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Polytope of Type {8,18,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,18,4}*1152a
Also Known As : {{8,18|2},{18,4|2}}. if this polytope has another name.
Group : SmallGroup(1152,119725)
Rank : 4
Schlafli Type : {8,18,4}
Number of vertices, edges, etc : 8, 72, 36, 4
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 : {4,18,4}*576a, {8,18,2}*576
   3-fold quotients : {8,6,4}*384a
   4-fold quotients : {2,18,4}*288a, {4,18,2}*288a
   6-fold quotients : {4,6,4}*192a, {8,6,2}*192
   8-fold quotients : {2,18,2}*144
   9-fold quotients : {8,2,4}*128
   12-fold quotients : {2,6,4}*96a, {4,6,2}*96a
   16-fold quotients : {2,9,2}*72
   18-fold quotients : {4,2,4}*64, {8,2,2}*64
   24-fold quotients : {2,6,2}*48
   36-fold quotients : {2,2,4}*32, {4,2,2}*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 := (  1,289)(  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)
( 73,397)( 74,398)( 75,399)( 76,400)( 77,401)( 78,402)( 79,403)( 80,404)
( 81,405)( 82,406)( 83,407)( 84,408)( 85,409)( 86,410)( 87,411)( 88,412)
( 89,413)( 90,414)( 91,415)( 92,416)( 93,417)( 94,418)( 95,419)( 96,420)
( 97,421)( 98,422)( 99,423)(100,424)(101,425)(102,426)(103,427)(104,428)
(105,429)(106,430)(107,431)(108,432)(109,361)(110,362)(111,363)(112,364)
(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)(120,372)
(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,379)(128,380)
(129,381)(130,382)(131,383)(132,384)(133,385)(134,386)(135,387)(136,388)
(137,389)(138,390)(139,391)(140,392)(141,393)(142,394)(143,395)(144,396)
(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)
(217,541)(218,542)(219,543)(220,544)(221,545)(222,546)(223,547)(224,548)
(225,549)(226,550)(227,551)(228,552)(229,553)(230,554)(231,555)(232,556)
(233,557)(234,558)(235,559)(236,560)(237,561)(238,562)(239,563)(240,564)
(241,565)(242,566)(243,567)(244,568)(245,569)(246,570)(247,571)(248,572)
(249,573)(250,574)(251,575)(252,576)(253,505)(254,506)(255,507)(256,508)
(257,509)(258,510)(259,511)(260,512)(261,513)(262,514)(263,515)(264,516)
(265,517)(266,518)(267,519)(268,520)(269,521)(270,522)(271,523)(272,524)
(273,525)(274,526)(275,527)(276,528)(277,529)(278,530)(279,531)(280,532)
(281,533)(282,534)(283,535)(284,536)(285,537)(286,538)(287,539)(288,540);;
s1 := (  1, 73)(  2, 75)(  3, 74)(  4, 81)(  5, 80)(  6, 79)(  7, 78)(  8, 77)
(  9, 76)( 10, 82)( 11, 84)( 12, 83)( 13, 90)( 14, 89)( 15, 88)( 16, 87)
( 17, 86)( 18, 85)( 19, 91)( 20, 93)( 21, 92)( 22, 99)( 23, 98)( 24, 97)
( 25, 96)( 26, 95)( 27, 94)( 28,100)( 29,102)( 30,101)( 31,108)( 32,107)
( 33,106)( 34,105)( 35,104)( 36,103)( 37,118)( 38,120)( 39,119)( 40,126)
( 41,125)( 42,124)( 43,123)( 44,122)( 45,121)( 46,109)( 47,111)( 48,110)
( 49,117)( 50,116)( 51,115)( 52,114)( 53,113)( 54,112)( 55,136)( 56,138)
( 57,137)( 58,144)( 59,143)( 60,142)( 61,141)( 62,140)( 63,139)( 64,127)
( 65,129)( 66,128)( 67,135)( 68,134)( 69,133)( 70,132)( 71,131)( 72,130)
(145,217)(146,219)(147,218)(148,225)(149,224)(150,223)(151,222)(152,221)
(153,220)(154,226)(155,228)(156,227)(157,234)(158,233)(159,232)(160,231)
(161,230)(162,229)(163,235)(164,237)(165,236)(166,243)(167,242)(168,241)
(169,240)(170,239)(171,238)(172,244)(173,246)(174,245)(175,252)(176,251)
(177,250)(178,249)(179,248)(180,247)(181,262)(182,264)(183,263)(184,270)
(185,269)(186,268)(187,267)(188,266)(189,265)(190,253)(191,255)(192,254)
(193,261)(194,260)(195,259)(196,258)(197,257)(198,256)(199,280)(200,282)
(201,281)(202,288)(203,287)(204,286)(205,285)(206,284)(207,283)(208,271)
(209,273)(210,272)(211,279)(212,278)(213,277)(214,276)(215,275)(216,274)
(289,361)(290,363)(291,362)(292,369)(293,368)(294,367)(295,366)(296,365)
(297,364)(298,370)(299,372)(300,371)(301,378)(302,377)(303,376)(304,375)
(305,374)(306,373)(307,379)(308,381)(309,380)(310,387)(311,386)(312,385)
(313,384)(314,383)(315,382)(316,388)(317,390)(318,389)(319,396)(320,395)
(321,394)(322,393)(323,392)(324,391)(325,406)(326,408)(327,407)(328,414)
(329,413)(330,412)(331,411)(332,410)(333,409)(334,397)(335,399)(336,398)
(337,405)(338,404)(339,403)(340,402)(341,401)(342,400)(343,424)(344,426)
(345,425)(346,432)(347,431)(348,430)(349,429)(350,428)(351,427)(352,415)
(353,417)(354,416)(355,423)(356,422)(357,421)(358,420)(359,419)(360,418)
(433,505)(434,507)(435,506)(436,513)(437,512)(438,511)(439,510)(440,509)
(441,508)(442,514)(443,516)(444,515)(445,522)(446,521)(447,520)(448,519)
(449,518)(450,517)(451,523)(452,525)(453,524)(454,531)(455,530)(456,529)
(457,528)(458,527)(459,526)(460,532)(461,534)(462,533)(463,540)(464,539)
(465,538)(466,537)(467,536)(468,535)(469,550)(470,552)(471,551)(472,558)
(473,557)(474,556)(475,555)(476,554)(477,553)(478,541)(479,543)(480,542)
(481,549)(482,548)(483,547)(484,546)(485,545)(486,544)(487,568)(488,570)
(489,569)(490,576)(491,575)(492,574)(493,573)(494,572)(495,571)(496,559)
(497,561)(498,560)(499,567)(500,566)(501,565)(502,564)(503,563)(504,562);;
s2 := (  1,112)(  2,114)(  3,113)(  4,109)(  5,111)(  6,110)(  7,117)(  8,116)
(  9,115)( 10,121)( 11,123)( 12,122)( 13,118)( 14,120)( 15,119)( 16,126)
( 17,125)( 18,124)( 19,130)( 20,132)( 21,131)( 22,127)( 23,129)( 24,128)
( 25,135)( 26,134)( 27,133)( 28,139)( 29,141)( 30,140)( 31,136)( 32,138)
( 33,137)( 34,144)( 35,143)( 36,142)( 37, 85)( 38, 87)( 39, 86)( 40, 82)
( 41, 84)( 42, 83)( 43, 90)( 44, 89)( 45, 88)( 46, 76)( 47, 78)( 48, 77)
( 49, 73)( 50, 75)( 51, 74)( 52, 81)( 53, 80)( 54, 79)( 55,103)( 56,105)
( 57,104)( 58,100)( 59,102)( 60,101)( 61,108)( 62,107)( 63,106)( 64, 94)
( 65, 96)( 66, 95)( 67, 91)( 68, 93)( 69, 92)( 70, 99)( 71, 98)( 72, 97)
(145,274)(146,276)(147,275)(148,271)(149,273)(150,272)(151,279)(152,278)
(153,277)(154,283)(155,285)(156,284)(157,280)(158,282)(159,281)(160,288)
(161,287)(162,286)(163,256)(164,258)(165,257)(166,253)(167,255)(168,254)
(169,261)(170,260)(171,259)(172,265)(173,267)(174,266)(175,262)(176,264)
(177,263)(178,270)(179,269)(180,268)(181,247)(182,249)(183,248)(184,244)
(185,246)(186,245)(187,252)(188,251)(189,250)(190,238)(191,240)(192,239)
(193,235)(194,237)(195,236)(196,243)(197,242)(198,241)(199,229)(200,231)
(201,230)(202,226)(203,228)(204,227)(205,234)(206,233)(207,232)(208,220)
(209,222)(210,221)(211,217)(212,219)(213,218)(214,225)(215,224)(216,223)
(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)
(433,526)(434,528)(435,527)(436,523)(437,525)(438,524)(439,531)(440,530)
(441,529)(442,535)(443,537)(444,536)(445,532)(446,534)(447,533)(448,540)
(449,539)(450,538)(451,508)(452,510)(453,509)(454,505)(455,507)(456,506)
(457,513)(458,512)(459,511)(460,517)(461,519)(462,518)(463,514)(464,516)
(465,515)(466,522)(467,521)(468,520)(469,562)(470,564)(471,563)(472,559)
(473,561)(474,560)(475,567)(476,566)(477,565)(478,571)(479,573)(480,572)
(481,568)(482,570)(483,569)(484,576)(485,575)(486,574)(487,544)(488,546)
(489,545)(490,541)(491,543)(492,542)(493,549)(494,548)(495,547)(496,553)
(497,555)(498,554)(499,550)(500,552)(501,551)(502,558)(503,557)(504,556);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)( 73,397)( 74,398)( 75,399)( 76,400)( 77,401)( 78,402)( 79,403)
( 80,404)( 81,405)( 82,406)( 83,407)( 84,408)( 85,409)( 86,410)( 87,411)
( 88,412)( 89,413)( 90,414)( 91,415)( 92,416)( 93,417)( 94,418)( 95,419)
( 96,420)( 97,421)( 98,422)( 99,423)(100,424)(101,425)(102,426)(103,427)
(104,428)(105,429)(106,430)(107,431)(108,432)(109,361)(110,362)(111,363)
(112,364)(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)
(120,372)(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,379)
(128,380)(129,381)(130,382)(131,383)(132,384)(133,385)(134,386)(135,387)
(136,388)(137,389)(138,390)(139,391)(140,392)(141,393)(142,394)(143,395)
(144,396)(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)(217,541)(218,542)(219,543)(220,544)(221,545)(222,546)(223,547)
(224,548)(225,549)(226,550)(227,551)(228,552)(229,553)(230,554)(231,555)
(232,556)(233,557)(234,558)(235,559)(236,560)(237,561)(238,562)(239,563)
(240,564)(241,565)(242,566)(243,567)(244,568)(245,569)(246,570)(247,571)
(248,572)(249,573)(250,574)(251,575)(252,576)(253,505)(254,506)(255,507)
(256,508)(257,509)(258,510)(259,511)(260,512)(261,513)(262,514)(263,515)
(264,516)(265,517)(266,518)(267,519)(268,520)(269,521)(270,522)(271,523)
(272,524)(273,525)(274,526)(275,527)(276,528)(277,529)(278,530)(279,531)
(280,532)(281,533)(282,534)(283,535)(284,536)(285,537)(286,538)(287,539)
(288,540);
s1 := Sym(576)!(  1, 73)(  2, 75)(  3, 74)(  4, 81)(  5, 80)(  6, 79)(  7, 78)
(  8, 77)(  9, 76)( 10, 82)( 11, 84)( 12, 83)( 13, 90)( 14, 89)( 15, 88)
( 16, 87)( 17, 86)( 18, 85)( 19, 91)( 20, 93)( 21, 92)( 22, 99)( 23, 98)
( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28,100)( 29,102)( 30,101)( 31,108)
( 32,107)( 33,106)( 34,105)( 35,104)( 36,103)( 37,118)( 38,120)( 39,119)
( 40,126)( 41,125)( 42,124)( 43,123)( 44,122)( 45,121)( 46,109)( 47,111)
( 48,110)( 49,117)( 50,116)( 51,115)( 52,114)( 53,113)( 54,112)( 55,136)
( 56,138)( 57,137)( 58,144)( 59,143)( 60,142)( 61,141)( 62,140)( 63,139)
( 64,127)( 65,129)( 66,128)( 67,135)( 68,134)( 69,133)( 70,132)( 71,131)
( 72,130)(145,217)(146,219)(147,218)(148,225)(149,224)(150,223)(151,222)
(152,221)(153,220)(154,226)(155,228)(156,227)(157,234)(158,233)(159,232)
(160,231)(161,230)(162,229)(163,235)(164,237)(165,236)(166,243)(167,242)
(168,241)(169,240)(170,239)(171,238)(172,244)(173,246)(174,245)(175,252)
(176,251)(177,250)(178,249)(179,248)(180,247)(181,262)(182,264)(183,263)
(184,270)(185,269)(186,268)(187,267)(188,266)(189,265)(190,253)(191,255)
(192,254)(193,261)(194,260)(195,259)(196,258)(197,257)(198,256)(199,280)
(200,282)(201,281)(202,288)(203,287)(204,286)(205,285)(206,284)(207,283)
(208,271)(209,273)(210,272)(211,279)(212,278)(213,277)(214,276)(215,275)
(216,274)(289,361)(290,363)(291,362)(292,369)(293,368)(294,367)(295,366)
(296,365)(297,364)(298,370)(299,372)(300,371)(301,378)(302,377)(303,376)
(304,375)(305,374)(306,373)(307,379)(308,381)(309,380)(310,387)(311,386)
(312,385)(313,384)(314,383)(315,382)(316,388)(317,390)(318,389)(319,396)
(320,395)(321,394)(322,393)(323,392)(324,391)(325,406)(326,408)(327,407)
(328,414)(329,413)(330,412)(331,411)(332,410)(333,409)(334,397)(335,399)
(336,398)(337,405)(338,404)(339,403)(340,402)(341,401)(342,400)(343,424)
(344,426)(345,425)(346,432)(347,431)(348,430)(349,429)(350,428)(351,427)
(352,415)(353,417)(354,416)(355,423)(356,422)(357,421)(358,420)(359,419)
(360,418)(433,505)(434,507)(435,506)(436,513)(437,512)(438,511)(439,510)
(440,509)(441,508)(442,514)(443,516)(444,515)(445,522)(446,521)(447,520)
(448,519)(449,518)(450,517)(451,523)(452,525)(453,524)(454,531)(455,530)
(456,529)(457,528)(458,527)(459,526)(460,532)(461,534)(462,533)(463,540)
(464,539)(465,538)(466,537)(467,536)(468,535)(469,550)(470,552)(471,551)
(472,558)(473,557)(474,556)(475,555)(476,554)(477,553)(478,541)(479,543)
(480,542)(481,549)(482,548)(483,547)(484,546)(485,545)(486,544)(487,568)
(488,570)(489,569)(490,576)(491,575)(492,574)(493,573)(494,572)(495,571)
(496,559)(497,561)(498,560)(499,567)(500,566)(501,565)(502,564)(503,563)
(504,562);
s2 := Sym(576)!(  1,112)(  2,114)(  3,113)(  4,109)(  5,111)(  6,110)(  7,117)
(  8,116)(  9,115)( 10,121)( 11,123)( 12,122)( 13,118)( 14,120)( 15,119)
( 16,126)( 17,125)( 18,124)( 19,130)( 20,132)( 21,131)( 22,127)( 23,129)
( 24,128)( 25,135)( 26,134)( 27,133)( 28,139)( 29,141)( 30,140)( 31,136)
( 32,138)( 33,137)( 34,144)( 35,143)( 36,142)( 37, 85)( 38, 87)( 39, 86)
( 40, 82)( 41, 84)( 42, 83)( 43, 90)( 44, 89)( 45, 88)( 46, 76)( 47, 78)
( 48, 77)( 49, 73)( 50, 75)( 51, 74)( 52, 81)( 53, 80)( 54, 79)( 55,103)
( 56,105)( 57,104)( 58,100)( 59,102)( 60,101)( 61,108)( 62,107)( 63,106)
( 64, 94)( 65, 96)( 66, 95)( 67, 91)( 68, 93)( 69, 92)( 70, 99)( 71, 98)
( 72, 97)(145,274)(146,276)(147,275)(148,271)(149,273)(150,272)(151,279)
(152,278)(153,277)(154,283)(155,285)(156,284)(157,280)(158,282)(159,281)
(160,288)(161,287)(162,286)(163,256)(164,258)(165,257)(166,253)(167,255)
(168,254)(169,261)(170,260)(171,259)(172,265)(173,267)(174,266)(175,262)
(176,264)(177,263)(178,270)(179,269)(180,268)(181,247)(182,249)(183,248)
(184,244)(185,246)(186,245)(187,252)(188,251)(189,250)(190,238)(191,240)
(192,239)(193,235)(194,237)(195,236)(196,243)(197,242)(198,241)(199,229)
(200,231)(201,230)(202,226)(203,228)(204,227)(205,234)(206,233)(207,232)
(208,220)(209,222)(210,221)(211,217)(212,219)(213,218)(214,225)(215,224)
(216,223)(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)(433,526)(434,528)(435,527)(436,523)(437,525)(438,524)(439,531)
(440,530)(441,529)(442,535)(443,537)(444,536)(445,532)(446,534)(447,533)
(448,540)(449,539)(450,538)(451,508)(452,510)(453,509)(454,505)(455,507)
(456,506)(457,513)(458,512)(459,511)(460,517)(461,519)(462,518)(463,514)
(464,516)(465,515)(466,522)(467,521)(468,520)(469,562)(470,564)(471,563)
(472,559)(473,561)(474,560)(475,567)(476,566)(477,565)(478,571)(479,573)
(480,572)(481,568)(482,570)(483,569)(484,576)(485,575)(486,574)(487,544)
(488,546)(489,545)(490,541)(491,543)(492,542)(493,549)(494,548)(495,547)
(496,553)(497,555)(498,554)(499,550)(500,552)(501,551)(502,558)(503,557)
(504,556);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope