Polytope of Type {8,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,119750)
Rank : 4
Schlafli Type : {8,6,12}
Number of vertices, edges, etc : 8, 24, 36, 12
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 : {8,6,6}*576b, {4,6,12}*576c
   3-fold quotients : {8,6,4}*384a
   4-fold quotients : {4,6,6}*288b, {2,6,12}*288c
   6-fold quotients : {4,6,4}*192a, {8,6,2}*192
   8-fold quotients : {2,6,6}*144c
   9-fold quotients : {8,2,4}*128
   12-fold quotients : {2,6,4}*96a, {4,6,2}*96a
   16-fold quotients : {2,3,6}*72
   18-fold quotients : {4,2,4}*64, {8,2,2}*64
   24-fold quotients : {2,6,2}*48
   36-fold quotients : {2,2,4}*32, {4,2,2}*32
   48-fold quotients : {2,3,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  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);;
s1 := (  1, 73)(  2, 75)(  3, 74)(  4, 79)(  5, 81)(  6, 80)(  7, 76)(  8, 78)
(  9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)( 16, 85)
( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)( 24, 98)
( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)( 32,108)
( 33,107)( 34,103)( 35,105)( 36,104)( 37,118)( 38,120)( 39,119)( 40,124)
( 41,126)( 42,125)( 43,121)( 44,123)( 45,122)( 46,109)( 47,111)( 48,110)
( 49,115)( 50,117)( 51,116)( 52,112)( 53,114)( 54,113)( 55,136)( 56,138)
( 57,137)( 58,142)( 59,144)( 60,143)( 61,139)( 62,141)( 63,140)( 64,127)
( 65,129)( 66,128)( 67,133)( 68,135)( 69,134)( 70,130)( 71,132)( 72,131)
(145,217)(146,219)(147,218)(148,223)(149,225)(150,224)(151,220)(152,222)
(153,221)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)(160,229)
(161,231)(162,230)(163,235)(164,237)(165,236)(166,241)(167,243)(168,242)
(169,238)(170,240)(171,239)(172,244)(173,246)(174,245)(175,250)(176,252)
(177,251)(178,247)(179,249)(180,248)(181,262)(182,264)(183,263)(184,268)
(185,270)(186,269)(187,265)(188,267)(189,266)(190,253)(191,255)(192,254)
(193,259)(194,261)(195,260)(196,256)(197,258)(198,257)(199,280)(200,282)
(201,281)(202,286)(203,288)(204,287)(205,283)(206,285)(207,284)(208,271)
(209,273)(210,272)(211,277)(212,279)(213,278)(214,274)(215,276)(216,275)
(289,361)(290,363)(291,362)(292,367)(293,369)(294,368)(295,364)(296,366)
(297,365)(298,370)(299,372)(300,371)(301,376)(302,378)(303,377)(304,373)
(305,375)(306,374)(307,379)(308,381)(309,380)(310,385)(311,387)(312,386)
(313,382)(314,384)(315,383)(316,388)(317,390)(318,389)(319,394)(320,396)
(321,395)(322,391)(323,393)(324,392)(325,406)(326,408)(327,407)(328,412)
(329,414)(330,413)(331,409)(332,411)(333,410)(334,397)(335,399)(336,398)
(337,403)(338,405)(339,404)(340,400)(341,402)(342,401)(343,424)(344,426)
(345,425)(346,430)(347,432)(348,431)(349,427)(350,429)(351,428)(352,415)
(353,417)(354,416)(355,421)(356,423)(357,422)(358,418)(359,420)(360,419)
(433,505)(434,507)(435,506)(436,511)(437,513)(438,512)(439,508)(440,510)
(441,509)(442,514)(443,516)(444,515)(445,520)(446,522)(447,521)(448,517)
(449,519)(450,518)(451,523)(452,525)(453,524)(454,529)(455,531)(456,530)
(457,526)(458,528)(459,527)(460,532)(461,534)(462,533)(463,538)(464,540)
(465,539)(466,535)(467,537)(468,536)(469,550)(470,552)(471,551)(472,556)
(473,558)(474,557)(475,553)(476,555)(477,554)(478,541)(479,543)(480,542)
(481,547)(482,549)(483,548)(484,544)(485,546)(486,545)(487,568)(488,570)
(489,569)(490,574)(491,576)(492,575)(493,571)(494,573)(495,572)(496,559)
(497,561)(498,560)(499,565)(500,567)(501,566)(502,562)(503,564)(504,563);;
s2 := (  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);;
s3 := (  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);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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)!(  1,289)(  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);
s1 := Sym(576)!(  1, 73)(  2, 75)(  3, 74)(  4, 79)(  5, 81)(  6, 80)(  7, 76)
(  8, 78)(  9, 77)( 10, 82)( 11, 84)( 12, 83)( 13, 88)( 14, 90)( 15, 89)
( 16, 85)( 17, 87)( 18, 86)( 19, 91)( 20, 93)( 21, 92)( 22, 97)( 23, 99)
( 24, 98)( 25, 94)( 26, 96)( 27, 95)( 28,100)( 29,102)( 30,101)( 31,106)
( 32,108)( 33,107)( 34,103)( 35,105)( 36,104)( 37,118)( 38,120)( 39,119)
( 40,124)( 41,126)( 42,125)( 43,121)( 44,123)( 45,122)( 46,109)( 47,111)
( 48,110)( 49,115)( 50,117)( 51,116)( 52,112)( 53,114)( 54,113)( 55,136)
( 56,138)( 57,137)( 58,142)( 59,144)( 60,143)( 61,139)( 62,141)( 63,140)
( 64,127)( 65,129)( 66,128)( 67,133)( 68,135)( 69,134)( 70,130)( 71,132)
( 72,131)(145,217)(146,219)(147,218)(148,223)(149,225)(150,224)(151,220)
(152,222)(153,221)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)
(160,229)(161,231)(162,230)(163,235)(164,237)(165,236)(166,241)(167,243)
(168,242)(169,238)(170,240)(171,239)(172,244)(173,246)(174,245)(175,250)
(176,252)(177,251)(178,247)(179,249)(180,248)(181,262)(182,264)(183,263)
(184,268)(185,270)(186,269)(187,265)(188,267)(189,266)(190,253)(191,255)
(192,254)(193,259)(194,261)(195,260)(196,256)(197,258)(198,257)(199,280)
(200,282)(201,281)(202,286)(203,288)(204,287)(205,283)(206,285)(207,284)
(208,271)(209,273)(210,272)(211,277)(212,279)(213,278)(214,274)(215,276)
(216,275)(289,361)(290,363)(291,362)(292,367)(293,369)(294,368)(295,364)
(296,366)(297,365)(298,370)(299,372)(300,371)(301,376)(302,378)(303,377)
(304,373)(305,375)(306,374)(307,379)(308,381)(309,380)(310,385)(311,387)
(312,386)(313,382)(314,384)(315,383)(316,388)(317,390)(318,389)(319,394)
(320,396)(321,395)(322,391)(323,393)(324,392)(325,406)(326,408)(327,407)
(328,412)(329,414)(330,413)(331,409)(332,411)(333,410)(334,397)(335,399)
(336,398)(337,403)(338,405)(339,404)(340,400)(341,402)(342,401)(343,424)
(344,426)(345,425)(346,430)(347,432)(348,431)(349,427)(350,429)(351,428)
(352,415)(353,417)(354,416)(355,421)(356,423)(357,422)(358,418)(359,420)
(360,419)(433,505)(434,507)(435,506)(436,511)(437,513)(438,512)(439,508)
(440,510)(441,509)(442,514)(443,516)(444,515)(445,520)(446,522)(447,521)
(448,517)(449,519)(450,518)(451,523)(452,525)(453,524)(454,529)(455,531)
(456,530)(457,526)(458,528)(459,527)(460,532)(461,534)(462,533)(463,538)
(464,540)(465,539)(466,535)(467,537)(468,536)(469,550)(470,552)(471,551)
(472,556)(473,558)(474,557)(475,553)(476,555)(477,554)(478,541)(479,543)
(480,542)(481,547)(482,549)(483,548)(484,544)(485,546)(486,545)(487,568)
(488,570)(489,569)(490,574)(491,576)(492,575)(493,571)(494,573)(495,572)
(496,559)(497,561)(498,560)(499,565)(500,567)(501,566)(502,562)(503,564)
(504,563);
s2 := 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);
s3 := 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);
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope