Polytope of Type {6,12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,8}*1152c
if this polytope has a name.
Group : SmallGroup(1152,97536)
Rank : 4
Schlafli Type : {6,12,8}
Number of vertices, edges, etc : 6, 36, 48, 8
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,6,8}*576c, {6,12,4}*576c
3-fold quotients : {6,4,8}*384a
4-fold quotients : {3,6,8}*288, {6,6,4}*288c, {6,12,2}*288c
6-fold quotients : {6,4,4}*192, {6,2,8}*192
8-fold quotients : {3,6,4}*144, {6,6,2}*144c
9-fold quotients : {2,4,8}*128a
12-fold quotients : {3,2,8}*96, {6,2,4}*96, {6,4,2}*96a
16-fold quotients : {3,6,2}*72
18-fold quotients : {2,4,4}*64, {2,2,8}*64
24-fold quotients : {3,2,4}*48, {6,2,2}*48
36-fold quotients : {2,2,4}*32, {2,4,2}*32
48-fold quotients : {3,2,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 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)( 37,109)( 38,111)( 39,110)( 40,115)
( 41,117)( 42,116)( 43,112)( 44,114)( 45,113)( 46,118)( 47,120)( 48,119)
( 49,124)( 50,126)( 51,125)( 52,121)( 53,123)( 54,122)( 55,127)( 56,129)
( 57,128)( 58,133)( 59,135)( 60,134)( 61,130)( 62,132)( 63,131)( 64,136)
( 65,138)( 66,137)( 67,142)( 68,144)( 69,143)( 70,139)( 71,141)( 72,140)
(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)(181,253)(182,255)(183,254)(184,259)
(185,261)(186,260)(187,256)(188,258)(189,257)(190,262)(191,264)(192,263)
(193,268)(194,270)(195,269)(196,265)(197,267)(198,266)(199,271)(200,273)
(201,272)(202,277)(203,279)(204,278)(205,274)(206,276)(207,275)(208,280)
(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)(216,284)
(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)(325,397)(326,399)(327,398)(328,403)
(329,405)(330,404)(331,400)(332,402)(333,401)(334,406)(335,408)(336,407)
(337,412)(338,414)(339,413)(340,409)(341,411)(342,410)(343,415)(344,417)
(345,416)(346,421)(347,423)(348,422)(349,418)(350,420)(351,419)(352,424)
(353,426)(354,425)(355,430)(356,432)(357,431)(358,427)(359,429)(360,428)
(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)(469,541)(470,543)(471,542)(472,547)
(473,549)(474,548)(475,544)(476,546)(477,545)(478,550)(479,552)(480,551)
(481,556)(482,558)(483,557)(484,553)(485,555)(486,554)(487,559)(488,561)
(489,560)(490,565)(491,567)(492,566)(493,562)(494,564)(495,563)(496,568)
(497,570)(498,569)(499,574)(500,576)(501,575)(502,571)(503,573)(504,572);;
s1 := ( 1,218)( 2,217)( 3,219)( 4,224)( 5,223)( 6,225)( 7,221)( 8,220)
( 9,222)( 10,227)( 11,226)( 12,228)( 13,233)( 14,232)( 15,234)( 16,230)
( 17,229)( 18,231)( 19,236)( 20,235)( 21,237)( 22,242)( 23,241)( 24,243)
( 25,239)( 26,238)( 27,240)( 28,245)( 29,244)( 30,246)( 31,251)( 32,250)
( 33,252)( 34,248)( 35,247)( 36,249)( 37,254)( 38,253)( 39,255)( 40,260)
( 41,259)( 42,261)( 43,257)( 44,256)( 45,258)( 46,263)( 47,262)( 48,264)
( 49,269)( 50,268)( 51,270)( 52,266)( 53,265)( 54,267)( 55,272)( 56,271)
( 57,273)( 58,278)( 59,277)( 60,279)( 61,275)( 62,274)( 63,276)( 64,281)
( 65,280)( 66,282)( 67,287)( 68,286)( 69,288)( 70,284)( 71,283)( 72,285)
( 73,146)( 74,145)( 75,147)( 76,152)( 77,151)( 78,153)( 79,149)( 80,148)
( 81,150)( 82,155)( 83,154)( 84,156)( 85,161)( 86,160)( 87,162)( 88,158)
( 89,157)( 90,159)( 91,164)( 92,163)( 93,165)( 94,170)( 95,169)( 96,171)
( 97,167)( 98,166)( 99,168)(100,173)(101,172)(102,174)(103,179)(104,178)
(105,180)(106,176)(107,175)(108,177)(109,182)(110,181)(111,183)(112,188)
(113,187)(114,189)(115,185)(116,184)(117,186)(118,191)(119,190)(120,192)
(121,197)(122,196)(123,198)(124,194)(125,193)(126,195)(127,200)(128,199)
(129,201)(130,206)(131,205)(132,207)(133,203)(134,202)(135,204)(136,209)
(137,208)(138,210)(139,215)(140,214)(141,216)(142,212)(143,211)(144,213)
(289,506)(290,505)(291,507)(292,512)(293,511)(294,513)(295,509)(296,508)
(297,510)(298,515)(299,514)(300,516)(301,521)(302,520)(303,522)(304,518)
(305,517)(306,519)(307,524)(308,523)(309,525)(310,530)(311,529)(312,531)
(313,527)(314,526)(315,528)(316,533)(317,532)(318,534)(319,539)(320,538)
(321,540)(322,536)(323,535)(324,537)(325,542)(326,541)(327,543)(328,548)
(329,547)(330,549)(331,545)(332,544)(333,546)(334,551)(335,550)(336,552)
(337,557)(338,556)(339,558)(340,554)(341,553)(342,555)(343,560)(344,559)
(345,561)(346,566)(347,565)(348,567)(349,563)(350,562)(351,564)(352,569)
(353,568)(354,570)(355,575)(356,574)(357,576)(358,572)(359,571)(360,573)
(361,434)(362,433)(363,435)(364,440)(365,439)(366,441)(367,437)(368,436)
(369,438)(370,443)(371,442)(372,444)(373,449)(374,448)(375,450)(376,446)
(377,445)(378,447)(379,452)(380,451)(381,453)(382,458)(383,457)(384,459)
(385,455)(386,454)(387,456)(388,461)(389,460)(390,462)(391,467)(392,466)
(393,468)(394,464)(395,463)(396,465)(397,470)(398,469)(399,471)(400,476)
(401,475)(402,477)(403,473)(404,472)(405,474)(406,479)(407,478)(408,480)
(409,485)(410,484)(411,486)(412,482)(413,481)(414,483)(415,488)(416,487)
(417,489)(418,494)(419,493)(420,495)(421,491)(422,490)(423,492)(424,497)
(425,496)(426,498)(427,503)(428,502)(429,504)(430,500)(431,499)(432,501);;
s2 := ( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)( 21, 26)
( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 37, 46)( 38, 51)( 39, 53)( 40, 49)
( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)( 57, 71)
( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 74, 78)( 75, 80)
( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)(101,105)
(102,107)(104,108)(109,118)(110,123)(111,125)(112,121)(113,126)(114,119)
(115,124)(116,120)(117,122)(127,136)(128,141)(129,143)(130,139)(131,144)
(132,137)(133,142)(134,138)(135,140)(145,163)(146,168)(147,170)(148,166)
(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)(156,179)
(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,208)(182,213)
(183,215)(184,211)(185,216)(186,209)(187,214)(188,210)(189,212)(190,199)
(191,204)(192,206)(193,202)(194,207)(195,200)(196,205)(197,201)(198,203)
(217,235)(218,240)(219,242)(220,238)(221,243)(222,236)(223,241)(224,237)
(225,239)(226,244)(227,249)(228,251)(229,247)(230,252)(231,245)(232,250)
(233,246)(234,248)(253,280)(254,285)(255,287)(256,283)(257,288)(258,281)
(259,286)(260,282)(261,284)(262,271)(263,276)(264,278)(265,274)(266,279)
(267,272)(268,277)(269,273)(270,275)(289,325)(290,330)(291,332)(292,328)
(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)(300,341)
(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)(308,348)
(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)(316,352)
(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)(324,356)
(361,397)(362,402)(363,404)(364,400)(365,405)(366,398)(367,403)(368,399)
(369,401)(370,406)(371,411)(372,413)(373,409)(374,414)(375,407)(376,412)
(377,408)(378,410)(379,415)(380,420)(381,422)(382,418)(383,423)(384,416)
(385,421)(386,417)(387,419)(388,424)(389,429)(390,431)(391,427)(392,432)
(393,425)(394,430)(395,426)(396,428)(433,487)(434,492)(435,494)(436,490)
(437,495)(438,488)(439,493)(440,489)(441,491)(442,496)(443,501)(444,503)
(445,499)(446,504)(447,497)(448,502)(449,498)(450,500)(451,469)(452,474)
(453,476)(454,472)(455,477)(456,470)(457,475)(458,471)(459,473)(460,478)
(461,483)(462,485)(463,481)(464,486)(465,479)(466,484)(467,480)(468,482)
(505,559)(506,564)(507,566)(508,562)(509,567)(510,560)(511,565)(512,561)
(513,563)(514,568)(515,573)(516,575)(517,571)(518,576)(519,569)(520,574)
(521,570)(522,572)(523,541)(524,546)(525,548)(526,544)(527,549)(528,542)
(529,547)(530,543)(531,545)(532,550)(533,555)(534,557)(535,553)(536,558)
(537,551)(538,556)(539,552)(540,554);;
s3 := ( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)( 8,296)
( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)
( 17,305)( 18,306)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)( 24,312)
( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)
( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)( 40,337)
( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)
( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,352)( 56,353)
( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)( 64,343)
( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)( 72,351)
( 73,361)( 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);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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, 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)( 37,109)( 38,111)( 39,110)
( 40,115)( 41,117)( 42,116)( 43,112)( 44,114)( 45,113)( 46,118)( 47,120)
( 48,119)( 49,124)( 50,126)( 51,125)( 52,121)( 53,123)( 54,122)( 55,127)
( 56,129)( 57,128)( 58,133)( 59,135)( 60,134)( 61,130)( 62,132)( 63,131)
( 64,136)( 65,138)( 66,137)( 67,142)( 68,144)( 69,143)( 70,139)( 71,141)
( 72,140)(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)(181,253)(182,255)(183,254)
(184,259)(185,261)(186,260)(187,256)(188,258)(189,257)(190,262)(191,264)
(192,263)(193,268)(194,270)(195,269)(196,265)(197,267)(198,266)(199,271)
(200,273)(201,272)(202,277)(203,279)(204,278)(205,274)(206,276)(207,275)
(208,280)(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)
(216,284)(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)(325,397)(326,399)(327,398)
(328,403)(329,405)(330,404)(331,400)(332,402)(333,401)(334,406)(335,408)
(336,407)(337,412)(338,414)(339,413)(340,409)(341,411)(342,410)(343,415)
(344,417)(345,416)(346,421)(347,423)(348,422)(349,418)(350,420)(351,419)
(352,424)(353,426)(354,425)(355,430)(356,432)(357,431)(358,427)(359,429)
(360,428)(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)(469,541)(470,543)(471,542)
(472,547)(473,549)(474,548)(475,544)(476,546)(477,545)(478,550)(479,552)
(480,551)(481,556)(482,558)(483,557)(484,553)(485,555)(486,554)(487,559)
(488,561)(489,560)(490,565)(491,567)(492,566)(493,562)(494,564)(495,563)
(496,568)(497,570)(498,569)(499,574)(500,576)(501,575)(502,571)(503,573)
(504,572);
s1 := Sym(576)!( 1,218)( 2,217)( 3,219)( 4,224)( 5,223)( 6,225)( 7,221)
( 8,220)( 9,222)( 10,227)( 11,226)( 12,228)( 13,233)( 14,232)( 15,234)
( 16,230)( 17,229)( 18,231)( 19,236)( 20,235)( 21,237)( 22,242)( 23,241)
( 24,243)( 25,239)( 26,238)( 27,240)( 28,245)( 29,244)( 30,246)( 31,251)
( 32,250)( 33,252)( 34,248)( 35,247)( 36,249)( 37,254)( 38,253)( 39,255)
( 40,260)( 41,259)( 42,261)( 43,257)( 44,256)( 45,258)( 46,263)( 47,262)
( 48,264)( 49,269)( 50,268)( 51,270)( 52,266)( 53,265)( 54,267)( 55,272)
( 56,271)( 57,273)( 58,278)( 59,277)( 60,279)( 61,275)( 62,274)( 63,276)
( 64,281)( 65,280)( 66,282)( 67,287)( 68,286)( 69,288)( 70,284)( 71,283)
( 72,285)( 73,146)( 74,145)( 75,147)( 76,152)( 77,151)( 78,153)( 79,149)
( 80,148)( 81,150)( 82,155)( 83,154)( 84,156)( 85,161)( 86,160)( 87,162)
( 88,158)( 89,157)( 90,159)( 91,164)( 92,163)( 93,165)( 94,170)( 95,169)
( 96,171)( 97,167)( 98,166)( 99,168)(100,173)(101,172)(102,174)(103,179)
(104,178)(105,180)(106,176)(107,175)(108,177)(109,182)(110,181)(111,183)
(112,188)(113,187)(114,189)(115,185)(116,184)(117,186)(118,191)(119,190)
(120,192)(121,197)(122,196)(123,198)(124,194)(125,193)(126,195)(127,200)
(128,199)(129,201)(130,206)(131,205)(132,207)(133,203)(134,202)(135,204)
(136,209)(137,208)(138,210)(139,215)(140,214)(141,216)(142,212)(143,211)
(144,213)(289,506)(290,505)(291,507)(292,512)(293,511)(294,513)(295,509)
(296,508)(297,510)(298,515)(299,514)(300,516)(301,521)(302,520)(303,522)
(304,518)(305,517)(306,519)(307,524)(308,523)(309,525)(310,530)(311,529)
(312,531)(313,527)(314,526)(315,528)(316,533)(317,532)(318,534)(319,539)
(320,538)(321,540)(322,536)(323,535)(324,537)(325,542)(326,541)(327,543)
(328,548)(329,547)(330,549)(331,545)(332,544)(333,546)(334,551)(335,550)
(336,552)(337,557)(338,556)(339,558)(340,554)(341,553)(342,555)(343,560)
(344,559)(345,561)(346,566)(347,565)(348,567)(349,563)(350,562)(351,564)
(352,569)(353,568)(354,570)(355,575)(356,574)(357,576)(358,572)(359,571)
(360,573)(361,434)(362,433)(363,435)(364,440)(365,439)(366,441)(367,437)
(368,436)(369,438)(370,443)(371,442)(372,444)(373,449)(374,448)(375,450)
(376,446)(377,445)(378,447)(379,452)(380,451)(381,453)(382,458)(383,457)
(384,459)(385,455)(386,454)(387,456)(388,461)(389,460)(390,462)(391,467)
(392,466)(393,468)(394,464)(395,463)(396,465)(397,470)(398,469)(399,471)
(400,476)(401,475)(402,477)(403,473)(404,472)(405,474)(406,479)(407,478)
(408,480)(409,485)(410,484)(411,486)(412,482)(413,481)(414,483)(415,488)
(416,487)(417,489)(418,494)(419,493)(420,495)(421,491)(422,490)(423,492)
(424,497)(425,496)(426,498)(427,503)(428,502)(429,504)(430,500)(431,499)
(432,501);
s2 := Sym(576)!( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)
( 21, 26)( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 37, 46)( 38, 51)( 39, 53)
( 40, 49)( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)
( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 74, 78)
( 75, 80)( 77, 81)( 83, 87)( 84, 89)( 86, 90)( 92, 96)( 93, 98)( 95, 99)
(101,105)(102,107)(104,108)(109,118)(110,123)(111,125)(112,121)(113,126)
(114,119)(115,124)(116,120)(117,122)(127,136)(128,141)(129,143)(130,139)
(131,144)(132,137)(133,142)(134,138)(135,140)(145,163)(146,168)(147,170)
(148,166)(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)
(156,179)(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,208)
(182,213)(183,215)(184,211)(185,216)(186,209)(187,214)(188,210)(189,212)
(190,199)(191,204)(192,206)(193,202)(194,207)(195,200)(196,205)(197,201)
(198,203)(217,235)(218,240)(219,242)(220,238)(221,243)(222,236)(223,241)
(224,237)(225,239)(226,244)(227,249)(228,251)(229,247)(230,252)(231,245)
(232,250)(233,246)(234,248)(253,280)(254,285)(255,287)(256,283)(257,288)
(258,281)(259,286)(260,282)(261,284)(262,271)(263,276)(264,278)(265,274)
(266,279)(267,272)(268,277)(269,273)(270,275)(289,325)(290,330)(291,332)
(292,328)(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)
(300,341)(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)
(308,348)(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)
(316,352)(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)
(324,356)(361,397)(362,402)(363,404)(364,400)(365,405)(366,398)(367,403)
(368,399)(369,401)(370,406)(371,411)(372,413)(373,409)(374,414)(375,407)
(376,412)(377,408)(378,410)(379,415)(380,420)(381,422)(382,418)(383,423)
(384,416)(385,421)(386,417)(387,419)(388,424)(389,429)(390,431)(391,427)
(392,432)(393,425)(394,430)(395,426)(396,428)(433,487)(434,492)(435,494)
(436,490)(437,495)(438,488)(439,493)(440,489)(441,491)(442,496)(443,501)
(444,503)(445,499)(446,504)(447,497)(448,502)(449,498)(450,500)(451,469)
(452,474)(453,476)(454,472)(455,477)(456,470)(457,475)(458,471)(459,473)
(460,478)(461,483)(462,485)(463,481)(464,486)(465,479)(466,484)(467,480)
(468,482)(505,559)(506,564)(507,566)(508,562)(509,567)(510,560)(511,565)
(512,561)(513,563)(514,568)(515,573)(516,575)(517,571)(518,576)(519,569)
(520,574)(521,570)(522,572)(523,541)(524,546)(525,548)(526,544)(527,549)
(528,542)(529,547)(530,543)(531,545)(532,550)(533,555)(534,557)(535,553)
(536,558)(537,551)(538,556)(539,552)(540,554);
s3 := Sym(576)!( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)
( 8,296)( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)
( 16,304)( 17,305)( 18,306)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)
( 24,312)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)
( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)
( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)
( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,352)
( 56,353)( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)
( 64,343)( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)
( 72,351)( 73,361)( 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);
poly := sub<Sym(576)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope