Polytope of Type {4,8,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,18}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98765)
Rank : 4
Schlafli Type : {4,8,18}
Number of vertices, edges, etc : 4, 16, 72, 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
3-fold quotients : {4,8,6}*384b
4-fold quotients : {2,4,18}*288a, {4,2,18}*288
6-fold quotients : {4,4,6}*192
8-fold quotients : {4,2,9}*144, {2,2,18}*144
9-fold quotients : {4,8,2}*128b
12-fold quotients : {2,4,6}*96a, {4,2,6}*96
16-fold quotients : {2,2,9}*72
18-fold quotients : {4,4,2}*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 := ( 1,145)( 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)( 37,190)( 38,191)( 39,192)( 40,193)
( 41,194)( 42,195)( 43,196)( 44,197)( 45,198)( 46,181)( 47,182)( 48,183)
( 49,184)( 50,185)( 51,186)( 52,187)( 53,188)( 54,189)( 55,208)( 56,209)
( 57,210)( 58,211)( 59,212)( 60,213)( 61,214)( 62,215)( 63,216)( 64,199)
( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)( 72,207)
( 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)(109,262)(110,263)(111,264)(112,265)
(113,266)(114,267)(115,268)(116,269)(117,270)(118,253)(119,254)(120,255)
(121,256)(122,257)(123,258)(124,259)(125,260)(126,261)(127,280)(128,281)
(129,282)(130,283)(131,284)(132,285)(133,286)(134,287)(135,288)(136,271)
(137,272)(138,273)(139,274)(140,275)(141,276)(142,277)(143,278)(144,279)
(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)(325,478)(326,479)(327,480)(328,481)
(329,482)(330,483)(331,484)(332,485)(333,486)(334,469)(335,470)(336,471)
(337,472)(338,473)(339,474)(340,475)(341,476)(342,477)(343,496)(344,497)
(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)(352,487)
(353,488)(354,489)(355,490)(356,491)(357,492)(358,493)(359,494)(360,495)
(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)(397,550)(398,551)(399,552)(400,553)
(401,554)(402,555)(403,556)(404,557)(405,558)(406,541)(407,542)(408,543)
(409,544)(410,545)(411,546)(412,547)(413,548)(414,549)(415,568)(416,569)
(417,570)(418,571)(419,572)(420,573)(421,574)(422,575)(423,576)(424,559)
(425,560)(426,561)(427,562)(428,563)(429,564)(430,565)(431,566)(432,567);;
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)(433,496)(434,497)(435,498)(436,499)
(437,500)(438,501)(439,502)(440,503)(441,504)(442,487)(443,488)(444,489)
(445,490)(446,491)(447,492)(448,493)(449,494)(450,495)(451,478)(452,479)
(453,480)(454,481)(455,482)(456,483)(457,484)(458,485)(459,486)(460,469)
(461,470)(462,471)(463,472)(464,473)(465,474)(466,475)(467,476)(468,477)
(505,568)(506,569)(507,570)(508,571)(509,572)(510,573)(511,574)(512,575)
(513,576)(514,559)(515,560)(516,561)(517,562)(518,563)(519,564)(520,565)
(521,566)(522,567)(523,550)(524,551)(525,552)(526,553)(527,554)(528,555)
(529,556)(530,557)(531,558)(532,541)(533,542)(534,543)(535,544)(536,545)
(537,546)(538,547)(539,548)(540,549);;
s2 := ( 1,361)( 2,363)( 3,362)( 4,369)( 5,368)( 6,367)( 7,366)( 8,365)
( 9,364)( 10,370)( 11,372)( 12,371)( 13,378)( 14,377)( 15,376)( 16,375)
( 17,374)( 18,373)( 19,388)( 20,390)( 21,389)( 22,396)( 23,395)( 24,394)
( 25,393)( 26,392)( 27,391)( 28,379)( 29,381)( 30,380)( 31,387)( 32,386)
( 33,385)( 34,384)( 35,383)( 36,382)( 37,406)( 38,408)( 39,407)( 40,414)
( 41,413)( 42,412)( 43,411)( 44,410)( 45,409)( 46,397)( 47,399)( 48,398)
( 49,405)( 50,404)( 51,403)( 52,402)( 53,401)( 54,400)( 55,415)( 56,417)
( 57,416)( 58,423)( 59,422)( 60,421)( 61,420)( 62,419)( 63,418)( 64,424)
( 65,426)( 66,425)( 67,432)( 68,431)( 69,430)( 70,429)( 71,428)( 72,427)
( 73,289)( 74,291)( 75,290)( 76,297)( 77,296)( 78,295)( 79,294)( 80,293)
( 81,292)( 82,298)( 83,300)( 84,299)( 85,306)( 86,305)( 87,304)( 88,303)
( 89,302)( 90,301)( 91,316)( 92,318)( 93,317)( 94,324)( 95,323)( 96,322)
( 97,321)( 98,320)( 99,319)(100,307)(101,309)(102,308)(103,315)(104,314)
(105,313)(106,312)(107,311)(108,310)(109,334)(110,336)(111,335)(112,342)
(113,341)(114,340)(115,339)(116,338)(117,337)(118,325)(119,327)(120,326)
(121,333)(122,332)(123,331)(124,330)(125,329)(126,328)(127,343)(128,345)
(129,344)(130,351)(131,350)(132,349)(133,348)(134,347)(135,346)(136,352)
(137,354)(138,353)(139,360)(140,359)(141,358)(142,357)(143,356)(144,355)
(145,505)(146,507)(147,506)(148,513)(149,512)(150,511)(151,510)(152,509)
(153,508)(154,514)(155,516)(156,515)(157,522)(158,521)(159,520)(160,519)
(161,518)(162,517)(163,532)(164,534)(165,533)(166,540)(167,539)(168,538)
(169,537)(170,536)(171,535)(172,523)(173,525)(174,524)(175,531)(176,530)
(177,529)(178,528)(179,527)(180,526)(181,550)(182,552)(183,551)(184,558)
(185,557)(186,556)(187,555)(188,554)(189,553)(190,541)(191,543)(192,542)
(193,549)(194,548)(195,547)(196,546)(197,545)(198,544)(199,559)(200,561)
(201,560)(202,567)(203,566)(204,565)(205,564)(206,563)(207,562)(208,568)
(209,570)(210,569)(211,576)(212,575)(213,574)(214,573)(215,572)(216,571)
(217,433)(218,435)(219,434)(220,441)(221,440)(222,439)(223,438)(224,437)
(225,436)(226,442)(227,444)(228,443)(229,450)(230,449)(231,448)(232,447)
(233,446)(234,445)(235,460)(236,462)(237,461)(238,468)(239,467)(240,466)
(241,465)(242,464)(243,463)(244,451)(245,453)(246,452)(247,459)(248,458)
(249,457)(250,456)(251,455)(252,454)(253,478)(254,480)(255,479)(256,486)
(257,485)(258,484)(259,483)(260,482)(261,481)(262,469)(263,471)(264,470)
(265,477)(266,476)(267,475)(268,474)(269,473)(270,472)(271,487)(272,489)
(273,488)(274,495)(275,494)(276,493)(277,492)(278,491)(279,490)(280,496)
(281,498)(282,497)(283,504)(284,503)(285,502)(286,501)(287,500)(288,499);;
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*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*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)!( 1,145)( 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)( 37,190)( 38,191)( 39,192)
( 40,193)( 41,194)( 42,195)( 43,196)( 44,197)( 45,198)( 46,181)( 47,182)
( 48,183)( 49,184)( 50,185)( 51,186)( 52,187)( 53,188)( 54,189)( 55,208)
( 56,209)( 57,210)( 58,211)( 59,212)( 60,213)( 61,214)( 62,215)( 63,216)
( 64,199)( 65,200)( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)
( 72,207)( 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)(109,262)(110,263)(111,264)
(112,265)(113,266)(114,267)(115,268)(116,269)(117,270)(118,253)(119,254)
(120,255)(121,256)(122,257)(123,258)(124,259)(125,260)(126,261)(127,280)
(128,281)(129,282)(130,283)(131,284)(132,285)(133,286)(134,287)(135,288)
(136,271)(137,272)(138,273)(139,274)(140,275)(141,276)(142,277)(143,278)
(144,279)(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)(325,478)(326,479)(327,480)
(328,481)(329,482)(330,483)(331,484)(332,485)(333,486)(334,469)(335,470)
(336,471)(337,472)(338,473)(339,474)(340,475)(341,476)(342,477)(343,496)
(344,497)(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)
(352,487)(353,488)(354,489)(355,490)(356,491)(357,492)(358,493)(359,494)
(360,495)(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)(397,550)(398,551)(399,552)
(400,553)(401,554)(402,555)(403,556)(404,557)(405,558)(406,541)(407,542)
(408,543)(409,544)(410,545)(411,546)(412,547)(413,548)(414,549)(415,568)
(416,569)(417,570)(418,571)(419,572)(420,573)(421,574)(422,575)(423,576)
(424,559)(425,560)(426,561)(427,562)(428,563)(429,564)(430,565)(431,566)
(432,567);
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)(433,496)(434,497)(435,498)
(436,499)(437,500)(438,501)(439,502)(440,503)(441,504)(442,487)(443,488)
(444,489)(445,490)(446,491)(447,492)(448,493)(449,494)(450,495)(451,478)
(452,479)(453,480)(454,481)(455,482)(456,483)(457,484)(458,485)(459,486)
(460,469)(461,470)(462,471)(463,472)(464,473)(465,474)(466,475)(467,476)
(468,477)(505,568)(506,569)(507,570)(508,571)(509,572)(510,573)(511,574)
(512,575)(513,576)(514,559)(515,560)(516,561)(517,562)(518,563)(519,564)
(520,565)(521,566)(522,567)(523,550)(524,551)(525,552)(526,553)(527,554)
(528,555)(529,556)(530,557)(531,558)(532,541)(533,542)(534,543)(535,544)
(536,545)(537,546)(538,547)(539,548)(540,549);
s2 := Sym(576)!( 1,361)( 2,363)( 3,362)( 4,369)( 5,368)( 6,367)( 7,366)
( 8,365)( 9,364)( 10,370)( 11,372)( 12,371)( 13,378)( 14,377)( 15,376)
( 16,375)( 17,374)( 18,373)( 19,388)( 20,390)( 21,389)( 22,396)( 23,395)
( 24,394)( 25,393)( 26,392)( 27,391)( 28,379)( 29,381)( 30,380)( 31,387)
( 32,386)( 33,385)( 34,384)( 35,383)( 36,382)( 37,406)( 38,408)( 39,407)
( 40,414)( 41,413)( 42,412)( 43,411)( 44,410)( 45,409)( 46,397)( 47,399)
( 48,398)( 49,405)( 50,404)( 51,403)( 52,402)( 53,401)( 54,400)( 55,415)
( 56,417)( 57,416)( 58,423)( 59,422)( 60,421)( 61,420)( 62,419)( 63,418)
( 64,424)( 65,426)( 66,425)( 67,432)( 68,431)( 69,430)( 70,429)( 71,428)
( 72,427)( 73,289)( 74,291)( 75,290)( 76,297)( 77,296)( 78,295)( 79,294)
( 80,293)( 81,292)( 82,298)( 83,300)( 84,299)( 85,306)( 86,305)( 87,304)
( 88,303)( 89,302)( 90,301)( 91,316)( 92,318)( 93,317)( 94,324)( 95,323)
( 96,322)( 97,321)( 98,320)( 99,319)(100,307)(101,309)(102,308)(103,315)
(104,314)(105,313)(106,312)(107,311)(108,310)(109,334)(110,336)(111,335)
(112,342)(113,341)(114,340)(115,339)(116,338)(117,337)(118,325)(119,327)
(120,326)(121,333)(122,332)(123,331)(124,330)(125,329)(126,328)(127,343)
(128,345)(129,344)(130,351)(131,350)(132,349)(133,348)(134,347)(135,346)
(136,352)(137,354)(138,353)(139,360)(140,359)(141,358)(142,357)(143,356)
(144,355)(145,505)(146,507)(147,506)(148,513)(149,512)(150,511)(151,510)
(152,509)(153,508)(154,514)(155,516)(156,515)(157,522)(158,521)(159,520)
(160,519)(161,518)(162,517)(163,532)(164,534)(165,533)(166,540)(167,539)
(168,538)(169,537)(170,536)(171,535)(172,523)(173,525)(174,524)(175,531)
(176,530)(177,529)(178,528)(179,527)(180,526)(181,550)(182,552)(183,551)
(184,558)(185,557)(186,556)(187,555)(188,554)(189,553)(190,541)(191,543)
(192,542)(193,549)(194,548)(195,547)(196,546)(197,545)(198,544)(199,559)
(200,561)(201,560)(202,567)(203,566)(204,565)(205,564)(206,563)(207,562)
(208,568)(209,570)(210,569)(211,576)(212,575)(213,574)(214,573)(215,572)
(216,571)(217,433)(218,435)(219,434)(220,441)(221,440)(222,439)(223,438)
(224,437)(225,436)(226,442)(227,444)(228,443)(229,450)(230,449)(231,448)
(232,447)(233,446)(234,445)(235,460)(236,462)(237,461)(238,468)(239,467)
(240,466)(241,465)(242,464)(243,463)(244,451)(245,453)(246,452)(247,459)
(248,458)(249,457)(250,456)(251,455)(252,454)(253,478)(254,480)(255,479)
(256,486)(257,485)(258,484)(259,483)(260,482)(261,481)(262,469)(263,471)
(264,470)(265,477)(266,476)(267,475)(268,474)(269,473)(270,472)(271,487)
(272,489)(273,488)(274,495)(275,494)(276,493)(277,492)(278,491)(279,490)
(280,496)(281,498)(282,497)(283,504)(284,503)(285,502)(286,501)(287,500)
(288,499);
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*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*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