Polytope of Type {6,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,8}*1152a
Also Known As : {{6,4}4,{4,8|2}}. if this polytope has another name.
Group : SmallGroup(1152,97552)
Rank : 4
Schlafli Type : {6,4,8}
Number of vertices, edges, etc : 18, 36, 48, 8
Order of s0s1s2s3 : 8
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 : {6,4,8}*576, {6,4,4}*576
4-fold quotients : {6,4,4}*288, {6,4,2}*288
8-fold quotients : {6,4,2}*144
9-fold quotients : {2,4,8}*128a
18-fold quotients : {2,4,4}*64, {2,2,8}*64
36-fold quotients : {2,2,4}*32, {2,4,2}*32
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 91)( 2, 93)( 3, 92)( 4, 97)( 5, 99)( 6, 98)( 7, 94)( 8, 96)
( 9, 95)( 10,100)( 11,102)( 12,101)( 13,106)( 14,108)( 15,107)( 16,103)
( 17,105)( 18,104)( 19, 73)( 20, 75)( 21, 74)( 22, 79)( 23, 81)( 24, 80)
( 25, 76)( 26, 78)( 27, 77)( 28, 82)( 29, 84)( 30, 83)( 31, 88)( 32, 90)
( 33, 89)( 34, 85)( 35, 87)( 36, 86)( 37,127)( 38,129)( 39,128)( 40,133)
( 41,135)( 42,134)( 43,130)( 44,132)( 45,131)( 46,136)( 47,138)( 48,137)
( 49,142)( 50,144)( 51,143)( 52,139)( 53,141)( 54,140)( 55,109)( 56,111)
( 57,110)( 58,115)( 59,117)( 60,116)( 61,112)( 62,114)( 63,113)( 64,118)
( 65,120)( 66,119)( 67,124)( 68,126)( 69,125)( 70,121)( 71,123)( 72,122)
(145,235)(146,237)(147,236)(148,241)(149,243)(150,242)(151,238)(152,240)
(153,239)(154,244)(155,246)(156,245)(157,250)(158,252)(159,251)(160,247)
(161,249)(162,248)(163,217)(164,219)(165,218)(166,223)(167,225)(168,224)
(169,220)(170,222)(171,221)(172,226)(173,228)(174,227)(175,232)(176,234)
(177,233)(178,229)(179,231)(180,230)(181,271)(182,273)(183,272)(184,277)
(185,279)(186,278)(187,274)(188,276)(189,275)(190,280)(191,282)(192,281)
(193,286)(194,288)(195,287)(196,283)(197,285)(198,284)(199,253)(200,255)
(201,254)(202,259)(203,261)(204,260)(205,256)(206,258)(207,257)(208,262)
(209,264)(210,263)(211,268)(212,270)(213,269)(214,265)(215,267)(216,266)
(289,379)(290,381)(291,380)(292,385)(293,387)(294,386)(295,382)(296,384)
(297,383)(298,388)(299,390)(300,389)(301,394)(302,396)(303,395)(304,391)
(305,393)(306,392)(307,361)(308,363)(309,362)(310,367)(311,369)(312,368)
(313,364)(314,366)(315,365)(316,370)(317,372)(318,371)(319,376)(320,378)
(321,377)(322,373)(323,375)(324,374)(325,415)(326,417)(327,416)(328,421)
(329,423)(330,422)(331,418)(332,420)(333,419)(334,424)(335,426)(336,425)
(337,430)(338,432)(339,431)(340,427)(341,429)(342,428)(343,397)(344,399)
(345,398)(346,403)(347,405)(348,404)(349,400)(350,402)(351,401)(352,406)
(353,408)(354,407)(355,412)(356,414)(357,413)(358,409)(359,411)(360,410)
(433,523)(434,525)(435,524)(436,529)(437,531)(438,530)(439,526)(440,528)
(441,527)(442,532)(443,534)(444,533)(445,538)(446,540)(447,539)(448,535)
(449,537)(450,536)(451,505)(452,507)(453,506)(454,511)(455,513)(456,512)
(457,508)(458,510)(459,509)(460,514)(461,516)(462,515)(463,520)(464,522)
(465,521)(466,517)(467,519)(468,518)(469,559)(470,561)(471,560)(472,565)
(473,567)(474,566)(475,562)(476,564)(477,563)(478,568)(479,570)(480,569)
(481,574)(482,576)(483,575)(484,571)(485,573)(486,572)(487,541)(488,543)
(489,542)(490,547)(491,549)(492,548)(493,544)(494,546)(495,545)(496,550)
(497,552)(498,551)(499,556)(500,558)(501,557)(502,553)(503,555)(504,554);;
s1 := ( 1,146)( 2,145)( 3,147)( 4,150)( 5,149)( 6,148)( 7,151)( 8,153)
( 9,152)( 10,155)( 11,154)( 12,156)( 13,159)( 14,158)( 15,157)( 16,160)
( 17,162)( 18,161)( 19,164)( 20,163)( 21,165)( 22,168)( 23,167)( 24,166)
( 25,169)( 26,171)( 27,170)( 28,173)( 29,172)( 30,174)( 31,177)( 32,176)
( 33,175)( 34,178)( 35,180)( 36,179)( 37,182)( 38,181)( 39,183)( 40,186)
( 41,185)( 42,184)( 43,187)( 44,189)( 45,188)( 46,191)( 47,190)( 48,192)
( 49,195)( 50,194)( 51,193)( 52,196)( 53,198)( 54,197)( 55,200)( 56,199)
( 57,201)( 58,204)( 59,203)( 60,202)( 61,205)( 62,207)( 63,206)( 64,209)
( 65,208)( 66,210)( 67,213)( 68,212)( 69,211)( 70,214)( 71,216)( 72,215)
( 73,218)( 74,217)( 75,219)( 76,222)( 77,221)( 78,220)( 79,223)( 80,225)
( 81,224)( 82,227)( 83,226)( 84,228)( 85,231)( 86,230)( 87,229)( 88,232)
( 89,234)( 90,233)( 91,236)( 92,235)( 93,237)( 94,240)( 95,239)( 96,238)
( 97,241)( 98,243)( 99,242)(100,245)(101,244)(102,246)(103,249)(104,248)
(105,247)(106,250)(107,252)(108,251)(109,254)(110,253)(111,255)(112,258)
(113,257)(114,256)(115,259)(116,261)(117,260)(118,263)(119,262)(120,264)
(121,267)(122,266)(123,265)(124,268)(125,270)(126,269)(127,272)(128,271)
(129,273)(130,276)(131,275)(132,274)(133,277)(134,279)(135,278)(136,281)
(137,280)(138,282)(139,285)(140,284)(141,283)(142,286)(143,288)(144,287)
(289,434)(290,433)(291,435)(292,438)(293,437)(294,436)(295,439)(296,441)
(297,440)(298,443)(299,442)(300,444)(301,447)(302,446)(303,445)(304,448)
(305,450)(306,449)(307,452)(308,451)(309,453)(310,456)(311,455)(312,454)
(313,457)(314,459)(315,458)(316,461)(317,460)(318,462)(319,465)(320,464)
(321,463)(322,466)(323,468)(324,467)(325,470)(326,469)(327,471)(328,474)
(329,473)(330,472)(331,475)(332,477)(333,476)(334,479)(335,478)(336,480)
(337,483)(338,482)(339,481)(340,484)(341,486)(342,485)(343,488)(344,487)
(345,489)(346,492)(347,491)(348,490)(349,493)(350,495)(351,494)(352,497)
(353,496)(354,498)(355,501)(356,500)(357,499)(358,502)(359,504)(360,503)
(361,506)(362,505)(363,507)(364,510)(365,509)(366,508)(367,511)(368,513)
(369,512)(370,515)(371,514)(372,516)(373,519)(374,518)(375,517)(376,520)
(377,522)(378,521)(379,524)(380,523)(381,525)(382,528)(383,527)(384,526)
(385,529)(386,531)(387,530)(388,533)(389,532)(390,534)(391,537)(392,536)
(393,535)(394,538)(395,540)(396,539)(397,542)(398,541)(399,543)(400,546)
(401,545)(402,544)(403,547)(404,549)(405,548)(406,551)(407,550)(408,552)
(409,555)(410,554)(411,553)(412,556)(413,558)(414,557)(415,560)(416,559)
(417,561)(418,564)(419,563)(420,562)(421,565)(422,567)(423,566)(424,569)
(425,568)(426,570)(427,573)(428,572)(429,571)(430,574)(431,576)(432,575);;
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*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*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, 91)( 2, 93)( 3, 92)( 4, 97)( 5, 99)( 6, 98)( 7, 94)
( 8, 96)( 9, 95)( 10,100)( 11,102)( 12,101)( 13,106)( 14,108)( 15,107)
( 16,103)( 17,105)( 18,104)( 19, 73)( 20, 75)( 21, 74)( 22, 79)( 23, 81)
( 24, 80)( 25, 76)( 26, 78)( 27, 77)( 28, 82)( 29, 84)( 30, 83)( 31, 88)
( 32, 90)( 33, 89)( 34, 85)( 35, 87)( 36, 86)( 37,127)( 38,129)( 39,128)
( 40,133)( 41,135)( 42,134)( 43,130)( 44,132)( 45,131)( 46,136)( 47,138)
( 48,137)( 49,142)( 50,144)( 51,143)( 52,139)( 53,141)( 54,140)( 55,109)
( 56,111)( 57,110)( 58,115)( 59,117)( 60,116)( 61,112)( 62,114)( 63,113)
( 64,118)( 65,120)( 66,119)( 67,124)( 68,126)( 69,125)( 70,121)( 71,123)
( 72,122)(145,235)(146,237)(147,236)(148,241)(149,243)(150,242)(151,238)
(152,240)(153,239)(154,244)(155,246)(156,245)(157,250)(158,252)(159,251)
(160,247)(161,249)(162,248)(163,217)(164,219)(165,218)(166,223)(167,225)
(168,224)(169,220)(170,222)(171,221)(172,226)(173,228)(174,227)(175,232)
(176,234)(177,233)(178,229)(179,231)(180,230)(181,271)(182,273)(183,272)
(184,277)(185,279)(186,278)(187,274)(188,276)(189,275)(190,280)(191,282)
(192,281)(193,286)(194,288)(195,287)(196,283)(197,285)(198,284)(199,253)
(200,255)(201,254)(202,259)(203,261)(204,260)(205,256)(206,258)(207,257)
(208,262)(209,264)(210,263)(211,268)(212,270)(213,269)(214,265)(215,267)
(216,266)(289,379)(290,381)(291,380)(292,385)(293,387)(294,386)(295,382)
(296,384)(297,383)(298,388)(299,390)(300,389)(301,394)(302,396)(303,395)
(304,391)(305,393)(306,392)(307,361)(308,363)(309,362)(310,367)(311,369)
(312,368)(313,364)(314,366)(315,365)(316,370)(317,372)(318,371)(319,376)
(320,378)(321,377)(322,373)(323,375)(324,374)(325,415)(326,417)(327,416)
(328,421)(329,423)(330,422)(331,418)(332,420)(333,419)(334,424)(335,426)
(336,425)(337,430)(338,432)(339,431)(340,427)(341,429)(342,428)(343,397)
(344,399)(345,398)(346,403)(347,405)(348,404)(349,400)(350,402)(351,401)
(352,406)(353,408)(354,407)(355,412)(356,414)(357,413)(358,409)(359,411)
(360,410)(433,523)(434,525)(435,524)(436,529)(437,531)(438,530)(439,526)
(440,528)(441,527)(442,532)(443,534)(444,533)(445,538)(446,540)(447,539)
(448,535)(449,537)(450,536)(451,505)(452,507)(453,506)(454,511)(455,513)
(456,512)(457,508)(458,510)(459,509)(460,514)(461,516)(462,515)(463,520)
(464,522)(465,521)(466,517)(467,519)(468,518)(469,559)(470,561)(471,560)
(472,565)(473,567)(474,566)(475,562)(476,564)(477,563)(478,568)(479,570)
(480,569)(481,574)(482,576)(483,575)(484,571)(485,573)(486,572)(487,541)
(488,543)(489,542)(490,547)(491,549)(492,548)(493,544)(494,546)(495,545)
(496,550)(497,552)(498,551)(499,556)(500,558)(501,557)(502,553)(503,555)
(504,554);
s1 := Sym(576)!( 1,146)( 2,145)( 3,147)( 4,150)( 5,149)( 6,148)( 7,151)
( 8,153)( 9,152)( 10,155)( 11,154)( 12,156)( 13,159)( 14,158)( 15,157)
( 16,160)( 17,162)( 18,161)( 19,164)( 20,163)( 21,165)( 22,168)( 23,167)
( 24,166)( 25,169)( 26,171)( 27,170)( 28,173)( 29,172)( 30,174)( 31,177)
( 32,176)( 33,175)( 34,178)( 35,180)( 36,179)( 37,182)( 38,181)( 39,183)
( 40,186)( 41,185)( 42,184)( 43,187)( 44,189)( 45,188)( 46,191)( 47,190)
( 48,192)( 49,195)( 50,194)( 51,193)( 52,196)( 53,198)( 54,197)( 55,200)
( 56,199)( 57,201)( 58,204)( 59,203)( 60,202)( 61,205)( 62,207)( 63,206)
( 64,209)( 65,208)( 66,210)( 67,213)( 68,212)( 69,211)( 70,214)( 71,216)
( 72,215)( 73,218)( 74,217)( 75,219)( 76,222)( 77,221)( 78,220)( 79,223)
( 80,225)( 81,224)( 82,227)( 83,226)( 84,228)( 85,231)( 86,230)( 87,229)
( 88,232)( 89,234)( 90,233)( 91,236)( 92,235)( 93,237)( 94,240)( 95,239)
( 96,238)( 97,241)( 98,243)( 99,242)(100,245)(101,244)(102,246)(103,249)
(104,248)(105,247)(106,250)(107,252)(108,251)(109,254)(110,253)(111,255)
(112,258)(113,257)(114,256)(115,259)(116,261)(117,260)(118,263)(119,262)
(120,264)(121,267)(122,266)(123,265)(124,268)(125,270)(126,269)(127,272)
(128,271)(129,273)(130,276)(131,275)(132,274)(133,277)(134,279)(135,278)
(136,281)(137,280)(138,282)(139,285)(140,284)(141,283)(142,286)(143,288)
(144,287)(289,434)(290,433)(291,435)(292,438)(293,437)(294,436)(295,439)
(296,441)(297,440)(298,443)(299,442)(300,444)(301,447)(302,446)(303,445)
(304,448)(305,450)(306,449)(307,452)(308,451)(309,453)(310,456)(311,455)
(312,454)(313,457)(314,459)(315,458)(316,461)(317,460)(318,462)(319,465)
(320,464)(321,463)(322,466)(323,468)(324,467)(325,470)(326,469)(327,471)
(328,474)(329,473)(330,472)(331,475)(332,477)(333,476)(334,479)(335,478)
(336,480)(337,483)(338,482)(339,481)(340,484)(341,486)(342,485)(343,488)
(344,487)(345,489)(346,492)(347,491)(348,490)(349,493)(350,495)(351,494)
(352,497)(353,496)(354,498)(355,501)(356,500)(357,499)(358,502)(359,504)
(360,503)(361,506)(362,505)(363,507)(364,510)(365,509)(366,508)(367,511)
(368,513)(369,512)(370,515)(371,514)(372,516)(373,519)(374,518)(375,517)
(376,520)(377,522)(378,521)(379,524)(380,523)(381,525)(382,528)(383,527)
(384,526)(385,529)(386,531)(387,530)(388,533)(389,532)(390,534)(391,537)
(392,536)(393,535)(394,538)(395,540)(396,539)(397,542)(398,541)(399,543)
(400,546)(401,545)(402,544)(403,547)(404,549)(405,548)(406,551)(407,550)
(408,552)(409,555)(410,554)(411,553)(412,556)(413,558)(414,557)(415,560)
(416,559)(417,561)(418,564)(419,563)(420,562)(421,565)(422,567)(423,566)
(424,569)(425,568)(426,570)(427,573)(428,572)(429,571)(430,574)(431,576)
(432,575);
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*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