,514)(371,516)(372,515)(373,520)(374,522)(375,521)
(376,517)(377,519)(378,518)(379,523)(380,525)(381,524)(382,529)(383,531)
(384,530)(385,526)(386,528)(387,527)(388,532)(389,534)(390,533)(391,538)
(392,540)(393,539)(394,535)(395,537)(396,536)(397,541)(398,543)(399,542)
(400,547)(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)
(408,551)(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)
(416,561)(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)
(424,568)(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)
(432,572);
s1 := Sym(576)!(  1,110)(  2,109)(  3,111)(  4,116)(  5,115)(  6,117)(  7,113)
(  8,112)(  9,114)( 10,119)( 11,118)( 12,120)( 13,125)( 14,124)( 15,126)
( 16,122)( 17,121)( 18,123)( 19,128)( 20,127)( 21,129)( 22,134)( 23,133)
( 24,135)( 25,131)( 26,130)( 27,132)( 28,137)( 29,136)( 30,138)( 31,143)
( 32,142)( 33,144)( 34,140)( 35,139)( 36,141)( 37, 83)( 38, 82)( 39, 84)
( 40, 89)( 41, 88)( 42, 90)( 43, 86)( 44, 85)( 45, 87)( 46, 74)( 47, 73)
( 48, 75)( 49, 80)( 50, 79)( 51, 81)( 52, 77)( 53, 76)( 54, 78)( 55,101)
( 56,100)( 57,102)( 58,107)( 59,106)( 60,108)( 61,104)( 62,103)( 63,105)
( 64, 92)( 65, 91)( 66, 93)( 67, 98)( 68, 97)( 69, 99)( 70, 95)( 71, 94)
( 72, 96)(145,272)(146,271)(147,273)(148,278)(149,277)(150,279)(151,275)
(152,274)(153,276)(154,281)(155,280)(156,282)(157,287)(158,286)(159,288)
(160,284)(161,283)(162,285)(163,254)(164,253)(165,255)(166,260)(167,259)
(168,261)(169,257)(170,256)(171,258)(172,263)(173,262)(174,264)(175,269)
(176,268)(177,270)(178,266)(179,265)(180,267)(181,245)(182,244)(183,246)
(184,251)(185,250)(186,252)(187,248)(188,247)(189,249)(190,236)(191,235)
(192,237)(193,242)(194,241)(195,243)(196,239)(197,238)(198,240)(199,227)
(200,226)(201,228)(202,233)(203,232)(204,234)(205,230)(206,229)(207,231)
(208,218)(209,217)(210,219)(211,224)(212,223)(213,225)(214,221)(215,220)
(216,222)(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)(307,380)(308,379)(309,381)(310,386)(311,385)
(312,387)(313,383)(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)
(320,394)(321,396)(322,392)(323,391)(324,393)(325,398)(326,397)(327,399)
(328,404)(329,403)(330,405)(331,401)(332,400)(333,402)(334,407)(335,406)
(336,408)(337,413)(338,412)(339,414)(340,410)(341,409)(342,411)(343,416)
(344,415)(345,417)(346,422)(347,421)(348,423)(349,419)(350,418)(351,420)
(352,425)(353,424)(354,426)(355,431)(356,430)(357,432)(358,428)(359,427)
(360,429)(433,524)(434,523)(435,525)(436,530)(437,529)(438,531)(439,527)
(440,526)(441,528)(442,533)(443,532)(444,534)(445,539)(446,538)(447,540)
(448,536)(449,535)(450,537)(451,506)(452,505)(453,507)(454,512)(455,511)
(456,513)(457,509)(458,508)(459,510)(460,515)(461,514)(462,516)(463,521)
(464,520)(465,522)(466,518)(467,517)(468,519)(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, 73)(  2, 78)(  3, 80)(  4, 76)(  5, 81)(  6, 74)(  7, 79)
(  8, 75)(  9, 77)( 10, 82)( 11, 87)( 12, 89)( 13, 85)( 14, 90)( 15, 83)
( 16, 88)( 17, 84)( 18, 86)( 19, 91)( 20, 96)( 21, 98)( 22, 94)( 23, 99)
( 24, 92)( 25, 97)( 26, 93)( 27, 95)( 28,100)( 29,105)( 30,107)( 31,103)
( 32,108)( 33,101)( 34,106)( 35,102)( 36,104)( 37,118)( 38,123)( 39,125)
( 40,121)( 41,126)( 42,119)( 43,124)( 44,120)( 45,122)( 46,109)( 47,114)
( 48,116)( 49,112)( 50,117)( 51,110)( 52,115)( 53,111)( 54,113)( 55,136)
( 56,141)( 57,143)( 58,139)( 59,144)( 60,137)( 61,142)( 62,138)( 63,140)
( 64,127)( 65,132)( 66,134)( 67,130)( 68,135)( 69,128)( 70,133)( 71,129)
( 72,131)(145,217)(146,222)(147,224)(148,220)(149,225)(150,218)(151,223)
(152,219)(153,221)(154,226)(155,231)(156,233)(157,229)(158,234)(159,227)
(160,232)(161,228)(162,230)(163,235)(164,240)(165,242)(166,238)(167,243)
(168,236)(169,241)(170,237)(171,239)(172,244)(173,249)(174,251)(175,247)
(176,252)(177,245)(178,250)(179,246)(180,248)(181,262)(182,267)(183,269)
(184,265)(185,270)(186,263)(187,268)(188,264)(189,266)(190,253)(191,258)
(192,260)(193,256)(194,261)(195,254)(196,259)(197,255)(198,257)(199,280)
(200,285)(201,287)(202,283)(203,288)(204,281)(205,286)(206,282)(207,284)
(208,271)(209,276)(210,278)(211,274)(212,279)(213,272)(214,277)(215,273)
(216,275)(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)(295,367)
(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)(303,371)
(304,376)(305,372)(306,374)(307,379)(308,384)(309,386)(310,382)(311,387)
(312,380)(313,385)(314,381)(315,383)(316,388)(317,393)(318,395)(319,391)
(320,396)(321,389)(322,394)(323,390)(324,392)(325,406)(326,411)(327,413)
(328,409)(329,414)(330,407)(331,412)(332,408)(333,410)(334,397)(335,402)
(336,404)(337,400)(338,405)(339,398)(340,403)(341,399)(342,401)(343,424)
(344,429)(345,431)(346,427)(347,432)(348,425)(349,430)(350,426)(351,428)
(352,415)(353,420)(354,422)(355,418)(356,423)(357,416)(358,421)(359,417)
(360,419)(433,505)(434,510)(435,512)(436,508)(437,513)(438,506)(439,511)
(440,507)(441,509)(442,514)(443,519)(444,521)(445,517)(446,522)(447,515)
(448,520)(449,516)(450,518)(451,523)(452,528)(453,530)(454,526)(455,531)
(456,524)(457,529)(458,525)(459,527)(460,532)(461,537)(462,539)(463,535)
(464,540)(465,533)(466,538)(467,534)(468,536)(469,550)(470,555)(471,557)
(472,553)(473,558)(474,551)(475,556)(476,552)(477,554)(478,541)(479,546)
(480,548)(481,544)(482,549)(483,542)(484,547)(485,543)(486,545)(487,568)
(488,573)(489,575)(490,571)(491,576)(492,569)(493,574)(494,570)(495,572)
(496,559)(497,564)(498,566)(499,562)(500,567)(501,560)(502,565)(503,561)
(504,563);
s3 := Sym(576)!(  1,289)(  2,290)(  3,291)(  4,292)(  5,293)(  6,294)(  7,295)
(  8,296)(  9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)
( 16,304)( 17,305)( 18,306)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)
( 24,312)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)
( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)
( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)
( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,352)
( 56,353)( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)
( 64,343)( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)
( 72,351)( 73,397)( 74,398)( 75,399)( 76,400)( 77,401)( 78,402)( 79,403)
( 80,404)( 81,405)( 82,406)( 83,407)( 84,408)( 85,409)( 86,410)( 87,411)
( 88,412)( 89,413)( 90,414)( 91,415)( 92,416)( 93,417)( 94,418)( 95,419)
( 96,420)( 97,421)( 98,422)( 99,423)(100,424)(101,425)(102,426)(103,427)
(104,428)(105,429)(106,430)(107,431)(108,432)(109,361)(110,362)(111,363)
(112,364)(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)
(120,372)(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,379)
(128,380)(129,381)(130,382)(131,383)(132,384)(133,385)(134,386)(135,387)
(136,388)(137,389)(138,390)(139,391)(140,392)(141,393)(142,394)(143,395)
(144,396)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)
(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)
(160,448)(161,449)(162,450)(163,451)(164,452)(165,453)(166,454)(167,455)
(168,456)(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)
(176,464)(177,465)(178,466)(179,467)(180,468)(181,478)(182,479)(183,480)
(184,481)(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)
(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,496)
(200,497)(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)
(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)
(216,495)(217,541)(218,542)(219,543)(220,544)(221,545)(222,546)(223,547)
(224,548)(225,549)(226,550)(227,551)(228,552)(229,553)(230,554)(231,555)
(232,556)(233,557)(234,558)(235,559)(236,560)(237,561)(238,562)(239,563)
(240,564)(241,565)(242,566)(243,567)(244,568)(245,569)(246,570)(247,571)
(248,572)(249,573)(250,574)(251,575)(252,576)(253,505)(254,506)(255,507)
(256,508)(257,509)(258,510)(259,511)(260,512)(261,513)(262,514)(263,515)
(264,516)(265,517)(266,518)(267,519)(268,520)(269,521)(270,522)(271,523)
(272,524)(273,525)(274,526)(275,527)(276,528)(277,529)(278,530)(279,531)
(280,532)(281,533)(282,534)(283,535)(284,536)(285,537)(286,538)(287,539)
(288,540);
poly := sub<Sym(576)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope