Polytope of Type {6,12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,8}*1152d
if this polytope has a name.
Group : SmallGroup(1152,98785)
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 : {6,12,4}*576b
3-fold quotients : {2,12,8}*384b
4-fold quotients : {6,12,2}*288b, {6,6,4}*288b
6-fold quotients : {2,12,4}*192a
8-fold quotients : {6,6,2}*144b
9-fold quotients : {2,4,8}*128b
12-fold quotients : {2,12,2}*96, {2,6,4}*96a
16-fold quotients : {6,3,2}*72
18-fold quotients : {2,4,4}*64
24-fold quotients : {2,6,2}*48
36-fold quotients : {2,2,4}*32, {2,4,2}*32
48-fold quotients : {2,3,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 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)( 37,109)( 38,114)( 39,116)( 40,112)
( 41,117)( 42,110)( 43,115)( 44,111)( 45,113)( 46,118)( 47,123)( 48,125)
( 49,121)( 50,126)( 51,119)( 52,124)( 53,120)( 54,122)( 55,127)( 56,132)
( 57,134)( 58,130)( 59,135)( 60,128)( 61,133)( 62,129)( 63,131)( 64,136)
( 65,141)( 66,143)( 67,139)( 68,144)( 69,137)( 70,142)( 71,138)( 72,140)
(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)(181,253)(182,258)(183,260)(184,256)
(185,261)(186,254)(187,259)(188,255)(189,257)(190,262)(191,267)(192,269)
(193,265)(194,270)(195,263)(196,268)(197,264)(198,266)(199,271)(200,276)
(201,278)(202,274)(203,279)(204,272)(205,277)(206,273)(207,275)(208,280)
(209,285)(210,287)(211,283)(212,288)(213,281)(214,286)(215,282)(216,284)
(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)(325,397)(326,402)(327,404)(328,400)
(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)(335,411)(336,413)
(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)(343,415)(344,420)
(345,422)(346,418)(347,423)(348,416)(349,421)(350,417)(351,419)(352,424)
(353,429)(354,431)(355,427)(356,432)(357,425)(358,430)(359,426)(360,428)
(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)(469,541)(470,546)(471,548)(472,544)
(473,549)(474,542)(475,547)(476,543)(477,545)(478,550)(479,555)(480,557)
(481,553)(482,558)(483,551)(484,556)(485,552)(486,554)(487,559)(488,564)
(489,566)(490,562)(491,567)(492,560)(493,565)(494,561)(495,563)(496,568)
(497,573)(498,575)(499,571)(500,576)(501,569)(502,574)(503,570)(504,572);;
s1 := ( 1,146)( 2,145)( 3,147)( 4,152)( 5,151)( 6,153)( 7,149)( 8,148)
( 9,150)( 10,155)( 11,154)( 12,156)( 13,161)( 14,160)( 15,162)( 16,158)
( 17,157)( 18,159)( 19,164)( 20,163)( 21,165)( 22,170)( 23,169)( 24,171)
( 25,167)( 26,166)( 27,168)( 28,173)( 29,172)( 30,174)( 31,179)( 32,178)
( 33,180)( 34,176)( 35,175)( 36,177)( 37,191)( 38,190)( 39,192)( 40,197)
( 41,196)( 42,198)( 43,194)( 44,193)( 45,195)( 46,182)( 47,181)( 48,183)
( 49,188)( 50,187)( 51,189)( 52,185)( 53,184)( 54,186)( 55,209)( 56,208)
( 57,210)( 58,215)( 59,214)( 60,216)( 61,212)( 62,211)( 63,213)( 64,200)
( 65,199)( 66,201)( 67,206)( 68,205)( 69,207)( 70,203)( 71,202)( 72,204)
( 73,218)( 74,217)( 75,219)( 76,224)( 77,223)( 78,225)( 79,221)( 80,220)
( 81,222)( 82,227)( 83,226)( 84,228)( 85,233)( 86,232)( 87,234)( 88,230)
( 89,229)( 90,231)( 91,236)( 92,235)( 93,237)( 94,242)( 95,241)( 96,243)
( 97,239)( 98,238)( 99,240)(100,245)(101,244)(102,246)(103,251)(104,250)
(105,252)(106,248)(107,247)(108,249)(109,263)(110,262)(111,264)(112,269)
(113,268)(114,270)(115,266)(116,265)(117,267)(118,254)(119,253)(120,255)
(121,260)(122,259)(123,261)(124,257)(125,256)(126,258)(127,281)(128,280)
(129,282)(130,287)(131,286)(132,288)(133,284)(134,283)(135,285)(136,272)
(137,271)(138,273)(139,278)(140,277)(141,279)(142,275)(143,274)(144,276)
(289,434)(290,433)(291,435)(292,440)(293,439)(294,441)(295,437)(296,436)
(297,438)(298,443)(299,442)(300,444)(301,449)(302,448)(303,450)(304,446)
(305,445)(306,447)(307,452)(308,451)(309,453)(310,458)(311,457)(312,459)
(313,455)(314,454)(315,456)(316,461)(317,460)(318,462)(319,467)(320,466)
(321,468)(322,464)(323,463)(324,465)(325,479)(326,478)(327,480)(328,485)
(329,484)(330,486)(331,482)(332,481)(333,483)(334,470)(335,469)(336,471)
(337,476)(338,475)(339,477)(340,473)(341,472)(342,474)(343,497)(344,496)
(345,498)(346,503)(347,502)(348,504)(349,500)(350,499)(351,501)(352,488)
(353,487)(354,489)(355,494)(356,493)(357,495)(358,491)(359,490)(360,492)
(361,506)(362,505)(363,507)(364,512)(365,511)(366,513)(367,509)(368,508)
(369,510)(370,515)(371,514)(372,516)(373,521)(374,520)(375,522)(376,518)
(377,517)(378,519)(379,524)(380,523)(381,525)(382,530)(383,529)(384,531)
(385,527)(386,526)(387,528)(388,533)(389,532)(390,534)(391,539)(392,538)
(393,540)(394,536)(395,535)(396,537)(397,551)(398,550)(399,552)(400,557)
(401,556)(402,558)(403,554)(404,553)(405,555)(406,542)(407,541)(408,543)
(409,548)(410,547)(411,549)(412,545)(413,544)(414,546)(415,569)(416,568)
(417,570)(418,575)(419,574)(420,576)(421,572)(422,571)(423,573)(424,560)
(425,559)(426,561)(427,566)(428,565)(429,567)(430,563)(431,562)(432,564);;
s2 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)
( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)( 43, 49)( 44, 51)
( 45, 50)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)( 60, 71)( 61, 67)
( 62, 69)( 63, 68)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)( 85, 88)
( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)
(104,108)(105,107)(109,118)(110,120)(111,119)(112,124)(113,126)(114,125)
(115,121)(116,123)(117,122)(127,136)(128,138)(129,137)(130,142)(131,144)
(132,143)(133,139)(134,141)(135,140)(145,163)(146,165)(147,164)(148,169)
(149,171)(150,170)(151,166)(152,168)(153,167)(154,172)(155,174)(156,173)
(157,178)(158,180)(159,179)(160,175)(161,177)(162,176)(181,208)(182,210)
(183,209)(184,214)(185,216)(186,215)(187,211)(188,213)(189,212)(190,199)
(191,201)(192,200)(193,205)(194,207)(195,206)(196,202)(197,204)(198,203)
(217,235)(218,237)(219,236)(220,241)(221,243)(222,242)(223,238)(224,240)
(225,239)(226,244)(227,246)(228,245)(229,250)(230,252)(231,251)(232,247)
(233,249)(234,248)(253,280)(254,282)(255,281)(256,286)(257,288)(258,287)
(259,283)(260,285)(261,284)(262,271)(263,273)(264,272)(265,277)(266,279)
(267,278)(268,274)(269,276)(270,275)(289,325)(290,327)(291,326)(292,331)
(293,333)(294,332)(295,328)(296,330)(297,329)(298,334)(299,336)(300,335)
(301,340)(302,342)(303,341)(304,337)(305,339)(306,338)(307,343)(308,345)
(309,344)(310,349)(311,351)(312,350)(313,346)(314,348)(315,347)(316,352)
(317,354)(318,353)(319,358)(320,360)(321,359)(322,355)(323,357)(324,356)
(361,397)(362,399)(363,398)(364,403)(365,405)(366,404)(367,400)(368,402)
(369,401)(370,406)(371,408)(372,407)(373,412)(374,414)(375,413)(376,409)
(377,411)(378,410)(379,415)(380,417)(381,416)(382,421)(383,423)(384,422)
(385,418)(386,420)(387,419)(388,424)(389,426)(390,425)(391,430)(392,432)
(393,431)(394,427)(395,429)(396,428)(433,496)(434,498)(435,497)(436,502)
(437,504)(438,503)(439,499)(440,501)(441,500)(442,487)(443,489)(444,488)
(445,493)(446,495)(447,494)(448,490)(449,492)(450,491)(451,478)(452,480)
(453,479)(454,484)(455,486)(456,485)(457,481)(458,483)(459,482)(460,469)
(461,471)(462,470)(463,475)(464,477)(465,476)(466,472)(467,474)(468,473)
(505,568)(506,570)(507,569)(508,574)(509,576)(510,575)(511,571)(512,573)
(513,572)(514,559)(515,561)(516,560)(517,565)(518,567)(519,566)(520,562)
(521,564)(522,563)(523,550)(524,552)(525,551)(526,556)(527,558)(528,557)
(529,553)(530,555)(531,554)(532,541)(533,543)(534,542)(535,547)(536,549)
(537,548)(538,544)(539,546)(540,545);;
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)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)( 24,321)
( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)( 32,311)
( 33,312)( 34,313)( 35,314)( 36,315)( 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)( 55,343)( 56,344)
( 57,345)( 58,346)( 59,347)( 60,348)( 61,349)( 62,350)( 63,351)( 64,352)
( 65,353)( 66,354)( 67,355)( 68,356)( 69,357)( 70,358)( 71,359)( 72,360)
( 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)( 91,388)( 92,389)( 93,390)( 94,391)( 95,392)( 96,393)
( 97,394)( 98,395)( 99,396)(100,379)(101,380)(102,381)(103,382)(104,383)
(105,384)(106,385)(107,386)(108,387)(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)(127,415)(128,416)
(129,417)(130,418)(131,419)(132,420)(133,421)(134,422)(135,423)(136,424)
(137,425)(138,426)(139,427)(140,428)(141,429)(142,430)(143,431)(144,432)
(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)(163,460)(164,461)(165,462)(166,463)(167,464)(168,465)
(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)(176,455)
(177,456)(178,457)(179,458)(180,459)(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)(199,487)(200,488)
(201,489)(202,490)(203,491)(204,492)(205,493)(206,494)(207,495)(208,496)
(209,497)(210,498)(211,499)(212,500)(213,501)(214,502)(215,503)(216,504)
(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)(235,532)(236,533)(237,534)(238,535)(239,536)(240,537)
(241,538)(242,539)(243,540)(244,523)(245,524)(246,525)(247,526)(248,527)
(249,528)(250,529)(251,530)(252,531)(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)(271,559)(272,560)
(273,561)(274,562)(275,563)(276,564)(277,565)(278,566)(279,567)(280,568)
(281,569)(282,570)(283,571)(284,572)(285,573)(286,574)(287,575)(288,576);;
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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
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, 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)( 37,109)( 38,114)( 39,116)
( 40,112)( 41,117)( 42,110)( 43,115)( 44,111)( 45,113)( 46,118)( 47,123)
( 48,125)( 49,121)( 50,126)( 51,119)( 52,124)( 53,120)( 54,122)( 55,127)
( 56,132)( 57,134)( 58,130)( 59,135)( 60,128)( 61,133)( 62,129)( 63,131)
( 64,136)( 65,141)( 66,143)( 67,139)( 68,144)( 69,137)( 70,142)( 71,138)
( 72,140)(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)(181,253)(182,258)(183,260)
(184,256)(185,261)(186,254)(187,259)(188,255)(189,257)(190,262)(191,267)
(192,269)(193,265)(194,270)(195,263)(196,268)(197,264)(198,266)(199,271)
(200,276)(201,278)(202,274)(203,279)(204,272)(205,277)(206,273)(207,275)
(208,280)(209,285)(210,287)(211,283)(212,288)(213,281)(214,286)(215,282)
(216,284)(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)(325,397)(326,402)(327,404)
(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)(335,411)
(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)(343,415)
(344,420)(345,422)(346,418)(347,423)(348,416)(349,421)(350,417)(351,419)
(352,424)(353,429)(354,431)(355,427)(356,432)(357,425)(358,430)(359,426)
(360,428)(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)(469,541)(470,546)(471,548)
(472,544)(473,549)(474,542)(475,547)(476,543)(477,545)(478,550)(479,555)
(480,557)(481,553)(482,558)(483,551)(484,556)(485,552)(486,554)(487,559)
(488,564)(489,566)(490,562)(491,567)(492,560)(493,565)(494,561)(495,563)
(496,568)(497,573)(498,575)(499,571)(500,576)(501,569)(502,574)(503,570)
(504,572);
s1 := Sym(576)!( 1,146)( 2,145)( 3,147)( 4,152)( 5,151)( 6,153)( 7,149)
( 8,148)( 9,150)( 10,155)( 11,154)( 12,156)( 13,161)( 14,160)( 15,162)
( 16,158)( 17,157)( 18,159)( 19,164)( 20,163)( 21,165)( 22,170)( 23,169)
( 24,171)( 25,167)( 26,166)( 27,168)( 28,173)( 29,172)( 30,174)( 31,179)
( 32,178)( 33,180)( 34,176)( 35,175)( 36,177)( 37,191)( 38,190)( 39,192)
( 40,197)( 41,196)( 42,198)( 43,194)( 44,193)( 45,195)( 46,182)( 47,181)
( 48,183)( 49,188)( 50,187)( 51,189)( 52,185)( 53,184)( 54,186)( 55,209)
( 56,208)( 57,210)( 58,215)( 59,214)( 60,216)( 61,212)( 62,211)( 63,213)
( 64,200)( 65,199)( 66,201)( 67,206)( 68,205)( 69,207)( 70,203)( 71,202)
( 72,204)( 73,218)( 74,217)( 75,219)( 76,224)( 77,223)( 78,225)( 79,221)
( 80,220)( 81,222)( 82,227)( 83,226)( 84,228)( 85,233)( 86,232)( 87,234)
( 88,230)( 89,229)( 90,231)( 91,236)( 92,235)( 93,237)( 94,242)( 95,241)
( 96,243)( 97,239)( 98,238)( 99,240)(100,245)(101,244)(102,246)(103,251)
(104,250)(105,252)(106,248)(107,247)(108,249)(109,263)(110,262)(111,264)
(112,269)(113,268)(114,270)(115,266)(116,265)(117,267)(118,254)(119,253)
(120,255)(121,260)(122,259)(123,261)(124,257)(125,256)(126,258)(127,281)
(128,280)(129,282)(130,287)(131,286)(132,288)(133,284)(134,283)(135,285)
(136,272)(137,271)(138,273)(139,278)(140,277)(141,279)(142,275)(143,274)
(144,276)(289,434)(290,433)(291,435)(292,440)(293,439)(294,441)(295,437)
(296,436)(297,438)(298,443)(299,442)(300,444)(301,449)(302,448)(303,450)
(304,446)(305,445)(306,447)(307,452)(308,451)(309,453)(310,458)(311,457)
(312,459)(313,455)(314,454)(315,456)(316,461)(317,460)(318,462)(319,467)
(320,466)(321,468)(322,464)(323,463)(324,465)(325,479)(326,478)(327,480)
(328,485)(329,484)(330,486)(331,482)(332,481)(333,483)(334,470)(335,469)
(336,471)(337,476)(338,475)(339,477)(340,473)(341,472)(342,474)(343,497)
(344,496)(345,498)(346,503)(347,502)(348,504)(349,500)(350,499)(351,501)
(352,488)(353,487)(354,489)(355,494)(356,493)(357,495)(358,491)(359,490)
(360,492)(361,506)(362,505)(363,507)(364,512)(365,511)(366,513)(367,509)
(368,508)(369,510)(370,515)(371,514)(372,516)(373,521)(374,520)(375,522)
(376,518)(377,517)(378,519)(379,524)(380,523)(381,525)(382,530)(383,529)
(384,531)(385,527)(386,526)(387,528)(388,533)(389,532)(390,534)(391,539)
(392,538)(393,540)(394,536)(395,535)(396,537)(397,551)(398,550)(399,552)
(400,557)(401,556)(402,558)(403,554)(404,553)(405,555)(406,542)(407,541)
(408,543)(409,548)(410,547)(411,549)(412,545)(413,544)(414,546)(415,569)
(416,568)(417,570)(418,575)(419,574)(420,576)(421,572)(422,571)(423,573)
(424,560)(425,559)(426,561)(427,566)(428,565)(429,567)(430,563)(431,562)
(432,564);
s2 := Sym(576)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)
( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)( 43, 49)
( 44, 51)( 45, 50)( 55, 64)( 56, 66)( 57, 65)( 58, 70)( 59, 72)( 60, 71)
( 61, 67)( 62, 69)( 63, 68)( 74, 75)( 76, 79)( 77, 81)( 78, 80)( 83, 84)
( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)
(103,106)(104,108)(105,107)(109,118)(110,120)(111,119)(112,124)(113,126)
(114,125)(115,121)(116,123)(117,122)(127,136)(128,138)(129,137)(130,142)
(131,144)(132,143)(133,139)(134,141)(135,140)(145,163)(146,165)(147,164)
(148,169)(149,171)(150,170)(151,166)(152,168)(153,167)(154,172)(155,174)
(156,173)(157,178)(158,180)(159,179)(160,175)(161,177)(162,176)(181,208)
(182,210)(183,209)(184,214)(185,216)(186,215)(187,211)(188,213)(189,212)
(190,199)(191,201)(192,200)(193,205)(194,207)(195,206)(196,202)(197,204)
(198,203)(217,235)(218,237)(219,236)(220,241)(221,243)(222,242)(223,238)
(224,240)(225,239)(226,244)(227,246)(228,245)(229,250)(230,252)(231,251)
(232,247)(233,249)(234,248)(253,280)(254,282)(255,281)(256,286)(257,288)
(258,287)(259,283)(260,285)(261,284)(262,271)(263,273)(264,272)(265,277)
(266,279)(267,278)(268,274)(269,276)(270,275)(289,325)(290,327)(291,326)
(292,331)(293,333)(294,332)(295,328)(296,330)(297,329)(298,334)(299,336)
(300,335)(301,340)(302,342)(303,341)(304,337)(305,339)(306,338)(307,343)
(308,345)(309,344)(310,349)(311,351)(312,350)(313,346)(314,348)(315,347)
(316,352)(317,354)(318,353)(319,358)(320,360)(321,359)(322,355)(323,357)
(324,356)(361,397)(362,399)(363,398)(364,403)(365,405)(366,404)(367,400)
(368,402)(369,401)(370,406)(371,408)(372,407)(373,412)(374,414)(375,413)
(376,409)(377,411)(378,410)(379,415)(380,417)(381,416)(382,421)(383,423)
(384,422)(385,418)(386,420)(387,419)(388,424)(389,426)(390,425)(391,430)
(392,432)(393,431)(394,427)(395,429)(396,428)(433,496)(434,498)(435,497)
(436,502)(437,504)(438,503)(439,499)(440,501)(441,500)(442,487)(443,489)
(444,488)(445,493)(446,495)(447,494)(448,490)(449,492)(450,491)(451,478)
(452,480)(453,479)(454,484)(455,486)(456,485)(457,481)(458,483)(459,482)
(460,469)(461,471)(462,470)(463,475)(464,477)(465,476)(466,472)(467,474)
(468,473)(505,568)(506,570)(507,569)(508,574)(509,576)(510,575)(511,571)
(512,573)(513,572)(514,559)(515,561)(516,560)(517,565)(518,567)(519,566)
(520,562)(521,564)(522,563)(523,550)(524,552)(525,551)(526,556)(527,558)
(528,557)(529,553)(530,555)(531,554)(532,541)(533,543)(534,542)(535,547)
(536,549)(537,548)(538,544)(539,546)(540,545);
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)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)
( 24,321)( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)
( 32,311)( 33,312)( 34,313)( 35,314)( 36,315)( 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)( 55,343)
( 56,344)( 57,345)( 58,346)( 59,347)( 60,348)( 61,349)( 62,350)( 63,351)
( 64,352)( 65,353)( 66,354)( 67,355)( 68,356)( 69,357)( 70,358)( 71,359)
( 72,360)( 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)( 91,388)( 92,389)( 93,390)( 94,391)( 95,392)
( 96,393)( 97,394)( 98,395)( 99,396)(100,379)(101,380)(102,381)(103,382)
(104,383)(105,384)(106,385)(107,386)(108,387)(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)(127,415)
(128,416)(129,417)(130,418)(131,419)(132,420)(133,421)(134,422)(135,423)
(136,424)(137,425)(138,426)(139,427)(140,428)(141,429)(142,430)(143,431)
(144,432)(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)(163,460)(164,461)(165,462)(166,463)(167,464)
(168,465)(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)
(176,455)(177,456)(178,457)(179,458)(180,459)(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)(199,487)
(200,488)(201,489)(202,490)(203,491)(204,492)(205,493)(206,494)(207,495)
(208,496)(209,497)(210,498)(211,499)(212,500)(213,501)(214,502)(215,503)
(216,504)(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)(235,532)(236,533)(237,534)(238,535)(239,536)
(240,537)(241,538)(242,539)(243,540)(244,523)(245,524)(246,525)(247,526)
(248,527)(249,528)(250,529)(251,530)(252,531)(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)(271,559)
(272,560)(273,561)(274,562)(275,563)(276,564)(277,565)(278,566)(279,567)
(280,568)(281,569)(282,570)(283,571)(284,572)(285,573)(286,574)(287,575)
(288,576);
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,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
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