Polytope of Type {4,18,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18,8}*1152a
Also Known As : {{4,18|2},{18,8|2}}. if this polytope has another name.
Group : SmallGroup(1152,119725)
Rank : 4
Schlafli Type : {4,18,8}
Number of vertices, edges, etc : 4, 36, 72, 8
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, {2,18,8}*576
3-fold quotients : {4,6,8}*384a
4-fold quotients : {2,18,4}*288a, {4,18,2}*288a
6-fold quotients : {4,6,4}*192a, {2,6,8}*192
8-fold quotients : {2,18,2}*144
9-fold quotients : {4,2,8}*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, {2,2,8}*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 := ( 1,145)( 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);;
s1 := ( 1,109)( 2,111)( 3,110)( 4,117)( 5,116)( 6,115)( 7,114)( 8,113)
( 9,112)( 10,118)( 11,120)( 12,119)( 13,126)( 14,125)( 15,124)( 16,123)
( 17,122)( 18,121)( 19,127)( 20,129)( 21,128)( 22,135)( 23,134)( 24,133)
( 25,132)( 26,131)( 27,130)( 28,136)( 29,138)( 30,137)( 31,144)( 32,143)
( 33,142)( 34,141)( 35,140)( 36,139)( 37, 82)( 38, 84)( 39, 83)( 40, 90)
( 41, 89)( 42, 88)( 43, 87)( 44, 86)( 45, 85)( 46, 73)( 47, 75)( 48, 74)
( 49, 81)( 50, 80)( 51, 79)( 52, 78)( 53, 77)( 54, 76)( 55,100)( 56,102)
( 57,101)( 58,108)( 59,107)( 60,106)( 61,105)( 62,104)( 63,103)( 64, 91)
( 65, 93)( 66, 92)( 67, 99)( 68, 98)( 69, 97)( 70, 96)( 71, 95)( 72, 94)
(145,271)(146,273)(147,272)(148,279)(149,278)(150,277)(151,276)(152,275)
(153,274)(154,280)(155,282)(156,281)(157,288)(158,287)(159,286)(160,285)
(161,284)(162,283)(163,253)(164,255)(165,254)(166,261)(167,260)(168,259)
(169,258)(170,257)(171,256)(172,262)(173,264)(174,263)(175,270)(176,269)
(177,268)(178,267)(179,266)(180,265)(181,244)(182,246)(183,245)(184,252)
(185,251)(186,250)(187,249)(188,248)(189,247)(190,235)(191,237)(192,236)
(193,243)(194,242)(195,241)(196,240)(197,239)(198,238)(199,226)(200,228)
(201,227)(202,234)(203,233)(204,232)(205,231)(206,230)(207,229)(208,217)
(209,219)(210,218)(211,225)(212,224)(213,223)(214,222)(215,221)(216,220)
(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)(325,397)(326,399)(327,398)(328,405)
(329,404)(330,403)(331,402)(332,401)(333,400)(334,406)(335,408)(336,407)
(337,414)(338,413)(339,412)(340,411)(341,410)(342,409)(343,415)(344,417)
(345,416)(346,423)(347,422)(348,421)(349,420)(350,419)(351,418)(352,424)
(353,426)(354,425)(355,432)(356,431)(357,430)(358,429)(359,428)(360,427)
(433,523)(434,525)(435,524)(436,531)(437,530)(438,529)(439,528)(440,527)
(441,526)(442,532)(443,534)(444,533)(445,540)(446,539)(447,538)(448,537)
(449,536)(450,535)(451,505)(452,507)(453,506)(454,513)(455,512)(456,511)
(457,510)(458,509)(459,508)(460,514)(461,516)(462,515)(463,522)(464,521)
(465,520)(466,519)(467,518)(468,517)(469,559)(470,561)(471,560)(472,567)
(473,566)(474,565)(475,564)(476,563)(477,562)(478,568)(479,570)(480,569)
(481,576)(482,575)(483,574)(484,573)(485,572)(486,571)(487,541)(488,543)
(489,542)(490,549)(491,548)(492,547)(493,546)(494,545)(495,544)(496,550)
(497,552)(498,551)(499,558)(500,557)(501,556)(502,555)(503,554)(504,553);;
s2 := ( 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)( 37,121)( 38,123)( 39,122)( 40,118)
( 41,120)( 42,119)( 43,126)( 44,125)( 45,124)( 46,112)( 47,114)( 48,113)
( 49,109)( 50,111)( 51,110)( 52,117)( 53,116)( 54,115)( 55,139)( 56,141)
( 57,140)( 58,136)( 59,138)( 60,137)( 61,144)( 62,143)( 63,142)( 64,130)
( 65,132)( 66,131)( 67,127)( 68,129)( 69,128)( 70,135)( 71,134)( 72,133)
(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)(181,265)(182,267)(183,266)(184,262)
(185,264)(186,263)(187,270)(188,269)(189,268)(190,256)(191,258)(192,257)
(193,253)(194,255)(195,254)(196,261)(197,260)(198,259)(199,283)(200,285)
(201,284)(202,280)(203,282)(204,281)(205,288)(206,287)(207,286)(208,274)
(209,276)(210,275)(211,271)(212,273)(213,272)(214,279)(215,278)(216,277)
(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)(325,409)(326,411)(327,410)(328,406)
(329,408)(330,407)(331,414)(332,413)(333,412)(334,400)(335,402)(336,401)
(337,397)(338,399)(339,398)(340,405)(341,404)(342,403)(343,427)(344,429)
(345,428)(346,424)(347,426)(348,425)(349,432)(350,431)(351,430)(352,418)
(353,420)(354,419)(355,415)(356,417)(357,416)(358,423)(359,422)(360,421)
(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)(469,553)(470,555)(471,554)(472,550)
(473,552)(474,551)(475,558)(476,557)(477,556)(478,544)(479,546)(480,545)
(481,541)(482,543)(483,542)(484,549)(485,548)(486,547)(487,571)(488,573)
(489,572)(490,568)(491,570)(492,569)(493,576)(494,575)(495,574)(496,562)
(497,564)(498,563)(499,559)(500,561)(501,560)(502,567)(503,566)(504,565);;
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)
( 73,397)( 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);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)( 73,217)( 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);
s1 := Sym(576)!( 1,109)( 2,111)( 3,110)( 4,117)( 5,116)( 6,115)( 7,114)
( 8,113)( 9,112)( 10,118)( 11,120)( 12,119)( 13,126)( 14,125)( 15,124)
( 16,123)( 17,122)( 18,121)( 19,127)( 20,129)( 21,128)( 22,135)( 23,134)
( 24,133)( 25,132)( 26,131)( 27,130)( 28,136)( 29,138)( 30,137)( 31,144)
( 32,143)( 33,142)( 34,141)( 35,140)( 36,139)( 37, 82)( 38, 84)( 39, 83)
( 40, 90)( 41, 89)( 42, 88)( 43, 87)( 44, 86)( 45, 85)( 46, 73)( 47, 75)
( 48, 74)( 49, 81)( 50, 80)( 51, 79)( 52, 78)( 53, 77)( 54, 76)( 55,100)
( 56,102)( 57,101)( 58,108)( 59,107)( 60,106)( 61,105)( 62,104)( 63,103)
( 64, 91)( 65, 93)( 66, 92)( 67, 99)( 68, 98)( 69, 97)( 70, 96)( 71, 95)
( 72, 94)(145,271)(146,273)(147,272)(148,279)(149,278)(150,277)(151,276)
(152,275)(153,274)(154,280)(155,282)(156,281)(157,288)(158,287)(159,286)
(160,285)(161,284)(162,283)(163,253)(164,255)(165,254)(166,261)(167,260)
(168,259)(169,258)(170,257)(171,256)(172,262)(173,264)(174,263)(175,270)
(176,269)(177,268)(178,267)(179,266)(180,265)(181,244)(182,246)(183,245)
(184,252)(185,251)(186,250)(187,249)(188,248)(189,247)(190,235)(191,237)
(192,236)(193,243)(194,242)(195,241)(196,240)(197,239)(198,238)(199,226)
(200,228)(201,227)(202,234)(203,233)(204,232)(205,231)(206,230)(207,229)
(208,217)(209,219)(210,218)(211,225)(212,224)(213,223)(214,222)(215,221)
(216,220)(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)(325,397)(326,399)(327,398)
(328,405)(329,404)(330,403)(331,402)(332,401)(333,400)(334,406)(335,408)
(336,407)(337,414)(338,413)(339,412)(340,411)(341,410)(342,409)(343,415)
(344,417)(345,416)(346,423)(347,422)(348,421)(349,420)(350,419)(351,418)
(352,424)(353,426)(354,425)(355,432)(356,431)(357,430)(358,429)(359,428)
(360,427)(433,523)(434,525)(435,524)(436,531)(437,530)(438,529)(439,528)
(440,527)(441,526)(442,532)(443,534)(444,533)(445,540)(446,539)(447,538)
(448,537)(449,536)(450,535)(451,505)(452,507)(453,506)(454,513)(455,512)
(456,511)(457,510)(458,509)(459,508)(460,514)(461,516)(462,515)(463,522)
(464,521)(465,520)(466,519)(467,518)(468,517)(469,559)(470,561)(471,560)
(472,567)(473,566)(474,565)(475,564)(476,563)(477,562)(478,568)(479,570)
(480,569)(481,576)(482,575)(483,574)(484,573)(485,572)(486,571)(487,541)
(488,543)(489,542)(490,549)(491,548)(492,547)(493,546)(494,545)(495,544)
(496,550)(497,552)(498,551)(499,558)(500,557)(501,556)(502,555)(503,554)
(504,553);
s2 := 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)( 37,121)( 38,123)( 39,122)
( 40,118)( 41,120)( 42,119)( 43,126)( 44,125)( 45,124)( 46,112)( 47,114)
( 48,113)( 49,109)( 50,111)( 51,110)( 52,117)( 53,116)( 54,115)( 55,139)
( 56,141)( 57,140)( 58,136)( 59,138)( 60,137)( 61,144)( 62,143)( 63,142)
( 64,130)( 65,132)( 66,131)( 67,127)( 68,129)( 69,128)( 70,135)( 71,134)
( 72,133)(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)(181,265)(182,267)(183,266)
(184,262)(185,264)(186,263)(187,270)(188,269)(189,268)(190,256)(191,258)
(192,257)(193,253)(194,255)(195,254)(196,261)(197,260)(198,259)(199,283)
(200,285)(201,284)(202,280)(203,282)(204,281)(205,288)(206,287)(207,286)
(208,274)(209,276)(210,275)(211,271)(212,273)(213,272)(214,279)(215,278)
(216,277)(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)(325,409)(326,411)(327,410)
(328,406)(329,408)(330,407)(331,414)(332,413)(333,412)(334,400)(335,402)
(336,401)(337,397)(338,399)(339,398)(340,405)(341,404)(342,403)(343,427)
(344,429)(345,428)(346,424)(347,426)(348,425)(349,432)(350,431)(351,430)
(352,418)(353,420)(354,419)(355,415)(356,417)(357,416)(358,423)(359,422)
(360,421)(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)(469,553)(470,555)(471,554)
(472,550)(473,552)(474,551)(475,558)(476,557)(477,556)(478,544)(479,546)
(480,545)(481,541)(482,543)(483,542)(484,549)(485,548)(486,547)(487,571)
(488,573)(489,572)(490,568)(491,570)(492,569)(493,576)(494,575)(495,574)
(496,562)(497,564)(498,563)(499,559)(500,561)(501,560)(502,567)(503,566)
(504,565);
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)( 73,397)( 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);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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