Polytope of Type {24,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6,4}*1152b
Also Known As : {{24,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1152,119763)
Rank : 4
Schlafli Type : {24,6,4}
Number of vertices, edges, etc : 24, 72, 12, 4
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}*576a, {24,6,2}*576a
3-fold quotients : {24,2,4}*384, {8,6,4}*384a
4-fold quotients : {12,6,2}*288a, {6,6,4}*288a
6-fold quotients : {12,2,4}*192, {4,6,4}*192a, {24,2,2}*192, {8,6,2}*192
8-fold quotients : {6,6,2}*144a
9-fold quotients : {8,2,4}*128
12-fold quotients : {12,2,2}*96, {2,6,4}*96a, {4,6,2}*96a, {6,2,4}*96
18-fold quotients : {4,2,4}*64, {8,2,2}*64
24-fold quotients : {3,2,4}*48, {2,6,2}*48, {6,2,2}*48
36-fold quotients : {2,2,4}*32, {4,2,2}*32
48-fold quotients : {2,3,2}*24, {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, 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);;
s1 := ( 1,290)( 2,289)( 3,291)( 4,296)( 5,295)( 6,297)( 7,293)( 8,292)
( 9,294)( 10,299)( 11,298)( 12,300)( 13,305)( 14,304)( 15,306)( 16,302)
( 17,301)( 18,303)( 19,308)( 20,307)( 21,309)( 22,314)( 23,313)( 24,315)
( 25,311)( 26,310)( 27,312)( 28,317)( 29,316)( 30,318)( 31,323)( 32,322)
( 33,324)( 34,320)( 35,319)( 36,321)( 37,335)( 38,334)( 39,336)( 40,341)
( 41,340)( 42,342)( 43,338)( 44,337)( 45,339)( 46,326)( 47,325)( 48,327)
( 49,332)( 50,331)( 51,333)( 52,329)( 53,328)( 54,330)( 55,353)( 56,352)
( 57,354)( 58,359)( 59,358)( 60,360)( 61,356)( 62,355)( 63,357)( 64,344)
( 65,343)( 66,345)( 67,350)( 68,349)( 69,351)( 70,347)( 71,346)( 72,348)
( 73,398)( 74,397)( 75,399)( 76,404)( 77,403)( 78,405)( 79,401)( 80,400)
( 81,402)( 82,407)( 83,406)( 84,408)( 85,413)( 86,412)( 87,414)( 88,410)
( 89,409)( 90,411)( 91,416)( 92,415)( 93,417)( 94,422)( 95,421)( 96,423)
( 97,419)( 98,418)( 99,420)(100,425)(101,424)(102,426)(103,431)(104,430)
(105,432)(106,428)(107,427)(108,429)(109,362)(110,361)(111,363)(112,368)
(113,367)(114,369)(115,365)(116,364)(117,366)(118,371)(119,370)(120,372)
(121,377)(122,376)(123,378)(124,374)(125,373)(126,375)(127,380)(128,379)
(129,381)(130,386)(131,385)(132,387)(133,383)(134,382)(135,384)(136,389)
(137,388)(138,390)(139,395)(140,394)(141,396)(142,392)(143,391)(144,393)
(145,434)(146,433)(147,435)(148,440)(149,439)(150,441)(151,437)(152,436)
(153,438)(154,443)(155,442)(156,444)(157,449)(158,448)(159,450)(160,446)
(161,445)(162,447)(163,452)(164,451)(165,453)(166,458)(167,457)(168,459)
(169,455)(170,454)(171,456)(172,461)(173,460)(174,462)(175,467)(176,466)
(177,468)(178,464)(179,463)(180,465)(181,479)(182,478)(183,480)(184,485)
(185,484)(186,486)(187,482)(188,481)(189,483)(190,470)(191,469)(192,471)
(193,476)(194,475)(195,477)(196,473)(197,472)(198,474)(199,497)(200,496)
(201,498)(202,503)(203,502)(204,504)(205,500)(206,499)(207,501)(208,488)
(209,487)(210,489)(211,494)(212,493)(213,495)(214,491)(215,490)(216,492)
(217,542)(218,541)(219,543)(220,548)(221,547)(222,549)(223,545)(224,544)
(225,546)(226,551)(227,550)(228,552)(229,557)(230,556)(231,558)(232,554)
(233,553)(234,555)(235,560)(236,559)(237,561)(238,566)(239,565)(240,567)
(241,563)(242,562)(243,564)(244,569)(245,568)(246,570)(247,575)(248,574)
(249,576)(250,572)(251,571)(252,573)(253,506)(254,505)(255,507)(256,512)
(257,511)(258,513)(259,509)(260,508)(261,510)(262,515)(263,514)(264,516)
(265,521)(266,520)(267,522)(268,518)(269,517)(270,519)(271,524)(272,523)
(273,525)(274,530)(275,529)(276,531)(277,527)(278,526)(279,528)(280,533)
(281,532)(282,534)(283,539)(284,538)(285,540)(286,536)(287,535)(288,537);;
s2 := ( 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);;
s3 := ( 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);;
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,
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*s0*s1*s0*s1*s0*s1*s0*s1*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, 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);
s1 := Sym(576)!( 1,290)( 2,289)( 3,291)( 4,296)( 5,295)( 6,297)( 7,293)
( 8,292)( 9,294)( 10,299)( 11,298)( 12,300)( 13,305)( 14,304)( 15,306)
( 16,302)( 17,301)( 18,303)( 19,308)( 20,307)( 21,309)( 22,314)( 23,313)
( 24,315)( 25,311)( 26,310)( 27,312)( 28,317)( 29,316)( 30,318)( 31,323)
( 32,322)( 33,324)( 34,320)( 35,319)( 36,321)( 37,335)( 38,334)( 39,336)
( 40,341)( 41,340)( 42,342)( 43,338)( 44,337)( 45,339)( 46,326)( 47,325)
( 48,327)( 49,332)( 50,331)( 51,333)( 52,329)( 53,328)( 54,330)( 55,353)
( 56,352)( 57,354)( 58,359)( 59,358)( 60,360)( 61,356)( 62,355)( 63,357)
( 64,344)( 65,343)( 66,345)( 67,350)( 68,349)( 69,351)( 70,347)( 71,346)
( 72,348)( 73,398)( 74,397)( 75,399)( 76,404)( 77,403)( 78,405)( 79,401)
( 80,400)( 81,402)( 82,407)( 83,406)( 84,408)( 85,413)( 86,412)( 87,414)
( 88,410)( 89,409)( 90,411)( 91,416)( 92,415)( 93,417)( 94,422)( 95,421)
( 96,423)( 97,419)( 98,418)( 99,420)(100,425)(101,424)(102,426)(103,431)
(104,430)(105,432)(106,428)(107,427)(108,429)(109,362)(110,361)(111,363)
(112,368)(113,367)(114,369)(115,365)(116,364)(117,366)(118,371)(119,370)
(120,372)(121,377)(122,376)(123,378)(124,374)(125,373)(126,375)(127,380)
(128,379)(129,381)(130,386)(131,385)(132,387)(133,383)(134,382)(135,384)
(136,389)(137,388)(138,390)(139,395)(140,394)(141,396)(142,392)(143,391)
(144,393)(145,434)(146,433)(147,435)(148,440)(149,439)(150,441)(151,437)
(152,436)(153,438)(154,443)(155,442)(156,444)(157,449)(158,448)(159,450)
(160,446)(161,445)(162,447)(163,452)(164,451)(165,453)(166,458)(167,457)
(168,459)(169,455)(170,454)(171,456)(172,461)(173,460)(174,462)(175,467)
(176,466)(177,468)(178,464)(179,463)(180,465)(181,479)(182,478)(183,480)
(184,485)(185,484)(186,486)(187,482)(188,481)(189,483)(190,470)(191,469)
(192,471)(193,476)(194,475)(195,477)(196,473)(197,472)(198,474)(199,497)
(200,496)(201,498)(202,503)(203,502)(204,504)(205,500)(206,499)(207,501)
(208,488)(209,487)(210,489)(211,494)(212,493)(213,495)(214,491)(215,490)
(216,492)(217,542)(218,541)(219,543)(220,548)(221,547)(222,549)(223,545)
(224,544)(225,546)(226,551)(227,550)(228,552)(229,557)(230,556)(231,558)
(232,554)(233,553)(234,555)(235,560)(236,559)(237,561)(238,566)(239,565)
(240,567)(241,563)(242,562)(243,564)(244,569)(245,568)(246,570)(247,575)
(248,574)(249,576)(250,572)(251,571)(252,573)(253,506)(254,505)(255,507)
(256,512)(257,511)(258,513)(259,509)(260,508)(261,510)(262,515)(263,514)
(264,516)(265,521)(266,520)(267,522)(268,518)(269,517)(270,519)(271,524)
(272,523)(273,525)(274,530)(275,529)(276,531)(277,527)(278,526)(279,528)
(280,533)(281,532)(282,534)(283,539)(284,538)(285,540)(286,536)(287,535)
(288,537);
s2 := 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);
s3 := 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);
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, 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*s0*s1*s0*s1*s0*s1*s0*s1*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