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Polytope of Type {8,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12,6}*1152b
Also Known As : {{8,12|2},{12,6|2}}. if this polytope has another name.
Group : SmallGroup(1152,97531)
Rank : 4
Schlafli Type : {8,12,6}
Number of vertices, edges, etc : 8, 48, 36, 6
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 : {4,12,6}*576a, {8,6,6}*576a
   3-fold quotients : {8,12,2}*384a, {8,4,6}*384a
   4-fold quotients : {2,12,6}*288a, {4,6,6}*288a
   6-fold quotients : {4,12,2}*192a, {4,4,6}*192, {8,2,6}*192, {8,6,2}*192
   8-fold quotients : {2,6,6}*144a
   9-fold quotients : {8,4,2}*128a
   12-fold quotients : {8,2,3}*96, {2,12,2}*96, {2,4,6}*96a, {4,2,6}*96, {4,6,2}*96a
   18-fold quotients : {4,4,2}*64, {8,2,2}*64
   24-fold quotients : {4,2,3}*48, {2,2,6}*48, {2,6,2}*48
   36-fold quotients : {2,4,2}*32, {4,2,2}*32
   48-fold quotients : {2,2,3}*24, {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)
( 73,361)( 74,362)( 75,363)( 76,364)( 77,365)( 78,366)( 79,367)( 80,368)
( 81,369)( 82,370)( 83,371)( 84,372)( 85,373)( 86,374)( 87,375)( 88,376)
( 89,377)( 90,378)( 91,379)( 92,380)( 93,381)( 94,382)( 95,383)( 96,384)
( 97,385)( 98,386)( 99,387)(100,388)(101,389)(102,390)(103,391)(104,392)
(105,393)(106,394)(107,395)(108,396)(109,406)(110,407)(111,408)(112,409)
(113,410)(114,411)(115,412)(116,413)(117,414)(118,397)(119,398)(120,399)
(121,400)(122,401)(123,402)(124,403)(125,404)(126,405)(127,424)(128,425)
(129,426)(130,427)(131,428)(132,429)(133,430)(134,431)(135,432)(136,415)
(137,416)(138,417)(139,418)(140,419)(141,420)(142,421)(143,422)(144,423)
(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)
(217,505)(218,506)(219,507)(220,508)(221,509)(222,510)(223,511)(224,512)
(225,513)(226,514)(227,515)(228,516)(229,517)(230,518)(231,519)(232,520)
(233,521)(234,522)(235,523)(236,524)(237,525)(238,526)(239,527)(240,528)
(241,529)(242,530)(243,531)(244,532)(245,533)(246,534)(247,535)(248,536)
(249,537)(250,538)(251,539)(252,540)(253,550)(254,551)(255,552)(256,553)
(257,554)(258,555)(259,556)(260,557)(261,558)(262,541)(263,542)(264,543)
(265,544)(266,545)(267,546)(268,547)(269,548)(270,549)(271,568)(272,569)
(273,570)(274,571)(275,572)(276,573)(277,574)(278,575)(279,576)(280,559)
(281,560)(282,561)(283,562)(284,563)(285,564)(286,565)(287,566)(288,567);;
s1 := (  1, 73)(  2, 80)(  3, 78)(  4, 79)(  5, 77)(  6, 75)(  7, 76)(  8, 74)
(  9, 81)( 10, 82)( 11, 89)( 12, 87)( 13, 88)( 14, 86)( 15, 84)( 16, 85)
( 17, 83)( 18, 90)( 19, 91)( 20, 98)( 21, 96)( 22, 97)( 23, 95)( 24, 93)
( 25, 94)( 26, 92)( 27, 99)( 28,100)( 29,107)( 30,105)( 31,106)( 32,104)
( 33,102)( 34,103)( 35,101)( 36,108)( 37,118)( 38,125)( 39,123)( 40,124)
( 41,122)( 42,120)( 43,121)( 44,119)( 45,126)( 46,109)( 47,116)( 48,114)
( 49,115)( 50,113)( 51,111)( 52,112)( 53,110)( 54,117)( 55,136)( 56,143)
( 57,141)( 58,142)( 59,140)( 60,138)( 61,139)( 62,137)( 63,144)( 64,127)
( 65,134)( 66,132)( 67,133)( 68,131)( 69,129)( 70,130)( 71,128)( 72,135)
(145,235)(146,242)(147,240)(148,241)(149,239)(150,237)(151,238)(152,236)
(153,243)(154,244)(155,251)(156,249)(157,250)(158,248)(159,246)(160,247)
(161,245)(162,252)(163,217)(164,224)(165,222)(166,223)(167,221)(168,219)
(169,220)(170,218)(171,225)(172,226)(173,233)(174,231)(175,232)(176,230)
(177,228)(178,229)(179,227)(180,234)(181,280)(182,287)(183,285)(184,286)
(185,284)(186,282)(187,283)(188,281)(189,288)(190,271)(191,278)(192,276)
(193,277)(194,275)(195,273)(196,274)(197,272)(198,279)(199,262)(200,269)
(201,267)(202,268)(203,266)(204,264)(205,265)(206,263)(207,270)(208,253)
(209,260)(210,258)(211,259)(212,257)(213,255)(214,256)(215,254)(216,261)
(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)(296,398)
(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)(304,409)
(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)(312,417)
(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)(320,428)
(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)(328,367)
(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)(336,375)
(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)(344,386)
(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)(352,388)
(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)(360,396)
(433,559)(434,566)(435,564)(436,565)(437,563)(438,561)(439,562)(440,560)
(441,567)(442,568)(443,575)(444,573)(445,574)(446,572)(447,570)(448,571)
(449,569)(450,576)(451,541)(452,548)(453,546)(454,547)(455,545)(456,543)
(457,544)(458,542)(459,549)(460,550)(461,557)(462,555)(463,556)(464,554)
(465,552)(466,553)(467,551)(468,558)(469,523)(470,530)(471,528)(472,529)
(473,527)(474,525)(475,526)(476,524)(477,531)(478,532)(479,539)(480,537)
(481,538)(482,536)(483,534)(484,535)(485,533)(486,540)(487,505)(488,512)
(489,510)(490,511)(491,509)(492,507)(493,508)(494,506)(495,513)(496,514)
(497,521)(498,519)(499,520)(500,518)(501,516)(502,517)(503,515)(504,522);;
s2 := (  1,148)(  2,150)(  3,149)(  4,145)(  5,147)(  6,146)(  7,151)(  8,153)
(  9,152)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)( 16,160)
( 17,162)( 18,161)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)( 24,164)
( 25,169)( 26,171)( 27,170)( 28,175)( 29,177)( 30,176)( 31,172)( 32,174)
( 33,173)( 34,178)( 35,180)( 36,179)( 37,184)( 38,186)( 39,185)( 40,181)
( 41,183)( 42,182)( 43,187)( 44,189)( 45,188)( 46,193)( 47,195)( 48,194)
( 49,190)( 50,192)( 51,191)( 52,196)( 53,198)( 54,197)( 55,202)( 56,204)
( 57,203)( 58,199)( 59,201)( 60,200)( 61,205)( 62,207)( 63,206)( 64,211)
( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,214)( 71,216)( 72,215)
( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,223)( 80,225)
( 81,224)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)( 88,232)
( 89,234)( 90,233)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)( 96,236)
( 97,241)( 98,243)( 99,242)(100,247)(101,249)(102,248)(103,244)(104,246)
(105,245)(106,250)(107,252)(108,251)(109,256)(110,258)(111,257)(112,253)
(113,255)(114,254)(115,259)(116,261)(117,260)(118,265)(119,267)(120,266)
(121,262)(122,264)(123,263)(124,268)(125,270)(126,269)(127,274)(128,276)
(129,275)(130,271)(131,273)(132,272)(133,277)(134,279)(135,278)(136,283)
(137,285)(138,284)(139,280)(140,282)(141,281)(142,286)(143,288)(144,287)
(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,439)(296,441)
(297,440)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)(304,448)
(305,450)(306,449)(307,454)(308,456)(309,455)(310,451)(311,453)(312,452)
(313,457)(314,459)(315,458)(316,463)(317,465)(318,464)(319,460)(320,462)
(321,461)(322,466)(323,468)(324,467)(325,472)(326,474)(327,473)(328,469)
(329,471)(330,470)(331,475)(332,477)(333,476)(334,481)(335,483)(336,482)
(337,478)(338,480)(339,479)(340,484)(341,486)(342,485)(343,490)(344,492)
(345,491)(346,487)(347,489)(348,488)(349,493)(350,495)(351,494)(352,499)
(353,501)(354,500)(355,496)(356,498)(357,497)(358,502)(359,504)(360,503)
(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,511)(368,513)
(369,512)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)(376,520)
(377,522)(378,521)(379,526)(380,528)(381,527)(382,523)(383,525)(384,524)
(385,529)(386,531)(387,530)(388,535)(389,537)(390,536)(391,532)(392,534)
(393,533)(394,538)(395,540)(396,539)(397,544)(398,546)(399,545)(400,541)
(401,543)(402,542)(403,547)(404,549)(405,548)(406,553)(407,555)(408,554)
(409,550)(410,552)(411,551)(412,556)(413,558)(414,557)(415,562)(416,564)
(417,563)(418,559)(419,561)(420,560)(421,565)(422,567)(423,566)(424,571)
(425,573)(426,572)(427,568)(428,570)(429,569)(430,574)(431,576)(432,575);;
s3 := (  1, 77)(  2, 79)(  3, 75)(  4, 80)(  5, 73)(  6, 78)(  7, 74)(  8, 76)
(  9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)( 16, 83)
( 17, 85)( 18, 90)( 19, 95)( 20, 97)( 21, 93)( 22, 98)( 23, 91)( 24, 96)
( 25, 92)( 26, 94)( 27, 99)( 28,104)( 29,106)( 30,102)( 31,107)( 32,100)
( 33,105)( 34,101)( 35,103)( 36,108)( 37,113)( 38,115)( 39,111)( 40,116)
( 41,109)( 42,114)( 43,110)( 44,112)( 45,117)( 46,122)( 47,124)( 48,120)
( 49,125)( 50,118)( 51,123)( 52,119)( 53,121)( 54,126)( 55,131)( 56,133)
( 57,129)( 58,134)( 59,127)( 60,132)( 61,128)( 62,130)( 63,135)( 64,140)
( 65,142)( 66,138)( 67,143)( 68,136)( 69,141)( 70,137)( 71,139)( 72,144)
(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)(152,220)
(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)(160,227)
(161,229)(162,234)(163,239)(164,241)(165,237)(166,242)(167,235)(168,240)
(169,236)(170,238)(171,243)(172,248)(173,250)(174,246)(175,251)(176,244)
(177,249)(178,245)(179,247)(180,252)(181,257)(182,259)(183,255)(184,260)
(185,253)(186,258)(187,254)(188,256)(189,261)(190,266)(191,268)(192,264)
(193,269)(194,262)(195,267)(196,263)(197,265)(198,270)(199,275)(200,277)
(201,273)(202,278)(203,271)(204,276)(205,272)(206,274)(207,279)(208,284)
(209,286)(210,282)(211,287)(212,280)(213,285)(214,281)(215,283)(216,288)
(289,365)(290,367)(291,363)(292,368)(293,361)(294,366)(295,362)(296,364)
(297,369)(298,374)(299,376)(300,372)(301,377)(302,370)(303,375)(304,371)
(305,373)(306,378)(307,383)(308,385)(309,381)(310,386)(311,379)(312,384)
(313,380)(314,382)(315,387)(316,392)(317,394)(318,390)(319,395)(320,388)
(321,393)(322,389)(323,391)(324,396)(325,401)(326,403)(327,399)(328,404)
(329,397)(330,402)(331,398)(332,400)(333,405)(334,410)(335,412)(336,408)
(337,413)(338,406)(339,411)(340,407)(341,409)(342,414)(343,419)(344,421)
(345,417)(346,422)(347,415)(348,420)(349,416)(350,418)(351,423)(352,428)
(353,430)(354,426)(355,431)(356,424)(357,429)(358,425)(359,427)(360,432)
(433,509)(434,511)(435,507)(436,512)(437,505)(438,510)(439,506)(440,508)
(441,513)(442,518)(443,520)(444,516)(445,521)(446,514)(447,519)(448,515)
(449,517)(450,522)(451,527)(452,529)(453,525)(454,530)(455,523)(456,528)
(457,524)(458,526)(459,531)(460,536)(461,538)(462,534)(463,539)(464,532)
(465,537)(466,533)(467,535)(468,540)(469,545)(470,547)(471,543)(472,548)
(473,541)(474,546)(475,542)(476,544)(477,549)(478,554)(479,556)(480,552)
(481,557)(482,550)(483,555)(484,551)(485,553)(486,558)(487,563)(488,565)
(489,561)(490,566)(491,559)(492,564)(493,560)(494,562)(495,567)(496,572)
(497,574)(498,570)(499,575)(500,568)(501,573)(502,569)(503,571)(504,576);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, 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, 
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)!(  1,289)(  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)( 73,361)( 74,362)( 75,363)( 76,364)( 77,365)( 78,366)( 79,367)
( 80,368)( 81,369)( 82,370)( 83,371)( 84,372)( 85,373)( 86,374)( 87,375)
( 88,376)( 89,377)( 90,378)( 91,379)( 92,380)( 93,381)( 94,382)( 95,383)
( 96,384)( 97,385)( 98,386)( 99,387)(100,388)(101,389)(102,390)(103,391)
(104,392)(105,393)(106,394)(107,395)(108,396)(109,406)(110,407)(111,408)
(112,409)(113,410)(114,411)(115,412)(116,413)(117,414)(118,397)(119,398)
(120,399)(121,400)(122,401)(123,402)(124,403)(125,404)(126,405)(127,424)
(128,425)(129,426)(130,427)(131,428)(132,429)(133,430)(134,431)(135,432)
(136,415)(137,416)(138,417)(139,418)(140,419)(141,420)(142,421)(143,422)
(144,423)(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)(217,505)(218,506)(219,507)(220,508)(221,509)(222,510)(223,511)
(224,512)(225,513)(226,514)(227,515)(228,516)(229,517)(230,518)(231,519)
(232,520)(233,521)(234,522)(235,523)(236,524)(237,525)(238,526)(239,527)
(240,528)(241,529)(242,530)(243,531)(244,532)(245,533)(246,534)(247,535)
(248,536)(249,537)(250,538)(251,539)(252,540)(253,550)(254,551)(255,552)
(256,553)(257,554)(258,555)(259,556)(260,557)(261,558)(262,541)(263,542)
(264,543)(265,544)(266,545)(267,546)(268,547)(269,548)(270,549)(271,568)
(272,569)(273,570)(274,571)(275,572)(276,573)(277,574)(278,575)(279,576)
(280,559)(281,560)(282,561)(283,562)(284,563)(285,564)(286,565)(287,566)
(288,567);
s1 := Sym(576)!(  1, 73)(  2, 80)(  3, 78)(  4, 79)(  5, 77)(  6, 75)(  7, 76)
(  8, 74)(  9, 81)( 10, 82)( 11, 89)( 12, 87)( 13, 88)( 14, 86)( 15, 84)
( 16, 85)( 17, 83)( 18, 90)( 19, 91)( 20, 98)( 21, 96)( 22, 97)( 23, 95)
( 24, 93)( 25, 94)( 26, 92)( 27, 99)( 28,100)( 29,107)( 30,105)( 31,106)
( 32,104)( 33,102)( 34,103)( 35,101)( 36,108)( 37,118)( 38,125)( 39,123)
( 40,124)( 41,122)( 42,120)( 43,121)( 44,119)( 45,126)( 46,109)( 47,116)
( 48,114)( 49,115)( 50,113)( 51,111)( 52,112)( 53,110)( 54,117)( 55,136)
( 56,143)( 57,141)( 58,142)( 59,140)( 60,138)( 61,139)( 62,137)( 63,144)
( 64,127)( 65,134)( 66,132)( 67,133)( 68,131)( 69,129)( 70,130)( 71,128)
( 72,135)(145,235)(146,242)(147,240)(148,241)(149,239)(150,237)(151,238)
(152,236)(153,243)(154,244)(155,251)(156,249)(157,250)(158,248)(159,246)
(160,247)(161,245)(162,252)(163,217)(164,224)(165,222)(166,223)(167,221)
(168,219)(169,220)(170,218)(171,225)(172,226)(173,233)(174,231)(175,232)
(176,230)(177,228)(178,229)(179,227)(180,234)(181,280)(182,287)(183,285)
(184,286)(185,284)(186,282)(187,283)(188,281)(189,288)(190,271)(191,278)
(192,276)(193,277)(194,275)(195,273)(196,274)(197,272)(198,279)(199,262)
(200,269)(201,267)(202,268)(203,266)(204,264)(205,265)(206,263)(207,270)
(208,253)(209,260)(210,258)(211,259)(212,257)(213,255)(214,256)(215,254)
(216,261)(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)
(296,398)(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)
(304,409)(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)
(312,417)(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)
(320,428)(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)
(328,367)(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)
(336,375)(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)
(344,386)(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)
(352,388)(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)
(360,396)(433,559)(434,566)(435,564)(436,565)(437,563)(438,561)(439,562)
(440,560)(441,567)(442,568)(443,575)(444,573)(445,574)(446,572)(447,570)
(448,571)(449,569)(450,576)(451,541)(452,548)(453,546)(454,547)(455,545)
(456,543)(457,544)(458,542)(459,549)(460,550)(461,557)(462,555)(463,556)
(464,554)(465,552)(466,553)(467,551)(468,558)(469,523)(470,530)(471,528)
(472,529)(473,527)(474,525)(475,526)(476,524)(477,531)(478,532)(479,539)
(480,537)(481,538)(482,536)(483,534)(484,535)(485,533)(486,540)(487,505)
(488,512)(489,510)(490,511)(491,509)(492,507)(493,508)(494,506)(495,513)
(496,514)(497,521)(498,519)(499,520)(500,518)(501,516)(502,517)(503,515)
(504,522);
s2 := Sym(576)!(  1,148)(  2,150)(  3,149)(  4,145)(  5,147)(  6,146)(  7,151)
(  8,153)(  9,152)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)
( 16,160)( 17,162)( 18,161)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)
( 24,164)( 25,169)( 26,171)( 27,170)( 28,175)( 29,177)( 30,176)( 31,172)
( 32,174)( 33,173)( 34,178)( 35,180)( 36,179)( 37,184)( 38,186)( 39,185)
( 40,181)( 41,183)( 42,182)( 43,187)( 44,189)( 45,188)( 46,193)( 47,195)
( 48,194)( 49,190)( 50,192)( 51,191)( 52,196)( 53,198)( 54,197)( 55,202)
( 56,204)( 57,203)( 58,199)( 59,201)( 60,200)( 61,205)( 62,207)( 63,206)
( 64,211)( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,214)( 71,216)
( 72,215)( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,223)
( 80,225)( 81,224)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)
( 88,232)( 89,234)( 90,233)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)
( 96,236)( 97,241)( 98,243)( 99,242)(100,247)(101,249)(102,248)(103,244)
(104,246)(105,245)(106,250)(107,252)(108,251)(109,256)(110,258)(111,257)
(112,253)(113,255)(114,254)(115,259)(116,261)(117,260)(118,265)(119,267)
(120,266)(121,262)(122,264)(123,263)(124,268)(125,270)(126,269)(127,274)
(128,276)(129,275)(130,271)(131,273)(132,272)(133,277)(134,279)(135,278)
(136,283)(137,285)(138,284)(139,280)(140,282)(141,281)(142,286)(143,288)
(144,287)(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,439)
(296,441)(297,440)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)
(304,448)(305,450)(306,449)(307,454)(308,456)(309,455)(310,451)(311,453)
(312,452)(313,457)(314,459)(315,458)(316,463)(317,465)(318,464)(319,460)
(320,462)(321,461)(322,466)(323,468)(324,467)(325,472)(326,474)(327,473)
(328,469)(329,471)(330,470)(331,475)(332,477)(333,476)(334,481)(335,483)
(336,482)(337,478)(338,480)(339,479)(340,484)(341,486)(342,485)(343,490)
(344,492)(345,491)(346,487)(347,489)(348,488)(349,493)(350,495)(351,494)
(352,499)(353,501)(354,500)(355,496)(356,498)(357,497)(358,502)(359,504)
(360,503)(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,511)
(368,513)(369,512)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)
(376,520)(377,522)(378,521)(379,526)(380,528)(381,527)(382,523)(383,525)
(384,524)(385,529)(386,531)(387,530)(388,535)(389,537)(390,536)(391,532)
(392,534)(393,533)(394,538)(395,540)(396,539)(397,544)(398,546)(399,545)
(400,541)(401,543)(402,542)(403,547)(404,549)(405,548)(406,553)(407,555)
(408,554)(409,550)(410,552)(411,551)(412,556)(413,558)(414,557)(415,562)
(416,564)(417,563)(418,559)(419,561)(420,560)(421,565)(422,567)(423,566)
(424,571)(425,573)(426,572)(427,568)(428,570)(429,569)(430,574)(431,576)
(432,575);
s3 := Sym(576)!(  1, 77)(  2, 79)(  3, 75)(  4, 80)(  5, 73)(  6, 78)(  7, 74)
(  8, 76)(  9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)
( 16, 83)( 17, 85)( 18, 90)( 19, 95)( 20, 97)( 21, 93)( 22, 98)( 23, 91)
( 24, 96)( 25, 92)( 26, 94)( 27, 99)( 28,104)( 29,106)( 30,102)( 31,107)
( 32,100)( 33,105)( 34,101)( 35,103)( 36,108)( 37,113)( 38,115)( 39,111)
( 40,116)( 41,109)( 42,114)( 43,110)( 44,112)( 45,117)( 46,122)( 47,124)
( 48,120)( 49,125)( 50,118)( 51,123)( 52,119)( 53,121)( 54,126)( 55,131)
( 56,133)( 57,129)( 58,134)( 59,127)( 60,132)( 61,128)( 62,130)( 63,135)
( 64,140)( 65,142)( 66,138)( 67,143)( 68,136)( 69,141)( 70,137)( 71,139)
( 72,144)(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)
(152,220)(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)
(160,227)(161,229)(162,234)(163,239)(164,241)(165,237)(166,242)(167,235)
(168,240)(169,236)(170,238)(171,243)(172,248)(173,250)(174,246)(175,251)
(176,244)(177,249)(178,245)(179,247)(180,252)(181,257)(182,259)(183,255)
(184,260)(185,253)(186,258)(187,254)(188,256)(189,261)(190,266)(191,268)
(192,264)(193,269)(194,262)(195,267)(196,263)(197,265)(198,270)(199,275)
(200,277)(201,273)(202,278)(203,271)(204,276)(205,272)(206,274)(207,279)
(208,284)(209,286)(210,282)(211,287)(212,280)(213,285)(214,281)(215,283)
(216,288)(289,365)(290,367)(291,363)(292,368)(293,361)(294,366)(295,362)
(296,364)(297,369)(298,374)(299,376)(300,372)(301,377)(302,370)(303,375)
(304,371)(305,373)(306,378)(307,383)(308,385)(309,381)(310,386)(311,379)
(312,384)(313,380)(314,382)(315,387)(316,392)(317,394)(318,390)(319,395)
(320,388)(321,393)(322,389)(323,391)(324,396)(325,401)(326,403)(327,399)
(328,404)(329,397)(330,402)(331,398)(332,400)(333,405)(334,410)(335,412)
(336,408)(337,413)(338,406)(339,411)(340,407)(341,409)(342,414)(343,419)
(344,421)(345,417)(346,422)(347,415)(348,420)(349,416)(350,418)(351,423)
(352,428)(353,430)(354,426)(355,431)(356,424)(357,429)(358,425)(359,427)
(360,432)(433,509)(434,511)(435,507)(436,512)(437,505)(438,510)(439,506)
(440,508)(441,513)(442,518)(443,520)(444,516)(445,521)(446,514)(447,519)
(448,515)(449,517)(450,522)(451,527)(452,529)(453,525)(454,530)(455,523)
(456,528)(457,524)(458,526)(459,531)(460,536)(461,538)(462,534)(463,539)
(464,532)(465,537)(466,533)(467,535)(468,540)(469,545)(470,547)(471,543)
(472,548)(473,541)(474,546)(475,542)(476,544)(477,549)(478,554)(479,556)
(480,552)(481,557)(482,550)(483,555)(484,551)(485,553)(486,558)(487,563)
(488,565)(489,561)(490,566)(491,559)(492,564)(493,560)(494,562)(495,567)
(496,572)(497,574)(498,570)(499,575)(500,568)(501,573)(502,569)(503,571)
(504,576);
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, s1*s2*s3*s2*s1*s2*s3*s2, 
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, 
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