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Polytope of Type {4,18,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,155402)
Rank : 4
Schlafli Type : {4,18,4}
Number of vertices, edges, etc : 4, 72, 72, 8
Order of s0s1s2s3 : 36
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}*576b, {2,18,4}*576
   3-fold quotients : {4,6,4}*384a
   4-fold quotients : {4,18,2}*288a, {2,9,4}*288, {2,18,4}*288b, {2,18,4}*288c
   6-fold quotients : {4,6,4}*192b, {2,6,4}*192
   8-fold quotients : {2,9,4}*144, {2,18,2}*144
   12-fold quotients : {4,6,2}*96a, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   16-fold quotients : {2,9,2}*72
   24-fold quotients : {2,3,4}*48, {2,6,2}*48
   36-fold quotients : {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 := (  1,145)(  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)
( 73,253)( 74,254)( 75,255)( 76,256)( 77,257)( 78,258)( 79,259)( 80,260)
( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)( 88,268)
( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)( 96,276)
( 97,277)( 98,278)( 99,279)(100,280)(101,281)(102,282)(103,283)(104,284)
(105,285)(106,286)(107,287)(108,288)(109,217)(110,218)(111,219)(112,220)
(113,221)(114,222)(115,223)(116,224)(117,225)(118,226)(119,227)(120,228)
(121,229)(122,230)(123,231)(124,232)(125,233)(126,234)(127,235)(128,236)
(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)(136,244)
(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,251)(144,252)
(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)
(361,541)(362,542)(363,543)(364,544)(365,545)(366,546)(367,547)(368,548)
(369,549)(370,550)(371,551)(372,552)(373,553)(374,554)(375,555)(376,556)
(377,557)(378,558)(379,559)(380,560)(381,561)(382,562)(383,563)(384,564)
(385,565)(386,566)(387,567)(388,568)(389,569)(390,570)(391,571)(392,572)
(393,573)(394,574)(395,575)(396,576)(397,505)(398,506)(399,507)(400,508)
(401,509)(402,510)(403,511)(404,512)(405,513)(406,514)(407,515)(408,516)
(409,517)(410,518)(411,519)(412,520)(413,521)(414,522)(415,523)(416,524)
(417,525)(418,526)(419,527)(420,528)(421,529)(422,530)(423,531)(424,532)
(425,533)(426,534)(427,535)(428,536)(429,537)(430,538)(431,539)(432,540);;
s1 := (  1, 73)(  2, 74)(  3, 76)(  4, 75)(  5, 81)(  6, 82)(  7, 84)(  8, 83)
(  9, 77)( 10, 78)( 11, 80)( 12, 79)( 13,105)( 14,106)( 15,108)( 16,107)
( 17,101)( 18,102)( 19,104)( 20,103)( 21, 97)( 22, 98)( 23,100)( 24, 99)
( 25, 93)( 26, 94)( 27, 96)( 28, 95)( 29, 89)( 30, 90)( 31, 92)( 32, 91)
( 33, 85)( 34, 86)( 35, 88)( 36, 87)( 37,109)( 38,110)( 39,112)( 40,111)
( 41,117)( 42,118)( 43,120)( 44,119)( 45,113)( 46,114)( 47,116)( 48,115)
( 49,141)( 50,142)( 51,144)( 52,143)( 53,137)( 54,138)( 55,140)( 56,139)
( 57,133)( 58,134)( 59,136)( 60,135)( 61,129)( 62,130)( 63,132)( 64,131)
( 65,125)( 66,126)( 67,128)( 68,127)( 69,121)( 70,122)( 71,124)( 72,123)
(145,217)(146,218)(147,220)(148,219)(149,225)(150,226)(151,228)(152,227)
(153,221)(154,222)(155,224)(156,223)(157,249)(158,250)(159,252)(160,251)
(161,245)(162,246)(163,248)(164,247)(165,241)(166,242)(167,244)(168,243)
(169,237)(170,238)(171,240)(172,239)(173,233)(174,234)(175,236)(176,235)
(177,229)(178,230)(179,232)(180,231)(181,253)(182,254)(183,256)(184,255)
(185,261)(186,262)(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)
(193,285)(194,286)(195,288)(196,287)(197,281)(198,282)(199,284)(200,283)
(201,277)(202,278)(203,280)(204,279)(205,273)(206,274)(207,276)(208,275)
(209,269)(210,270)(211,272)(212,271)(213,265)(214,266)(215,268)(216,267)
(289,361)(290,362)(291,364)(292,363)(293,369)(294,370)(295,372)(296,371)
(297,365)(298,366)(299,368)(300,367)(301,393)(302,394)(303,396)(304,395)
(305,389)(306,390)(307,392)(308,391)(309,385)(310,386)(311,388)(312,387)
(313,381)(314,382)(315,384)(316,383)(317,377)(318,378)(319,380)(320,379)
(321,373)(322,374)(323,376)(324,375)(325,397)(326,398)(327,400)(328,399)
(329,405)(330,406)(331,408)(332,407)(333,401)(334,402)(335,404)(336,403)
(337,429)(338,430)(339,432)(340,431)(341,425)(342,426)(343,428)(344,427)
(345,421)(346,422)(347,424)(348,423)(349,417)(350,418)(351,420)(352,419)
(353,413)(354,414)(355,416)(356,415)(357,409)(358,410)(359,412)(360,411)
(433,505)(434,506)(435,508)(436,507)(437,513)(438,514)(439,516)(440,515)
(441,509)(442,510)(443,512)(444,511)(445,537)(446,538)(447,540)(448,539)
(449,533)(450,534)(451,536)(452,535)(453,529)(454,530)(455,532)(456,531)
(457,525)(458,526)(459,528)(460,527)(461,521)(462,522)(463,524)(464,523)
(465,517)(466,518)(467,520)(468,519)(469,541)(470,542)(471,544)(472,543)
(473,549)(474,550)(475,552)(476,551)(477,545)(478,546)(479,548)(480,547)
(481,573)(482,574)(483,576)(484,575)(485,569)(486,570)(487,572)(488,571)
(489,565)(490,566)(491,568)(492,567)(493,561)(494,562)(495,564)(496,563)
(497,557)(498,558)(499,560)(500,559)(501,553)(502,554)(503,556)(504,555);;
s2 := (  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 21)(  6, 24)(  7, 23)(  8, 22)
(  9, 17)( 10, 20)( 11, 19)( 12, 18)( 25, 33)( 26, 36)( 27, 35)( 28, 34)
( 30, 32)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)( 43, 59)
( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 61, 69)( 62, 72)( 63, 71)
( 64, 70)( 66, 68)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)( 78, 96)
( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 97,105)( 98,108)
( 99,107)(100,106)(102,104)(109,121)(110,124)(111,123)(112,122)(113,129)
(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)(133,141)
(134,144)(135,143)(136,142)(138,140)(145,157)(146,160)(147,159)(148,158)
(149,165)(150,168)(151,167)(152,166)(153,161)(154,164)(155,163)(156,162)
(169,177)(170,180)(171,179)(172,178)(174,176)(181,193)(182,196)(183,195)
(184,194)(185,201)(186,204)(187,203)(188,202)(189,197)(190,200)(191,199)
(192,198)(205,213)(206,216)(207,215)(208,214)(210,212)(217,229)(218,232)
(219,231)(220,230)(221,237)(222,240)(223,239)(224,238)(225,233)(226,236)
(227,235)(228,234)(241,249)(242,252)(243,251)(244,250)(246,248)(253,265)
(254,268)(255,267)(256,266)(257,273)(258,276)(259,275)(260,274)(261,269)
(262,272)(263,271)(264,270)(277,285)(278,288)(279,287)(280,286)(282,284)
(289,301)(290,304)(291,303)(292,302)(293,309)(294,312)(295,311)(296,310)
(297,305)(298,308)(299,307)(300,306)(313,321)(314,324)(315,323)(316,322)
(318,320)(325,337)(326,340)(327,339)(328,338)(329,345)(330,348)(331,347)
(332,346)(333,341)(334,344)(335,343)(336,342)(349,357)(350,360)(351,359)
(352,358)(354,356)(361,373)(362,376)(363,375)(364,374)(365,381)(366,384)
(367,383)(368,382)(369,377)(370,380)(371,379)(372,378)(385,393)(386,396)
(387,395)(388,394)(390,392)(397,409)(398,412)(399,411)(400,410)(401,417)
(402,420)(403,419)(404,418)(405,413)(406,416)(407,415)(408,414)(421,429)
(422,432)(423,431)(424,430)(426,428)(433,445)(434,448)(435,447)(436,446)
(437,453)(438,456)(439,455)(440,454)(441,449)(442,452)(443,451)(444,450)
(457,465)(458,468)(459,467)(460,466)(462,464)(469,481)(470,484)(471,483)
(472,482)(473,489)(474,492)(475,491)(476,490)(477,485)(478,488)(479,487)
(480,486)(493,501)(494,504)(495,503)(496,502)(498,500)(505,517)(506,520)
(507,519)(508,518)(509,525)(510,528)(511,527)(512,526)(513,521)(514,524)
(515,523)(516,522)(529,537)(530,540)(531,539)(532,538)(534,536)(541,553)
(542,556)(543,555)(544,554)(545,561)(546,564)(547,563)(548,562)(549,557)
(550,560)(551,559)(552,558)(565,573)(566,576)(567,575)(568,574)(570,572);;
s3 := (  1,290)(  2,289)(  3,292)(  4,291)(  5,294)(  6,293)(  7,296)(  8,295)
(  9,298)( 10,297)( 11,300)( 12,299)( 13,302)( 14,301)( 15,304)( 16,303)
( 17,306)( 18,305)( 19,308)( 20,307)( 21,310)( 22,309)( 23,312)( 24,311)
( 25,314)( 26,313)( 27,316)( 28,315)( 29,318)( 30,317)( 31,320)( 32,319)
( 33,322)( 34,321)( 35,324)( 36,323)( 37,326)( 38,325)( 39,328)( 40,327)
( 41,330)( 42,329)( 43,332)( 44,331)( 45,334)( 46,333)( 47,336)( 48,335)
( 49,338)( 50,337)( 51,340)( 52,339)( 53,342)( 54,341)( 55,344)( 56,343)
( 57,346)( 58,345)( 59,348)( 60,347)( 61,350)( 62,349)( 63,352)( 64,351)
( 65,354)( 66,353)( 67,356)( 68,355)( 69,358)( 70,357)( 71,360)( 72,359)
( 73,362)( 74,361)( 75,364)( 76,363)( 77,366)( 78,365)( 79,368)( 80,367)
( 81,370)( 82,369)( 83,372)( 84,371)( 85,374)( 86,373)( 87,376)( 88,375)
( 89,378)( 90,377)( 91,380)( 92,379)( 93,382)( 94,381)( 95,384)( 96,383)
( 97,386)( 98,385)( 99,388)(100,387)(101,390)(102,389)(103,392)(104,391)
(105,394)(106,393)(107,396)(108,395)(109,398)(110,397)(111,400)(112,399)
(113,402)(114,401)(115,404)(116,403)(117,406)(118,405)(119,408)(120,407)
(121,410)(122,409)(123,412)(124,411)(125,414)(126,413)(127,416)(128,415)
(129,418)(130,417)(131,420)(132,419)(133,422)(134,421)(135,424)(136,423)
(137,426)(138,425)(139,428)(140,427)(141,430)(142,429)(143,432)(144,431)
(145,434)(146,433)(147,436)(148,435)(149,438)(150,437)(151,440)(152,439)
(153,442)(154,441)(155,444)(156,443)(157,446)(158,445)(159,448)(160,447)
(161,450)(162,449)(163,452)(164,451)(165,454)(166,453)(167,456)(168,455)
(169,458)(170,457)(171,460)(172,459)(173,462)(174,461)(175,464)(176,463)
(177,466)(178,465)(179,468)(180,467)(181,470)(182,469)(183,472)(184,471)
(185,474)(186,473)(187,476)(188,475)(189,478)(190,477)(191,480)(192,479)
(193,482)(194,481)(195,484)(196,483)(197,486)(198,485)(199,488)(200,487)
(201,490)(202,489)(203,492)(204,491)(205,494)(206,493)(207,496)(208,495)
(209,498)(210,497)(211,500)(212,499)(213,502)(214,501)(215,504)(216,503)
(217,506)(218,505)(219,508)(220,507)(221,510)(222,509)(223,512)(224,511)
(225,514)(226,513)(227,516)(228,515)(229,518)(230,517)(231,520)(232,519)
(233,522)(234,521)(235,524)(236,523)(237,526)(238,525)(239,528)(240,527)
(241,530)(242,529)(243,532)(244,531)(245,534)(246,533)(247,536)(248,535)
(249,538)(250,537)(251,540)(252,539)(253,542)(254,541)(255,544)(256,543)
(257,546)(258,545)(259,548)(260,547)(261,550)(262,549)(263,552)(264,551)
(265,554)(266,553)(267,556)(268,555)(269,558)(270,557)(271,560)(272,559)
(273,562)(274,561)(275,564)(276,563)(277,566)(278,565)(279,568)(280,567)
(281,570)(282,569)(283,572)(284,571)(285,574)(286,573)(287,576)(288,575);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := 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)( 73,253)( 74,254)( 75,255)( 76,256)( 77,257)( 78,258)( 79,259)
( 80,260)( 81,261)( 82,262)( 83,263)( 84,264)( 85,265)( 86,266)( 87,267)
( 88,268)( 89,269)( 90,270)( 91,271)( 92,272)( 93,273)( 94,274)( 95,275)
( 96,276)( 97,277)( 98,278)( 99,279)(100,280)(101,281)(102,282)(103,283)
(104,284)(105,285)(106,286)(107,287)(108,288)(109,217)(110,218)(111,219)
(112,220)(113,221)(114,222)(115,223)(116,224)(117,225)(118,226)(119,227)
(120,228)(121,229)(122,230)(123,231)(124,232)(125,233)(126,234)(127,235)
(128,236)(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)
(136,244)(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,251)
(144,252)(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)(361,541)(362,542)(363,543)(364,544)(365,545)(366,546)(367,547)
(368,548)(369,549)(370,550)(371,551)(372,552)(373,553)(374,554)(375,555)
(376,556)(377,557)(378,558)(379,559)(380,560)(381,561)(382,562)(383,563)
(384,564)(385,565)(386,566)(387,567)(388,568)(389,569)(390,570)(391,571)
(392,572)(393,573)(394,574)(395,575)(396,576)(397,505)(398,506)(399,507)
(400,508)(401,509)(402,510)(403,511)(404,512)(405,513)(406,514)(407,515)
(408,516)(409,517)(410,518)(411,519)(412,520)(413,521)(414,522)(415,523)
(416,524)(417,525)(418,526)(419,527)(420,528)(421,529)(422,530)(423,531)
(424,532)(425,533)(426,534)(427,535)(428,536)(429,537)(430,538)(431,539)
(432,540);
s1 := Sym(576)!(  1, 73)(  2, 74)(  3, 76)(  4, 75)(  5, 81)(  6, 82)(  7, 84)
(  8, 83)(  9, 77)( 10, 78)( 11, 80)( 12, 79)( 13,105)( 14,106)( 15,108)
( 16,107)( 17,101)( 18,102)( 19,104)( 20,103)( 21, 97)( 22, 98)( 23,100)
( 24, 99)( 25, 93)( 26, 94)( 27, 96)( 28, 95)( 29, 89)( 30, 90)( 31, 92)
( 32, 91)( 33, 85)( 34, 86)( 35, 88)( 36, 87)( 37,109)( 38,110)( 39,112)
( 40,111)( 41,117)( 42,118)( 43,120)( 44,119)( 45,113)( 46,114)( 47,116)
( 48,115)( 49,141)( 50,142)( 51,144)( 52,143)( 53,137)( 54,138)( 55,140)
( 56,139)( 57,133)( 58,134)( 59,136)( 60,135)( 61,129)( 62,130)( 63,132)
( 64,131)( 65,125)( 66,126)( 67,128)( 68,127)( 69,121)( 70,122)( 71,124)
( 72,123)(145,217)(146,218)(147,220)(148,219)(149,225)(150,226)(151,228)
(152,227)(153,221)(154,222)(155,224)(156,223)(157,249)(158,250)(159,252)
(160,251)(161,245)(162,246)(163,248)(164,247)(165,241)(166,242)(167,244)
(168,243)(169,237)(170,238)(171,240)(172,239)(173,233)(174,234)(175,236)
(176,235)(177,229)(178,230)(179,232)(180,231)(181,253)(182,254)(183,256)
(184,255)(185,261)(186,262)(187,264)(188,263)(189,257)(190,258)(191,260)
(192,259)(193,285)(194,286)(195,288)(196,287)(197,281)(198,282)(199,284)
(200,283)(201,277)(202,278)(203,280)(204,279)(205,273)(206,274)(207,276)
(208,275)(209,269)(210,270)(211,272)(212,271)(213,265)(214,266)(215,268)
(216,267)(289,361)(290,362)(291,364)(292,363)(293,369)(294,370)(295,372)
(296,371)(297,365)(298,366)(299,368)(300,367)(301,393)(302,394)(303,396)
(304,395)(305,389)(306,390)(307,392)(308,391)(309,385)(310,386)(311,388)
(312,387)(313,381)(314,382)(315,384)(316,383)(317,377)(318,378)(319,380)
(320,379)(321,373)(322,374)(323,376)(324,375)(325,397)(326,398)(327,400)
(328,399)(329,405)(330,406)(331,408)(332,407)(333,401)(334,402)(335,404)
(336,403)(337,429)(338,430)(339,432)(340,431)(341,425)(342,426)(343,428)
(344,427)(345,421)(346,422)(347,424)(348,423)(349,417)(350,418)(351,420)
(352,419)(353,413)(354,414)(355,416)(356,415)(357,409)(358,410)(359,412)
(360,411)(433,505)(434,506)(435,508)(436,507)(437,513)(438,514)(439,516)
(440,515)(441,509)(442,510)(443,512)(444,511)(445,537)(446,538)(447,540)
(448,539)(449,533)(450,534)(451,536)(452,535)(453,529)(454,530)(455,532)
(456,531)(457,525)(458,526)(459,528)(460,527)(461,521)(462,522)(463,524)
(464,523)(465,517)(466,518)(467,520)(468,519)(469,541)(470,542)(471,544)
(472,543)(473,549)(474,550)(475,552)(476,551)(477,545)(478,546)(479,548)
(480,547)(481,573)(482,574)(483,576)(484,575)(485,569)(486,570)(487,572)
(488,571)(489,565)(490,566)(491,568)(492,567)(493,561)(494,562)(495,564)
(496,563)(497,557)(498,558)(499,560)(500,559)(501,553)(502,554)(503,556)
(504,555);
s2 := Sym(576)!(  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 21)(  6, 24)(  7, 23)
(  8, 22)(  9, 17)( 10, 20)( 11, 19)( 12, 18)( 25, 33)( 26, 36)( 27, 35)
( 28, 34)( 30, 32)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)
( 43, 59)( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 61, 69)( 62, 72)
( 63, 71)( 64, 70)( 66, 68)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)
( 78, 96)( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 97,105)
( 98,108)( 99,107)(100,106)(102,104)(109,121)(110,124)(111,123)(112,122)
(113,129)(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)
(133,141)(134,144)(135,143)(136,142)(138,140)(145,157)(146,160)(147,159)
(148,158)(149,165)(150,168)(151,167)(152,166)(153,161)(154,164)(155,163)
(156,162)(169,177)(170,180)(171,179)(172,178)(174,176)(181,193)(182,196)
(183,195)(184,194)(185,201)(186,204)(187,203)(188,202)(189,197)(190,200)
(191,199)(192,198)(205,213)(206,216)(207,215)(208,214)(210,212)(217,229)
(218,232)(219,231)(220,230)(221,237)(222,240)(223,239)(224,238)(225,233)
(226,236)(227,235)(228,234)(241,249)(242,252)(243,251)(244,250)(246,248)
(253,265)(254,268)(255,267)(256,266)(257,273)(258,276)(259,275)(260,274)
(261,269)(262,272)(263,271)(264,270)(277,285)(278,288)(279,287)(280,286)
(282,284)(289,301)(290,304)(291,303)(292,302)(293,309)(294,312)(295,311)
(296,310)(297,305)(298,308)(299,307)(300,306)(313,321)(314,324)(315,323)
(316,322)(318,320)(325,337)(326,340)(327,339)(328,338)(329,345)(330,348)
(331,347)(332,346)(333,341)(334,344)(335,343)(336,342)(349,357)(350,360)
(351,359)(352,358)(354,356)(361,373)(362,376)(363,375)(364,374)(365,381)
(366,384)(367,383)(368,382)(369,377)(370,380)(371,379)(372,378)(385,393)
(386,396)(387,395)(388,394)(390,392)(397,409)(398,412)(399,411)(400,410)
(401,417)(402,420)(403,419)(404,418)(405,413)(406,416)(407,415)(408,414)
(421,429)(422,432)(423,431)(424,430)(426,428)(433,445)(434,448)(435,447)
(436,446)(437,453)(438,456)(439,455)(440,454)(441,449)(442,452)(443,451)
(444,450)(457,465)(458,468)(459,467)(460,466)(462,464)(469,481)(470,484)
(471,483)(472,482)(473,489)(474,492)(475,491)(476,490)(477,485)(478,488)
(479,487)(480,486)(493,501)(494,504)(495,503)(496,502)(498,500)(505,517)
(506,520)(507,519)(508,518)(509,525)(510,528)(511,527)(512,526)(513,521)
(514,524)(515,523)(516,522)(529,537)(530,540)(531,539)(532,538)(534,536)
(541,553)(542,556)(543,555)(544,554)(545,561)(546,564)(547,563)(548,562)
(549,557)(550,560)(551,559)(552,558)(565,573)(566,576)(567,575)(568,574)
(570,572);
s3 := Sym(576)!(  1,290)(  2,289)(  3,292)(  4,291)(  5,294)(  6,293)(  7,296)
(  8,295)(  9,298)( 10,297)( 11,300)( 12,299)( 13,302)( 14,301)( 15,304)
( 16,303)( 17,306)( 18,305)( 19,308)( 20,307)( 21,310)( 22,309)( 23,312)
( 24,311)( 25,314)( 26,313)( 27,316)( 28,315)( 29,318)( 30,317)( 31,320)
( 32,319)( 33,322)( 34,321)( 35,324)( 36,323)( 37,326)( 38,325)( 39,328)
( 40,327)( 41,330)( 42,329)( 43,332)( 44,331)( 45,334)( 46,333)( 47,336)
( 48,335)( 49,338)( 50,337)( 51,340)( 52,339)( 53,342)( 54,341)( 55,344)
( 56,343)( 57,346)( 58,345)( 59,348)( 60,347)( 61,350)( 62,349)( 63,352)
( 64,351)( 65,354)( 66,353)( 67,356)( 68,355)( 69,358)( 70,357)( 71,360)
( 72,359)( 73,362)( 74,361)( 75,364)( 76,363)( 77,366)( 78,365)( 79,368)
( 80,367)( 81,370)( 82,369)( 83,372)( 84,371)( 85,374)( 86,373)( 87,376)
( 88,375)( 89,378)( 90,377)( 91,380)( 92,379)( 93,382)( 94,381)( 95,384)
( 96,383)( 97,386)( 98,385)( 99,388)(100,387)(101,390)(102,389)(103,392)
(104,391)(105,394)(106,393)(107,396)(108,395)(109,398)(110,397)(111,400)
(112,399)(113,402)(114,401)(115,404)(116,403)(117,406)(118,405)(119,408)
(120,407)(121,410)(122,409)(123,412)(124,411)(125,414)(126,413)(127,416)
(128,415)(129,418)(130,417)(131,420)(132,419)(133,422)(134,421)(135,424)
(136,423)(137,426)(138,425)(139,428)(140,427)(141,430)(142,429)(143,432)
(144,431)(145,434)(146,433)(147,436)(148,435)(149,438)(150,437)(151,440)
(152,439)(153,442)(154,441)(155,444)(156,443)(157,446)(158,445)(159,448)
(160,447)(161,450)(162,449)(163,452)(164,451)(165,454)(166,453)(167,456)
(168,455)(169,458)(170,457)(171,460)(172,459)(173,462)(174,461)(175,464)
(176,463)(177,466)(178,465)(179,468)(180,467)(181,470)(182,469)(183,472)
(184,471)(185,474)(186,473)(187,476)(188,475)(189,478)(190,477)(191,480)
(192,479)(193,482)(194,481)(195,484)(196,483)(197,486)(198,485)(199,488)
(200,487)(201,490)(202,489)(203,492)(204,491)(205,494)(206,493)(207,496)
(208,495)(209,498)(210,497)(211,500)(212,499)(213,502)(214,501)(215,504)
(216,503)(217,506)(218,505)(219,508)(220,507)(221,510)(222,509)(223,512)
(224,511)(225,514)(226,513)(227,516)(228,515)(229,518)(230,517)(231,520)
(232,519)(233,522)(234,521)(235,524)(236,523)(237,526)(238,525)(239,528)
(240,527)(241,530)(242,529)(243,532)(244,531)(245,534)(246,533)(247,536)
(248,535)(249,538)(250,537)(251,540)(252,539)(253,542)(254,541)(255,544)
(256,543)(257,546)(258,545)(259,548)(260,547)(261,550)(262,549)(263,552)
(264,551)(265,554)(266,553)(267,556)(268,555)(269,558)(270,557)(271,560)
(272,559)(273,562)(274,561)(275,564)(276,563)(277,566)(278,565)(279,568)
(280,567)(281,570)(282,569)(283,572)(284,571)(285,574)(286,573)(287,576)
(288,575);
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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope