Polytope of Type {8,4,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,18}*1152a
Also Known As : {{8,4|2},{4,18|2}}. if this polytope has another name.
Group : SmallGroup(1152,97511)
Rank : 4
Schlafli Type : {8,4,18}
Number of vertices, edges, etc : 8, 16, 36, 18
Order of s0s1s2s3 : 72
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 : {4,4,18}*576, {8,2,18}*576
   3-fold quotients : {8,4,6}*384a
   4-fold quotients : {8,2,9}*288, {2,4,18}*288a, {4,2,18}*288
   6-fold quotients : {4,4,6}*192, {8,2,6}*192
   8-fold quotients : {4,2,9}*144, {2,2,18}*144
   9-fold quotients : {8,4,2}*128a
   12-fold quotients : {8,2,3}*96, {2,4,6}*96a, {4,2,6}*96
   16-fold quotients : {2,2,9}*72
   18-fold quotients : {4,4,2}*64, {8,2,2}*64
   24-fold quotients : {4,2,3}*48, {2,2,6}*48
   36-fold quotients : {2,4,2}*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 := (  1,289)(  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);;
s1 := ( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)
( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)( 61, 70)
( 62, 71)( 63, 72)(109,118)(110,119)(111,120)(112,121)(113,122)(114,123)
(115,124)(116,125)(117,126)(127,136)(128,137)(129,138)(130,139)(131,140)
(132,141)(133,142)(134,143)(135,144)(145,163)(146,164)(147,165)(148,166)
(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)(156,174)
(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,208)(182,209)
(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216)(190,199)
(191,200)(192,201)(193,202)(194,203)(195,204)(196,205)(197,206)(198,207)
(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)(224,242)
(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(231,249)(232,250)
(233,251)(234,252)(253,280)(254,281)(255,282)(256,283)(257,284)(258,285)
(259,286)(260,287)(261,288)(262,271)(263,272)(264,273)(265,274)(266,275)
(267,276)(268,277)(269,278)(270,279)(289,325)(290,326)(291,327)(292,328)
(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)(300,336)
(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)(308,344)
(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)(316,352)
(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)(324,360)
(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)(368,404)
(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)(376,412)
(377,413)(378,414)(379,415)(380,416)(381,417)(382,418)(383,419)(384,420)
(385,421)(386,422)(387,423)(388,424)(389,425)(390,426)(391,427)(392,428)
(393,429)(394,430)(395,431)(396,432)(433,487)(434,488)(435,489)(436,490)
(437,491)(438,492)(439,493)(440,494)(441,495)(442,496)(443,497)(444,498)
(445,499)(446,500)(447,501)(448,502)(449,503)(450,504)(451,469)(452,470)
(453,471)(454,472)(455,473)(456,474)(457,475)(458,476)(459,477)(460,478)
(461,479)(462,480)(463,481)(464,482)(465,483)(466,484)(467,485)(468,486)
(505,559)(506,560)(507,561)(508,562)(509,563)(510,564)(511,565)(512,566)
(513,567)(514,568)(515,569)(516,570)(517,571)(518,572)(519,573)(520,574)
(521,575)(522,576)(523,541)(524,542)(525,543)(526,544)(527,545)(528,546)
(529,547)(530,548)(531,549)(532,550)(533,551)(534,552)(535,553)(536,554)
(537,555)(538,556)(539,557)(540,558);;
s2 := (  1,217)(  2,219)(  3,218)(  4,225)(  5,224)(  6,223)(  7,222)(  8,221)
(  9,220)( 10,226)( 11,228)( 12,227)( 13,234)( 14,233)( 15,232)( 16,231)
( 17,230)( 18,229)( 19,235)( 20,237)( 21,236)( 22,243)( 23,242)( 24,241)
( 25,240)( 26,239)( 27,238)( 28,244)( 29,246)( 30,245)( 31,252)( 32,251)
( 33,250)( 34,249)( 35,248)( 36,247)( 37,253)( 38,255)( 39,254)( 40,261)
( 41,260)( 42,259)( 43,258)( 44,257)( 45,256)( 46,262)( 47,264)( 48,263)
( 49,270)( 50,269)( 51,268)( 52,267)( 53,266)( 54,265)( 55,271)( 56,273)
( 57,272)( 58,279)( 59,278)( 60,277)( 61,276)( 62,275)( 63,274)( 64,280)
( 65,282)( 66,281)( 67,288)( 68,287)( 69,286)( 70,285)( 71,284)( 72,283)
( 73,145)( 74,147)( 75,146)( 76,153)( 77,152)( 78,151)( 79,150)( 80,149)
( 81,148)( 82,154)( 83,156)( 84,155)( 85,162)( 86,161)( 87,160)( 88,159)
( 89,158)( 90,157)( 91,163)( 92,165)( 93,164)( 94,171)( 95,170)( 96,169)
( 97,168)( 98,167)( 99,166)(100,172)(101,174)(102,173)(103,180)(104,179)
(105,178)(106,177)(107,176)(108,175)(109,181)(110,183)(111,182)(112,189)
(113,188)(114,187)(115,186)(116,185)(117,184)(118,190)(119,192)(120,191)
(121,198)(122,197)(123,196)(124,195)(125,194)(126,193)(127,199)(128,201)
(129,200)(130,207)(131,206)(132,205)(133,204)(134,203)(135,202)(136,208)
(137,210)(138,209)(139,216)(140,215)(141,214)(142,213)(143,212)(144,211)
(289,505)(290,507)(291,506)(292,513)(293,512)(294,511)(295,510)(296,509)
(297,508)(298,514)(299,516)(300,515)(301,522)(302,521)(303,520)(304,519)
(305,518)(306,517)(307,523)(308,525)(309,524)(310,531)(311,530)(312,529)
(313,528)(314,527)(315,526)(316,532)(317,534)(318,533)(319,540)(320,539)
(321,538)(322,537)(323,536)(324,535)(325,541)(326,543)(327,542)(328,549)
(329,548)(330,547)(331,546)(332,545)(333,544)(334,550)(335,552)(336,551)
(337,558)(338,557)(339,556)(340,555)(341,554)(342,553)(343,559)(344,561)
(345,560)(346,567)(347,566)(348,565)(349,564)(350,563)(351,562)(352,568)
(353,570)(354,569)(355,576)(356,575)(357,574)(358,573)(359,572)(360,571)
(361,433)(362,435)(363,434)(364,441)(365,440)(366,439)(367,438)(368,437)
(369,436)(370,442)(371,444)(372,443)(373,450)(374,449)(375,448)(376,447)
(377,446)(378,445)(379,451)(380,453)(381,452)(382,459)(383,458)(384,457)
(385,456)(386,455)(387,454)(388,460)(389,462)(390,461)(391,468)(392,467)
(393,466)(394,465)(395,464)(396,463)(397,469)(398,471)(399,470)(400,477)
(401,476)(402,475)(403,474)(404,473)(405,472)(406,478)(407,480)(408,479)
(409,486)(410,485)(411,484)(412,483)(413,482)(414,481)(415,487)(416,489)
(417,488)(418,495)(419,494)(420,493)(421,492)(422,491)(423,490)(424,496)
(425,498)(426,497)(427,504)(428,503)(429,502)(430,501)(431,500)(432,499);;
s3 := (  1, 76)(  2, 78)(  3, 77)(  4, 73)(  5, 75)(  6, 74)(  7, 81)(  8, 80)
(  9, 79)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)( 16, 90)
( 17, 89)( 18, 88)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)( 24, 92)
( 25, 99)( 26, 98)( 27, 97)( 28,103)( 29,105)( 30,104)( 31,100)( 32,102)
( 33,101)( 34,108)( 35,107)( 36,106)( 37,112)( 38,114)( 39,113)( 40,109)
( 41,111)( 42,110)( 43,117)( 44,116)( 45,115)( 46,121)( 47,123)( 48,122)
( 49,118)( 50,120)( 51,119)( 52,126)( 53,125)( 54,124)( 55,130)( 56,132)
( 57,131)( 58,127)( 59,129)( 60,128)( 61,135)( 62,134)( 63,133)( 64,139)
( 65,141)( 66,140)( 67,136)( 68,138)( 69,137)( 70,144)( 71,143)( 72,142)
(145,220)(146,222)(147,221)(148,217)(149,219)(150,218)(151,225)(152,224)
(153,223)(154,229)(155,231)(156,230)(157,226)(158,228)(159,227)(160,234)
(161,233)(162,232)(163,238)(164,240)(165,239)(166,235)(167,237)(168,236)
(169,243)(170,242)(171,241)(172,247)(173,249)(174,248)(175,244)(176,246)
(177,245)(178,252)(179,251)(180,250)(181,256)(182,258)(183,257)(184,253)
(185,255)(186,254)(187,261)(188,260)(189,259)(190,265)(191,267)(192,266)
(193,262)(194,264)(195,263)(196,270)(197,269)(198,268)(199,274)(200,276)
(201,275)(202,271)(203,273)(204,272)(205,279)(206,278)(207,277)(208,283)
(209,285)(210,284)(211,280)(212,282)(213,281)(214,288)(215,287)(216,286)
(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,369)(296,368)
(297,367)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,378)
(305,377)(306,376)(307,382)(308,384)(309,383)(310,379)(311,381)(312,380)
(313,387)(314,386)(315,385)(316,391)(317,393)(318,392)(319,388)(320,390)
(321,389)(322,396)(323,395)(324,394)(325,400)(326,402)(327,401)(328,397)
(329,399)(330,398)(331,405)(332,404)(333,403)(334,409)(335,411)(336,410)
(337,406)(338,408)(339,407)(340,414)(341,413)(342,412)(343,418)(344,420)
(345,419)(346,415)(347,417)(348,416)(349,423)(350,422)(351,421)(352,427)
(353,429)(354,428)(355,424)(356,426)(357,425)(358,432)(359,431)(360,430)
(433,508)(434,510)(435,509)(436,505)(437,507)(438,506)(439,513)(440,512)
(441,511)(442,517)(443,519)(444,518)(445,514)(446,516)(447,515)(448,522)
(449,521)(450,520)(451,526)(452,528)(453,527)(454,523)(455,525)(456,524)
(457,531)(458,530)(459,529)(460,535)(461,537)(462,536)(463,532)(464,534)
(465,533)(466,540)(467,539)(468,538)(469,544)(470,546)(471,545)(472,541)
(473,543)(474,542)(475,549)(476,548)(477,547)(478,553)(479,555)(480,554)
(481,550)(482,552)(483,551)(484,558)(485,557)(486,556)(487,562)(488,564)
(489,563)(490,559)(491,561)(492,560)(493,567)(494,566)(495,565)(496,571)
(497,573)(498,572)(499,568)(500,570)(501,569)(502,576)(503,575)(504,574);;
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*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*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)!(  1,289)(  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);
s1 := Sym(576)!( 37, 46)( 38, 47)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)
( 44, 53)( 45, 54)( 55, 64)( 56, 65)( 57, 66)( 58, 67)( 59, 68)( 60, 69)
( 61, 70)( 62, 71)( 63, 72)(109,118)(110,119)(111,120)(112,121)(113,122)
(114,123)(115,124)(116,125)(117,126)(127,136)(128,137)(129,138)(130,139)
(131,140)(132,141)(133,142)(134,143)(135,144)(145,163)(146,164)(147,165)
(148,166)(149,167)(150,168)(151,169)(152,170)(153,171)(154,172)(155,173)
(156,174)(157,175)(158,176)(159,177)(160,178)(161,179)(162,180)(181,208)
(182,209)(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216)
(190,199)(191,200)(192,201)(193,202)(194,203)(195,204)(196,205)(197,206)
(198,207)(217,235)(218,236)(219,237)(220,238)(221,239)(222,240)(223,241)
(224,242)(225,243)(226,244)(227,245)(228,246)(229,247)(230,248)(231,249)
(232,250)(233,251)(234,252)(253,280)(254,281)(255,282)(256,283)(257,284)
(258,285)(259,286)(260,287)(261,288)(262,271)(263,272)(264,273)(265,274)
(266,275)(267,276)(268,277)(269,278)(270,279)(289,325)(290,326)(291,327)
(292,328)(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)
(300,336)(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,343)
(308,344)(309,345)(310,346)(311,347)(312,348)(313,349)(314,350)(315,351)
(316,352)(317,353)(318,354)(319,355)(320,356)(321,357)(322,358)(323,359)
(324,360)(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)
(368,404)(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)
(376,412)(377,413)(378,414)(379,415)(380,416)(381,417)(382,418)(383,419)
(384,420)(385,421)(386,422)(387,423)(388,424)(389,425)(390,426)(391,427)
(392,428)(393,429)(394,430)(395,431)(396,432)(433,487)(434,488)(435,489)
(436,490)(437,491)(438,492)(439,493)(440,494)(441,495)(442,496)(443,497)
(444,498)(445,499)(446,500)(447,501)(448,502)(449,503)(450,504)(451,469)
(452,470)(453,471)(454,472)(455,473)(456,474)(457,475)(458,476)(459,477)
(460,478)(461,479)(462,480)(463,481)(464,482)(465,483)(466,484)(467,485)
(468,486)(505,559)(506,560)(507,561)(508,562)(509,563)(510,564)(511,565)
(512,566)(513,567)(514,568)(515,569)(516,570)(517,571)(518,572)(519,573)
(520,574)(521,575)(522,576)(523,541)(524,542)(525,543)(526,544)(527,545)
(528,546)(529,547)(530,548)(531,549)(532,550)(533,551)(534,552)(535,553)
(536,554)(537,555)(538,556)(539,557)(540,558);
s2 := Sym(576)!(  1,217)(  2,219)(  3,218)(  4,225)(  5,224)(  6,223)(  7,222)
(  8,221)(  9,220)( 10,226)( 11,228)( 12,227)( 13,234)( 14,233)( 15,232)
( 16,231)( 17,230)( 18,229)( 19,235)( 20,237)( 21,236)( 22,243)( 23,242)
( 24,241)( 25,240)( 26,239)( 27,238)( 28,244)( 29,246)( 30,245)( 31,252)
( 32,251)( 33,250)( 34,249)( 35,248)( 36,247)( 37,253)( 38,255)( 39,254)
( 40,261)( 41,260)( 42,259)( 43,258)( 44,257)( 45,256)( 46,262)( 47,264)
( 48,263)( 49,270)( 50,269)( 51,268)( 52,267)( 53,266)( 54,265)( 55,271)
( 56,273)( 57,272)( 58,279)( 59,278)( 60,277)( 61,276)( 62,275)( 63,274)
( 64,280)( 65,282)( 66,281)( 67,288)( 68,287)( 69,286)( 70,285)( 71,284)
( 72,283)( 73,145)( 74,147)( 75,146)( 76,153)( 77,152)( 78,151)( 79,150)
( 80,149)( 81,148)( 82,154)( 83,156)( 84,155)( 85,162)( 86,161)( 87,160)
( 88,159)( 89,158)( 90,157)( 91,163)( 92,165)( 93,164)( 94,171)( 95,170)
( 96,169)( 97,168)( 98,167)( 99,166)(100,172)(101,174)(102,173)(103,180)
(104,179)(105,178)(106,177)(107,176)(108,175)(109,181)(110,183)(111,182)
(112,189)(113,188)(114,187)(115,186)(116,185)(117,184)(118,190)(119,192)
(120,191)(121,198)(122,197)(123,196)(124,195)(125,194)(126,193)(127,199)
(128,201)(129,200)(130,207)(131,206)(132,205)(133,204)(134,203)(135,202)
(136,208)(137,210)(138,209)(139,216)(140,215)(141,214)(142,213)(143,212)
(144,211)(289,505)(290,507)(291,506)(292,513)(293,512)(294,511)(295,510)
(296,509)(297,508)(298,514)(299,516)(300,515)(301,522)(302,521)(303,520)
(304,519)(305,518)(306,517)(307,523)(308,525)(309,524)(310,531)(311,530)
(312,529)(313,528)(314,527)(315,526)(316,532)(317,534)(318,533)(319,540)
(320,539)(321,538)(322,537)(323,536)(324,535)(325,541)(326,543)(327,542)
(328,549)(329,548)(330,547)(331,546)(332,545)(333,544)(334,550)(335,552)
(336,551)(337,558)(338,557)(339,556)(340,555)(341,554)(342,553)(343,559)
(344,561)(345,560)(346,567)(347,566)(348,565)(349,564)(350,563)(351,562)
(352,568)(353,570)(354,569)(355,576)(356,575)(357,574)(358,573)(359,572)
(360,571)(361,433)(362,435)(363,434)(364,441)(365,440)(366,439)(367,438)
(368,437)(369,436)(370,442)(371,444)(372,443)(373,450)(374,449)(375,448)
(376,447)(377,446)(378,445)(379,451)(380,453)(381,452)(382,459)(383,458)
(384,457)(385,456)(386,455)(387,454)(388,460)(389,462)(390,461)(391,468)
(392,467)(393,466)(394,465)(395,464)(396,463)(397,469)(398,471)(399,470)
(400,477)(401,476)(402,475)(403,474)(404,473)(405,472)(406,478)(407,480)
(408,479)(409,486)(410,485)(411,484)(412,483)(413,482)(414,481)(415,487)
(416,489)(417,488)(418,495)(419,494)(420,493)(421,492)(422,491)(423,490)
(424,496)(425,498)(426,497)(427,504)(428,503)(429,502)(430,501)(431,500)
(432,499);
s3 := Sym(576)!(  1, 76)(  2, 78)(  3, 77)(  4, 73)(  5, 75)(  6, 74)(  7, 81)
(  8, 80)(  9, 79)( 10, 85)( 11, 87)( 12, 86)( 13, 82)( 14, 84)( 15, 83)
( 16, 90)( 17, 89)( 18, 88)( 19, 94)( 20, 96)( 21, 95)( 22, 91)( 23, 93)
( 24, 92)( 25, 99)( 26, 98)( 27, 97)( 28,103)( 29,105)( 30,104)( 31,100)
( 32,102)( 33,101)( 34,108)( 35,107)( 36,106)( 37,112)( 38,114)( 39,113)
( 40,109)( 41,111)( 42,110)( 43,117)( 44,116)( 45,115)( 46,121)( 47,123)
( 48,122)( 49,118)( 50,120)( 51,119)( 52,126)( 53,125)( 54,124)( 55,130)
( 56,132)( 57,131)( 58,127)( 59,129)( 60,128)( 61,135)( 62,134)( 63,133)
( 64,139)( 65,141)( 66,140)( 67,136)( 68,138)( 69,137)( 70,144)( 71,143)
( 72,142)(145,220)(146,222)(147,221)(148,217)(149,219)(150,218)(151,225)
(152,224)(153,223)(154,229)(155,231)(156,230)(157,226)(158,228)(159,227)
(160,234)(161,233)(162,232)(163,238)(164,240)(165,239)(166,235)(167,237)
(168,236)(169,243)(170,242)(171,241)(172,247)(173,249)(174,248)(175,244)
(176,246)(177,245)(178,252)(179,251)(180,250)(181,256)(182,258)(183,257)
(184,253)(185,255)(186,254)(187,261)(188,260)(189,259)(190,265)(191,267)
(192,266)(193,262)(194,264)(195,263)(196,270)(197,269)(198,268)(199,274)
(200,276)(201,275)(202,271)(203,273)(204,272)(205,279)(206,278)(207,277)
(208,283)(209,285)(210,284)(211,280)(212,282)(213,281)(214,288)(215,287)
(216,286)(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,369)
(296,368)(297,367)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)
(304,378)(305,377)(306,376)(307,382)(308,384)(309,383)(310,379)(311,381)
(312,380)(313,387)(314,386)(315,385)(316,391)(317,393)(318,392)(319,388)
(320,390)(321,389)(322,396)(323,395)(324,394)(325,400)(326,402)(327,401)
(328,397)(329,399)(330,398)(331,405)(332,404)(333,403)(334,409)(335,411)
(336,410)(337,406)(338,408)(339,407)(340,414)(341,413)(342,412)(343,418)
(344,420)(345,419)(346,415)(347,417)(348,416)(349,423)(350,422)(351,421)
(352,427)(353,429)(354,428)(355,424)(356,426)(357,425)(358,432)(359,431)
(360,430)(433,508)(434,510)(435,509)(436,505)(437,507)(438,506)(439,513)
(440,512)(441,511)(442,517)(443,519)(444,518)(445,514)(446,516)(447,515)
(448,522)(449,521)(450,520)(451,526)(452,528)(453,527)(454,523)(455,525)
(456,524)(457,531)(458,530)(459,529)(460,535)(461,537)(462,536)(463,532)
(464,534)(465,533)(466,540)(467,539)(468,538)(469,544)(470,546)(471,545)
(472,541)(473,543)(474,542)(475,549)(476,548)(477,547)(478,553)(479,555)
(480,554)(481,550)(482,552)(483,551)(484,558)(485,557)(486,556)(487,562)
(488,564)(489,563)(490,559)(491,561)(492,560)(493,567)(494,566)(495,565)
(496,571)(497,573)(498,572)(499,568)(500,570)(501,569)(502,576)(503,575)
(504,574);
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*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*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*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