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Polytope of Type {4,6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,24}*1152c
if this polytope has a name.
Group : SmallGroup(1152,119768)
Rank : 4
Schlafli Type : {4,6,24}
Number of vertices, edges, etc : 4, 12, 72, 24
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 : {2,6,24}*576b, {4,6,12}*576b
   3-fold quotients : {4,2,24}*384
   4-fold quotients : {2,6,12}*288b, {4,6,6}*288c
   6-fold quotients : {4,2,12}*192, {2,2,24}*192
   8-fold quotients : {4,6,3}*144, {2,6,6}*144b
   9-fold quotients : {4,2,8}*128
   12-fold quotients : {2,2,12}*96, {4,2,6}*96
   16-fold quotients : {2,6,3}*72
   18-fold quotients : {4,2,4}*64, {2,2,8}*64
   24-fold quotients : {4,2,3}*48, {2,2,6}*48
   36-fold quotients : {2,2,4}*32, {4,2,2}*32
   48-fold quotients : {2,2,3}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)(  8,152)
(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)( 16,160)
( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)( 24,168)
( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)( 32,176)
( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)( 40,184)
( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)( 48,192)
( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)( 56,200)
( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)( 64,208)
( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)( 72,216)
( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)( 80,224)
( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)( 88,232)
( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)( 96,240)
( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)(104,248)
(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)(112,256)
(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)(120,264)
(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)(128,272)
(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)(136,280)
(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)(144,288)
(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)(296,440)
(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)(304,448)
(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)(312,456)
(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)(320,464)
(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)(328,472)
(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)(336,480)
(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)(344,488)
(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)(352,496)
(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)(360,504)
(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)(368,512)
(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)(376,520)
(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)(384,528)
(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)(392,536)
(393,537)(394,538)(395,539)(396,540)(397,541)(398,542)(399,543)(400,544)
(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)(408,552)
(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)(416,560)
(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)(424,568)
(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)(432,576);;
s1 := (  1,109)(  2,116)(  3,114)(  4,115)(  5,113)(  6,111)(  7,112)(  8,110)
(  9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)( 16,121)
( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)( 24,129)
( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)( 32,140)
( 33,138)( 34,139)( 35,137)( 36,144)( 37, 82)( 38, 89)( 39, 87)( 40, 88)
( 41, 86)( 42, 84)( 43, 85)( 44, 83)( 45, 90)( 46, 73)( 47, 80)( 48, 78)
( 49, 79)( 50, 77)( 51, 75)( 52, 76)( 53, 74)( 54, 81)( 55,100)( 56,107)
( 57,105)( 58,106)( 59,104)( 60,102)( 61,103)( 62,101)( 63,108)( 64, 91)
( 65, 98)( 66, 96)( 67, 97)( 68, 95)( 69, 93)( 70, 94)( 71, 92)( 72, 99)
(145,271)(146,278)(147,276)(148,277)(149,275)(150,273)(151,274)(152,272)
(153,279)(154,280)(155,287)(156,285)(157,286)(158,284)(159,282)(160,283)
(161,281)(162,288)(163,253)(164,260)(165,258)(166,259)(167,257)(168,255)
(169,256)(170,254)(171,261)(172,262)(173,269)(174,267)(175,268)(176,266)
(177,264)(178,265)(179,263)(180,270)(181,244)(182,251)(183,249)(184,250)
(185,248)(186,246)(187,247)(188,245)(189,252)(190,235)(191,242)(192,240)
(193,241)(194,239)(195,237)(196,238)(197,236)(198,243)(199,226)(200,233)
(201,231)(202,232)(203,230)(204,228)(205,229)(206,227)(207,234)(208,217)
(209,224)(210,222)(211,223)(212,221)(213,219)(214,220)(215,218)(216,225)
(289,361)(290,368)(291,366)(292,367)(293,365)(294,363)(295,364)(296,362)
(297,369)(298,370)(299,377)(300,375)(301,376)(302,374)(303,372)(304,373)
(305,371)(306,378)(307,379)(308,386)(309,384)(310,385)(311,383)(312,381)
(313,382)(314,380)(315,387)(316,388)(317,395)(318,393)(319,394)(320,392)
(321,390)(322,391)(323,389)(324,396)(325,397)(326,404)(327,402)(328,403)
(329,401)(330,399)(331,400)(332,398)(333,405)(334,406)(335,413)(336,411)
(337,412)(338,410)(339,408)(340,409)(341,407)(342,414)(343,415)(344,422)
(345,420)(346,421)(347,419)(348,417)(349,418)(350,416)(351,423)(352,424)
(353,431)(354,429)(355,430)(356,428)(357,426)(358,427)(359,425)(360,432)
(433,523)(434,530)(435,528)(436,529)(437,527)(438,525)(439,526)(440,524)
(441,531)(442,532)(443,539)(444,537)(445,538)(446,536)(447,534)(448,535)
(449,533)(450,540)(451,505)(452,512)(453,510)(454,511)(455,509)(456,507)
(457,508)(458,506)(459,513)(460,514)(461,521)(462,519)(463,520)(464,518)
(465,516)(466,517)(467,515)(468,522)(469,559)(470,566)(471,564)(472,565)
(473,563)(474,561)(475,562)(476,560)(477,567)(478,568)(479,575)(480,573)
(481,574)(482,572)(483,570)(484,571)(485,569)(486,576)(487,541)(488,548)
(489,546)(490,547)(491,545)(492,543)(493,544)(494,542)(495,549)(496,550)
(497,557)(498,555)(499,556)(500,554)(501,552)(502,553)(503,551)(504,558);;
s2 := (  1,292)(  2,294)(  3,293)(  4,289)(  5,291)(  6,290)(  7,295)(  8,297)
(  9,296)( 10,301)( 11,303)( 12,302)( 13,298)( 14,300)( 15,299)( 16,304)
( 17,306)( 18,305)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)( 24,308)
( 25,313)( 26,315)( 27,314)( 28,319)( 29,321)( 30,320)( 31,316)( 32,318)
( 33,317)( 34,322)( 35,324)( 36,323)( 37,337)( 38,339)( 39,338)( 40,334)
( 41,336)( 42,335)( 43,340)( 44,342)( 45,341)( 46,328)( 47,330)( 48,329)
( 49,325)( 50,327)( 51,326)( 52,331)( 53,333)( 54,332)( 55,355)( 56,357)
( 57,356)( 58,352)( 59,354)( 60,353)( 61,358)( 62,360)( 63,359)( 64,346)
( 65,348)( 66,347)( 67,343)( 68,345)( 69,344)( 70,349)( 71,351)( 72,350)
( 73,400)( 74,402)( 75,401)( 76,397)( 77,399)( 78,398)( 79,403)( 80,405)
( 81,404)( 82,409)( 83,411)( 84,410)( 85,406)( 86,408)( 87,407)( 88,412)
( 89,414)( 90,413)( 91,418)( 92,420)( 93,419)( 94,415)( 95,417)( 96,416)
( 97,421)( 98,423)( 99,422)(100,427)(101,429)(102,428)(103,424)(104,426)
(105,425)(106,430)(107,432)(108,431)(109,364)(110,366)(111,365)(112,361)
(113,363)(114,362)(115,367)(116,369)(117,368)(118,373)(119,375)(120,374)
(121,370)(122,372)(123,371)(124,376)(125,378)(126,377)(127,382)(128,384)
(129,383)(130,379)(131,381)(132,380)(133,385)(134,387)(135,386)(136,391)
(137,393)(138,392)(139,388)(140,390)(141,389)(142,394)(143,396)(144,395)
(145,436)(146,438)(147,437)(148,433)(149,435)(150,434)(151,439)(152,441)
(153,440)(154,445)(155,447)(156,446)(157,442)(158,444)(159,443)(160,448)
(161,450)(162,449)(163,454)(164,456)(165,455)(166,451)(167,453)(168,452)
(169,457)(170,459)(171,458)(172,463)(173,465)(174,464)(175,460)(176,462)
(177,461)(178,466)(179,468)(180,467)(181,481)(182,483)(183,482)(184,478)
(185,480)(186,479)(187,484)(188,486)(189,485)(190,472)(191,474)(192,473)
(193,469)(194,471)(195,470)(196,475)(197,477)(198,476)(199,499)(200,501)
(201,500)(202,496)(203,498)(204,497)(205,502)(206,504)(207,503)(208,490)
(209,492)(210,491)(211,487)(212,489)(213,488)(214,493)(215,495)(216,494)
(217,544)(218,546)(219,545)(220,541)(221,543)(222,542)(223,547)(224,549)
(225,548)(226,553)(227,555)(228,554)(229,550)(230,552)(231,551)(232,556)
(233,558)(234,557)(235,562)(236,564)(237,563)(238,559)(239,561)(240,560)
(241,565)(242,567)(243,566)(244,571)(245,573)(246,572)(247,568)(248,570)
(249,569)(250,574)(251,576)(252,575)(253,508)(254,510)(255,509)(256,505)
(257,507)(258,506)(259,511)(260,513)(261,512)(262,517)(263,519)(264,518)
(265,514)(266,516)(267,515)(268,520)(269,522)(270,521)(271,526)(272,528)
(273,527)(274,523)(275,525)(276,524)(277,529)(278,531)(279,530)(280,535)
(281,537)(282,536)(283,532)(284,534)(285,533)(286,538)(287,540)(288,539);;
s3 := (  1, 77)(  2, 76)(  3, 78)(  4, 74)(  5, 73)(  6, 75)(  7, 80)(  8, 79)
(  9, 81)( 10, 86)( 11, 85)( 12, 87)( 13, 83)( 14, 82)( 15, 84)( 16, 89)
( 17, 88)( 18, 90)( 19, 95)( 20, 94)( 21, 96)( 22, 92)( 23, 91)( 24, 93)
( 25, 98)( 26, 97)( 27, 99)( 28,104)( 29,103)( 30,105)( 31,101)( 32,100)
( 33,102)( 34,107)( 35,106)( 36,108)( 37,122)( 38,121)( 39,123)( 40,119)
( 41,118)( 42,120)( 43,125)( 44,124)( 45,126)( 46,113)( 47,112)( 48,114)
( 49,110)( 50,109)( 51,111)( 52,116)( 53,115)( 54,117)( 55,140)( 56,139)
( 57,141)( 58,137)( 59,136)( 60,138)( 61,143)( 62,142)( 63,144)( 64,131)
( 65,130)( 66,132)( 67,128)( 68,127)( 69,129)( 70,134)( 71,133)( 72,135)
(145,221)(146,220)(147,222)(148,218)(149,217)(150,219)(151,224)(152,223)
(153,225)(154,230)(155,229)(156,231)(157,227)(158,226)(159,228)(160,233)
(161,232)(162,234)(163,239)(164,238)(165,240)(166,236)(167,235)(168,237)
(169,242)(170,241)(171,243)(172,248)(173,247)(174,249)(175,245)(176,244)
(177,246)(178,251)(179,250)(180,252)(181,266)(182,265)(183,267)(184,263)
(185,262)(186,264)(187,269)(188,268)(189,270)(190,257)(191,256)(192,258)
(193,254)(194,253)(195,255)(196,260)(197,259)(198,261)(199,284)(200,283)
(201,285)(202,281)(203,280)(204,282)(205,287)(206,286)(207,288)(208,275)
(209,274)(210,276)(211,272)(212,271)(213,273)(214,278)(215,277)(216,279)
(289,365)(290,364)(291,366)(292,362)(293,361)(294,363)(295,368)(296,367)
(297,369)(298,374)(299,373)(300,375)(301,371)(302,370)(303,372)(304,377)
(305,376)(306,378)(307,383)(308,382)(309,384)(310,380)(311,379)(312,381)
(313,386)(314,385)(315,387)(316,392)(317,391)(318,393)(319,389)(320,388)
(321,390)(322,395)(323,394)(324,396)(325,410)(326,409)(327,411)(328,407)
(329,406)(330,408)(331,413)(332,412)(333,414)(334,401)(335,400)(336,402)
(337,398)(338,397)(339,399)(340,404)(341,403)(342,405)(343,428)(344,427)
(345,429)(346,425)(347,424)(348,426)(349,431)(350,430)(351,432)(352,419)
(353,418)(354,420)(355,416)(356,415)(357,417)(358,422)(359,421)(360,423)
(433,509)(434,508)(435,510)(436,506)(437,505)(438,507)(439,512)(440,511)
(441,513)(442,518)(443,517)(444,519)(445,515)(446,514)(447,516)(448,521)
(449,520)(450,522)(451,527)(452,526)(453,528)(454,524)(455,523)(456,525)
(457,530)(458,529)(459,531)(460,536)(461,535)(462,537)(463,533)(464,532)
(465,534)(466,539)(467,538)(468,540)(469,554)(470,553)(471,555)(472,551)
(473,550)(474,552)(475,557)(476,556)(477,558)(478,545)(479,544)(480,546)
(481,542)(482,541)(483,543)(484,548)(485,547)(486,549)(487,572)(488,571)
(489,573)(490,569)(491,568)(492,570)(493,575)(494,574)(495,576)(496,563)
(497,562)(498,564)(499,560)(500,559)(501,561)(502,566)(503,565)(504,567);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,145)(  2,146)(  3,147)(  4,148)(  5,149)(  6,150)(  7,151)
(  8,152)(  9,153)( 10,154)( 11,155)( 12,156)( 13,157)( 14,158)( 15,159)
( 16,160)( 17,161)( 18,162)( 19,163)( 20,164)( 21,165)( 22,166)( 23,167)
( 24,168)( 25,169)( 26,170)( 27,171)( 28,172)( 29,173)( 30,174)( 31,175)
( 32,176)( 33,177)( 34,178)( 35,179)( 36,180)( 37,181)( 38,182)( 39,183)
( 40,184)( 41,185)( 42,186)( 43,187)( 44,188)( 45,189)( 46,190)( 47,191)
( 48,192)( 49,193)( 50,194)( 51,195)( 52,196)( 53,197)( 54,198)( 55,199)
( 56,200)( 57,201)( 58,202)( 59,203)( 60,204)( 61,205)( 62,206)( 63,207)
( 64,208)( 65,209)( 66,210)( 67,211)( 68,212)( 69,213)( 70,214)( 71,215)
( 72,216)( 73,217)( 74,218)( 75,219)( 76,220)( 77,221)( 78,222)( 79,223)
( 80,224)( 81,225)( 82,226)( 83,227)( 84,228)( 85,229)( 86,230)( 87,231)
( 88,232)( 89,233)( 90,234)( 91,235)( 92,236)( 93,237)( 94,238)( 95,239)
( 96,240)( 97,241)( 98,242)( 99,243)(100,244)(101,245)(102,246)(103,247)
(104,248)(105,249)(106,250)(107,251)(108,252)(109,253)(110,254)(111,255)
(112,256)(113,257)(114,258)(115,259)(116,260)(117,261)(118,262)(119,263)
(120,264)(121,265)(122,266)(123,267)(124,268)(125,269)(126,270)(127,271)
(128,272)(129,273)(130,274)(131,275)(132,276)(133,277)(134,278)(135,279)
(136,280)(137,281)(138,282)(139,283)(140,284)(141,285)(142,286)(143,287)
(144,288)(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)
(296,440)(297,441)(298,442)(299,443)(300,444)(301,445)(302,446)(303,447)
(304,448)(305,449)(306,450)(307,451)(308,452)(309,453)(310,454)(311,455)
(312,456)(313,457)(314,458)(315,459)(316,460)(317,461)(318,462)(319,463)
(320,464)(321,465)(322,466)(323,467)(324,468)(325,469)(326,470)(327,471)
(328,472)(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)
(336,480)(337,481)(338,482)(339,483)(340,484)(341,485)(342,486)(343,487)
(344,488)(345,489)(346,490)(347,491)(348,492)(349,493)(350,494)(351,495)
(352,496)(353,497)(354,498)(355,499)(356,500)(357,501)(358,502)(359,503)
(360,504)(361,505)(362,506)(363,507)(364,508)(365,509)(366,510)(367,511)
(368,512)(369,513)(370,514)(371,515)(372,516)(373,517)(374,518)(375,519)
(376,520)(377,521)(378,522)(379,523)(380,524)(381,525)(382,526)(383,527)
(384,528)(385,529)(386,530)(387,531)(388,532)(389,533)(390,534)(391,535)
(392,536)(393,537)(394,538)(395,539)(396,540)(397,541)(398,542)(399,543)
(400,544)(401,545)(402,546)(403,547)(404,548)(405,549)(406,550)(407,551)
(408,552)(409,553)(410,554)(411,555)(412,556)(413,557)(414,558)(415,559)
(416,560)(417,561)(418,562)(419,563)(420,564)(421,565)(422,566)(423,567)
(424,568)(425,569)(426,570)(427,571)(428,572)(429,573)(430,574)(431,575)
(432,576);
s1 := Sym(576)!(  1,109)(  2,116)(  3,114)(  4,115)(  5,113)(  6,111)(  7,112)
(  8,110)(  9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)
( 16,121)( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)
( 24,129)( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)
( 32,140)( 33,138)( 34,139)( 35,137)( 36,144)( 37, 82)( 38, 89)( 39, 87)
( 40, 88)( 41, 86)( 42, 84)( 43, 85)( 44, 83)( 45, 90)( 46, 73)( 47, 80)
( 48, 78)( 49, 79)( 50, 77)( 51, 75)( 52, 76)( 53, 74)( 54, 81)( 55,100)
( 56,107)( 57,105)( 58,106)( 59,104)( 60,102)( 61,103)( 62,101)( 63,108)
( 64, 91)( 65, 98)( 66, 96)( 67, 97)( 68, 95)( 69, 93)( 70, 94)( 71, 92)
( 72, 99)(145,271)(146,278)(147,276)(148,277)(149,275)(150,273)(151,274)
(152,272)(153,279)(154,280)(155,287)(156,285)(157,286)(158,284)(159,282)
(160,283)(161,281)(162,288)(163,253)(164,260)(165,258)(166,259)(167,257)
(168,255)(169,256)(170,254)(171,261)(172,262)(173,269)(174,267)(175,268)
(176,266)(177,264)(178,265)(179,263)(180,270)(181,244)(182,251)(183,249)
(184,250)(185,248)(186,246)(187,247)(188,245)(189,252)(190,235)(191,242)
(192,240)(193,241)(194,239)(195,237)(196,238)(197,236)(198,243)(199,226)
(200,233)(201,231)(202,232)(203,230)(204,228)(205,229)(206,227)(207,234)
(208,217)(209,224)(210,222)(211,223)(212,221)(213,219)(214,220)(215,218)
(216,225)(289,361)(290,368)(291,366)(292,367)(293,365)(294,363)(295,364)
(296,362)(297,369)(298,370)(299,377)(300,375)(301,376)(302,374)(303,372)
(304,373)(305,371)(306,378)(307,379)(308,386)(309,384)(310,385)(311,383)
(312,381)(313,382)(314,380)(315,387)(316,388)(317,395)(318,393)(319,394)
(320,392)(321,390)(322,391)(323,389)(324,396)(325,397)(326,404)(327,402)
(328,403)(329,401)(330,399)(331,400)(332,398)(333,405)(334,406)(335,413)
(336,411)(337,412)(338,410)(339,408)(340,409)(341,407)(342,414)(343,415)
(344,422)(345,420)(346,421)(347,419)(348,417)(349,418)(350,416)(351,423)
(352,424)(353,431)(354,429)(355,430)(356,428)(357,426)(358,427)(359,425)
(360,432)(433,523)(434,530)(435,528)(436,529)(437,527)(438,525)(439,526)
(440,524)(441,531)(442,532)(443,539)(444,537)(445,538)(446,536)(447,534)
(448,535)(449,533)(450,540)(451,505)(452,512)(453,510)(454,511)(455,509)
(456,507)(457,508)(458,506)(459,513)(460,514)(461,521)(462,519)(463,520)
(464,518)(465,516)(466,517)(467,515)(468,522)(469,559)(470,566)(471,564)
(472,565)(473,563)(474,561)(475,562)(476,560)(477,567)(478,568)(479,575)
(480,573)(481,574)(482,572)(483,570)(484,571)(485,569)(486,576)(487,541)
(488,548)(489,546)(490,547)(491,545)(492,543)(493,544)(494,542)(495,549)
(496,550)(497,557)(498,555)(499,556)(500,554)(501,552)(502,553)(503,551)
(504,558);
s2 := Sym(576)!(  1,292)(  2,294)(  3,293)(  4,289)(  5,291)(  6,290)(  7,295)
(  8,297)(  9,296)( 10,301)( 11,303)( 12,302)( 13,298)( 14,300)( 15,299)
( 16,304)( 17,306)( 18,305)( 19,310)( 20,312)( 21,311)( 22,307)( 23,309)
( 24,308)( 25,313)( 26,315)( 27,314)( 28,319)( 29,321)( 30,320)( 31,316)
( 32,318)( 33,317)( 34,322)( 35,324)( 36,323)( 37,337)( 38,339)( 39,338)
( 40,334)( 41,336)( 42,335)( 43,340)( 44,342)( 45,341)( 46,328)( 47,330)
( 48,329)( 49,325)( 50,327)( 51,326)( 52,331)( 53,333)( 54,332)( 55,355)
( 56,357)( 57,356)( 58,352)( 59,354)( 60,353)( 61,358)( 62,360)( 63,359)
( 64,346)( 65,348)( 66,347)( 67,343)( 68,345)( 69,344)( 70,349)( 71,351)
( 72,350)( 73,400)( 74,402)( 75,401)( 76,397)( 77,399)( 78,398)( 79,403)
( 80,405)( 81,404)( 82,409)( 83,411)( 84,410)( 85,406)( 86,408)( 87,407)
( 88,412)( 89,414)( 90,413)( 91,418)( 92,420)( 93,419)( 94,415)( 95,417)
( 96,416)( 97,421)( 98,423)( 99,422)(100,427)(101,429)(102,428)(103,424)
(104,426)(105,425)(106,430)(107,432)(108,431)(109,364)(110,366)(111,365)
(112,361)(113,363)(114,362)(115,367)(116,369)(117,368)(118,373)(119,375)
(120,374)(121,370)(122,372)(123,371)(124,376)(125,378)(126,377)(127,382)
(128,384)(129,383)(130,379)(131,381)(132,380)(133,385)(134,387)(135,386)
(136,391)(137,393)(138,392)(139,388)(140,390)(141,389)(142,394)(143,396)
(144,395)(145,436)(146,438)(147,437)(148,433)(149,435)(150,434)(151,439)
(152,441)(153,440)(154,445)(155,447)(156,446)(157,442)(158,444)(159,443)
(160,448)(161,450)(162,449)(163,454)(164,456)(165,455)(166,451)(167,453)
(168,452)(169,457)(170,459)(171,458)(172,463)(173,465)(174,464)(175,460)
(176,462)(177,461)(178,466)(179,468)(180,467)(181,481)(182,483)(183,482)
(184,478)(185,480)(186,479)(187,484)(188,486)(189,485)(190,472)(191,474)
(192,473)(193,469)(194,471)(195,470)(196,475)(197,477)(198,476)(199,499)
(200,501)(201,500)(202,496)(203,498)(204,497)(205,502)(206,504)(207,503)
(208,490)(209,492)(210,491)(211,487)(212,489)(213,488)(214,493)(215,495)
(216,494)(217,544)(218,546)(219,545)(220,541)(221,543)(222,542)(223,547)
(224,549)(225,548)(226,553)(227,555)(228,554)(229,550)(230,552)(231,551)
(232,556)(233,558)(234,557)(235,562)(236,564)(237,563)(238,559)(239,561)
(240,560)(241,565)(242,567)(243,566)(244,571)(245,573)(246,572)(247,568)
(248,570)(249,569)(250,574)(251,576)(252,575)(253,508)(254,510)(255,509)
(256,505)(257,507)(258,506)(259,511)(260,513)(261,512)(262,517)(263,519)
(264,518)(265,514)(266,516)(267,515)(268,520)(269,522)(270,521)(271,526)
(272,528)(273,527)(274,523)(275,525)(276,524)(277,529)(278,531)(279,530)
(280,535)(281,537)(282,536)(283,532)(284,534)(285,533)(286,538)(287,540)
(288,539);
s3 := Sym(576)!(  1, 77)(  2, 76)(  3, 78)(  4, 74)(  5, 73)(  6, 75)(  7, 80)
(  8, 79)(  9, 81)( 10, 86)( 11, 85)( 12, 87)( 13, 83)( 14, 82)( 15, 84)
( 16, 89)( 17, 88)( 18, 90)( 19, 95)( 20, 94)( 21, 96)( 22, 92)( 23, 91)
( 24, 93)( 25, 98)( 26, 97)( 27, 99)( 28,104)( 29,103)( 30,105)( 31,101)
( 32,100)( 33,102)( 34,107)( 35,106)( 36,108)( 37,122)( 38,121)( 39,123)
( 40,119)( 41,118)( 42,120)( 43,125)( 44,124)( 45,126)( 46,113)( 47,112)
( 48,114)( 49,110)( 50,109)( 51,111)( 52,116)( 53,115)( 54,117)( 55,140)
( 56,139)( 57,141)( 58,137)( 59,136)( 60,138)( 61,143)( 62,142)( 63,144)
( 64,131)( 65,130)( 66,132)( 67,128)( 68,127)( 69,129)( 70,134)( 71,133)
( 72,135)(145,221)(146,220)(147,222)(148,218)(149,217)(150,219)(151,224)
(152,223)(153,225)(154,230)(155,229)(156,231)(157,227)(158,226)(159,228)
(160,233)(161,232)(162,234)(163,239)(164,238)(165,240)(166,236)(167,235)
(168,237)(169,242)(170,241)(171,243)(172,248)(173,247)(174,249)(175,245)
(176,244)(177,246)(178,251)(179,250)(180,252)(181,266)(182,265)(183,267)
(184,263)(185,262)(186,264)(187,269)(188,268)(189,270)(190,257)(191,256)
(192,258)(193,254)(194,253)(195,255)(196,260)(197,259)(198,261)(199,284)
(200,283)(201,285)(202,281)(203,280)(204,282)(205,287)(206,286)(207,288)
(208,275)(209,274)(210,276)(211,272)(212,271)(213,273)(214,278)(215,277)
(216,279)(289,365)(290,364)(291,366)(292,362)(293,361)(294,363)(295,368)
(296,367)(297,369)(298,374)(299,373)(300,375)(301,371)(302,370)(303,372)
(304,377)(305,376)(306,378)(307,383)(308,382)(309,384)(310,380)(311,379)
(312,381)(313,386)(314,385)(315,387)(316,392)(317,391)(318,393)(319,389)
(320,388)(321,390)(322,395)(323,394)(324,396)(325,410)(326,409)(327,411)
(328,407)(329,406)(330,408)(331,413)(332,412)(333,414)(334,401)(335,400)
(336,402)(337,398)(338,397)(339,399)(340,404)(341,403)(342,405)(343,428)
(344,427)(345,429)(346,425)(347,424)(348,426)(349,431)(350,430)(351,432)
(352,419)(353,418)(354,420)(355,416)(356,415)(357,417)(358,422)(359,421)
(360,423)(433,509)(434,508)(435,510)(436,506)(437,505)(438,507)(439,512)
(440,511)(441,513)(442,518)(443,517)(444,519)(445,515)(446,514)(447,516)
(448,521)(449,520)(450,522)(451,527)(452,526)(453,528)(454,524)(455,523)
(456,525)(457,530)(458,529)(459,531)(460,536)(461,535)(462,537)(463,533)
(464,532)(465,534)(466,539)(467,538)(468,540)(469,554)(470,553)(471,555)
(472,551)(473,550)(474,552)(475,557)(476,556)(477,558)(478,545)(479,544)
(480,546)(481,542)(482,541)(483,543)(484,548)(485,547)(486,549)(487,572)
(488,571)(489,573)(490,569)(491,568)(492,570)(493,575)(494,574)(495,576)
(496,563)(497,562)(498,564)(499,560)(500,559)(501,561)(502,566)(503,565)
(504,567);
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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope