Polytope of Type {18,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,8}*1152d
if this polytope has a name.
Group : SmallGroup(1152,154283)
Rank : 3
Schlafli Type : {18,8}
Number of vertices, edges, etc : 72, 288, 32
Order of s0s1s2 : 18
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {18,8}*576a
3-fold quotients : {6,8}*384d
4-fold quotients : {18,4}*288
6-fold quotients : {6,8}*192a
8-fold quotients : {9,4}*144, {18,4}*144b, {18,4}*144c
12-fold quotients : {6,4}*96
16-fold quotients : {9,4}*72, {18,2}*72
24-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
32-fold quotients : {9,2}*36
48-fold quotients : {3,4}*24, {6,2}*24
96-fold quotients : {3,2}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 33)( 18, 34)
( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 46)( 26, 45)
( 27, 47)( 28, 48)( 29, 42)( 30, 41)( 31, 43)( 32, 44)( 49,129)( 50,130)
( 51,132)( 52,131)( 53,134)( 54,133)( 55,135)( 56,136)( 57,142)( 58,141)
( 59,143)( 60,144)( 61,138)( 62,137)( 63,139)( 64,140)( 65,113)( 66,114)
( 67,116)( 68,115)( 69,118)( 70,117)( 71,119)( 72,120)( 73,126)( 74,125)
( 75,127)( 76,128)( 77,122)( 78,121)( 79,123)( 80,124)( 81, 97)( 82, 98)
( 83,100)( 84, 99)( 85,102)( 86,101)( 87,103)( 88,104)( 89,110)( 90,109)
( 91,111)( 92,112)( 93,106)( 94,105)( 95,107)( 96,108)(147,148)(149,150)
(153,158)(154,157)(155,159)(156,160)(161,177)(162,178)(163,180)(164,179)
(165,182)(166,181)(167,183)(168,184)(169,190)(170,189)(171,191)(172,192)
(173,186)(174,185)(175,187)(176,188)(193,273)(194,274)(195,276)(196,275)
(197,278)(198,277)(199,279)(200,280)(201,286)(202,285)(203,287)(204,288)
(205,282)(206,281)(207,283)(208,284)(209,257)(210,258)(211,260)(212,259)
(213,262)(214,261)(215,263)(216,264)(217,270)(218,269)(219,271)(220,272)
(221,266)(222,265)(223,267)(224,268)(225,241)(226,242)(227,244)(228,243)
(229,246)(230,245)(231,247)(232,248)(233,254)(234,253)(235,255)(236,256)
(237,250)(238,249)(239,251)(240,252)(291,292)(293,294)(297,302)(298,301)
(299,303)(300,304)(305,321)(306,322)(307,324)(308,323)(309,326)(310,325)
(311,327)(312,328)(313,334)(314,333)(315,335)(316,336)(317,330)(318,329)
(319,331)(320,332)(337,417)(338,418)(339,420)(340,419)(341,422)(342,421)
(343,423)(344,424)(345,430)(346,429)(347,431)(348,432)(349,426)(350,425)
(351,427)(352,428)(353,401)(354,402)(355,404)(356,403)(357,406)(358,405)
(359,407)(360,408)(361,414)(362,413)(363,415)(364,416)(365,410)(366,409)
(367,411)(368,412)(369,385)(370,386)(371,388)(372,387)(373,390)(374,389)
(375,391)(376,392)(377,398)(378,397)(379,399)(380,400)(381,394)(382,393)
(383,395)(384,396)(435,436)(437,438)(441,446)(442,445)(443,447)(444,448)
(449,465)(450,466)(451,468)(452,467)(453,470)(454,469)(455,471)(456,472)
(457,478)(458,477)(459,479)(460,480)(461,474)(462,473)(463,475)(464,476)
(481,561)(482,562)(483,564)(484,563)(485,566)(486,565)(487,567)(488,568)
(489,574)(490,573)(491,575)(492,576)(493,570)(494,569)(495,571)(496,572)
(497,545)(498,546)(499,548)(500,547)(501,550)(502,549)(503,551)(504,552)
(505,558)(506,557)(507,559)(508,560)(509,554)(510,553)(511,555)(512,556)
(513,529)(514,530)(515,532)(516,531)(517,534)(518,533)(519,535)(520,536)
(521,542)(522,541)(523,543)(524,544)(525,538)(526,537)(527,539)(528,540);;
s1 := ( 1,193)( 2,196)( 3,195)( 4,194)( 5,205)( 6,208)( 7,207)( 8,206)
( 9,203)( 10,202)( 11,201)( 12,204)( 13,197)( 14,200)( 15,199)( 16,198)
( 17,225)( 18,228)( 19,227)( 20,226)( 21,237)( 22,240)( 23,239)( 24,238)
( 25,235)( 26,234)( 27,233)( 28,236)( 29,229)( 30,232)( 31,231)( 32,230)
( 33,209)( 34,212)( 35,211)( 36,210)( 37,221)( 38,224)( 39,223)( 40,222)
( 41,219)( 42,218)( 43,217)( 44,220)( 45,213)( 46,216)( 47,215)( 48,214)
( 49,145)( 50,148)( 51,147)( 52,146)( 53,157)( 54,160)( 55,159)( 56,158)
( 57,155)( 58,154)( 59,153)( 60,156)( 61,149)( 62,152)( 63,151)( 64,150)
( 65,177)( 66,180)( 67,179)( 68,178)( 69,189)( 70,192)( 71,191)( 72,190)
( 73,187)( 74,186)( 75,185)( 76,188)( 77,181)( 78,184)( 79,183)( 80,182)
( 81,161)( 82,164)( 83,163)( 84,162)( 85,173)( 86,176)( 87,175)( 88,174)
( 89,171)( 90,170)( 91,169)( 92,172)( 93,165)( 94,168)( 95,167)( 96,166)
( 97,273)( 98,276)( 99,275)(100,274)(101,285)(102,288)(103,287)(104,286)
(105,283)(106,282)(107,281)(108,284)(109,277)(110,280)(111,279)(112,278)
(113,257)(114,260)(115,259)(116,258)(117,269)(118,272)(119,271)(120,270)
(121,267)(122,266)(123,265)(124,268)(125,261)(126,264)(127,263)(128,262)
(129,241)(130,244)(131,243)(132,242)(133,253)(134,256)(135,255)(136,254)
(137,251)(138,250)(139,249)(140,252)(141,245)(142,248)(143,247)(144,246)
(289,481)(290,484)(291,483)(292,482)(293,493)(294,496)(295,495)(296,494)
(297,491)(298,490)(299,489)(300,492)(301,485)(302,488)(303,487)(304,486)
(305,513)(306,516)(307,515)(308,514)(309,525)(310,528)(311,527)(312,526)
(313,523)(314,522)(315,521)(316,524)(317,517)(318,520)(319,519)(320,518)
(321,497)(322,500)(323,499)(324,498)(325,509)(326,512)(327,511)(328,510)
(329,507)(330,506)(331,505)(332,508)(333,501)(334,504)(335,503)(336,502)
(337,433)(338,436)(339,435)(340,434)(341,445)(342,448)(343,447)(344,446)
(345,443)(346,442)(347,441)(348,444)(349,437)(350,440)(351,439)(352,438)
(353,465)(354,468)(355,467)(356,466)(357,477)(358,480)(359,479)(360,478)
(361,475)(362,474)(363,473)(364,476)(365,469)(366,472)(367,471)(368,470)
(369,449)(370,452)(371,451)(372,450)(373,461)(374,464)(375,463)(376,462)
(377,459)(378,458)(379,457)(380,460)(381,453)(382,456)(383,455)(384,454)
(385,561)(386,564)(387,563)(388,562)(389,573)(390,576)(391,575)(392,574)
(393,571)(394,570)(395,569)(396,572)(397,565)(398,568)(399,567)(400,566)
(401,545)(402,548)(403,547)(404,546)(405,557)(406,560)(407,559)(408,558)
(409,555)(410,554)(411,553)(412,556)(413,549)(414,552)(415,551)(416,550)
(417,529)(418,532)(419,531)(420,530)(421,541)(422,544)(423,543)(424,542)
(425,539)(426,538)(427,537)(428,540)(429,533)(430,536)(431,535)(432,534);;
s2 := ( 1,439)( 2,440)( 3,437)( 4,438)( 5,435)( 6,436)( 7,433)( 8,434)
( 9,445)( 10,446)( 11,447)( 12,448)( 13,441)( 14,442)( 15,443)( 16,444)
( 17,455)( 18,456)( 19,453)( 20,454)( 21,451)( 22,452)( 23,449)( 24,450)
( 25,461)( 26,462)( 27,463)( 28,464)( 29,457)( 30,458)( 31,459)( 32,460)
( 33,471)( 34,472)( 35,469)( 36,470)( 37,467)( 38,468)( 39,465)( 40,466)
( 41,477)( 42,478)( 43,479)( 44,480)( 45,473)( 46,474)( 47,475)( 48,476)
( 49,487)( 50,488)( 51,485)( 52,486)( 53,483)( 54,484)( 55,481)( 56,482)
( 57,493)( 58,494)( 59,495)( 60,496)( 61,489)( 62,490)( 63,491)( 64,492)
( 65,503)( 66,504)( 67,501)( 68,502)( 69,499)( 70,500)( 71,497)( 72,498)
( 73,509)( 74,510)( 75,511)( 76,512)( 77,505)( 78,506)( 79,507)( 80,508)
( 81,519)( 82,520)( 83,517)( 84,518)( 85,515)( 86,516)( 87,513)( 88,514)
( 89,525)( 90,526)( 91,527)( 92,528)( 93,521)( 94,522)( 95,523)( 96,524)
( 97,535)( 98,536)( 99,533)(100,534)(101,531)(102,532)(103,529)(104,530)
(105,541)(106,542)(107,543)(108,544)(109,537)(110,538)(111,539)(112,540)
(113,551)(114,552)(115,549)(116,550)(117,547)(118,548)(119,545)(120,546)
(121,557)(122,558)(123,559)(124,560)(125,553)(126,554)(127,555)(128,556)
(129,567)(130,568)(131,565)(132,566)(133,563)(134,564)(135,561)(136,562)
(137,573)(138,574)(139,575)(140,576)(141,569)(142,570)(143,571)(144,572)
(145,295)(146,296)(147,293)(148,294)(149,291)(150,292)(151,289)(152,290)
(153,301)(154,302)(155,303)(156,304)(157,297)(158,298)(159,299)(160,300)
(161,311)(162,312)(163,309)(164,310)(165,307)(166,308)(167,305)(168,306)
(169,317)(170,318)(171,319)(172,320)(173,313)(174,314)(175,315)(176,316)
(177,327)(178,328)(179,325)(180,326)(181,323)(182,324)(183,321)(184,322)
(185,333)(186,334)(187,335)(188,336)(189,329)(190,330)(191,331)(192,332)
(193,343)(194,344)(195,341)(196,342)(197,339)(198,340)(199,337)(200,338)
(201,349)(202,350)(203,351)(204,352)(205,345)(206,346)(207,347)(208,348)
(209,359)(210,360)(211,357)(212,358)(213,355)(214,356)(215,353)(216,354)
(217,365)(218,366)(219,367)(220,368)(221,361)(222,362)(223,363)(224,364)
(225,375)(226,376)(227,373)(228,374)(229,371)(230,372)(231,369)(232,370)
(233,381)(234,382)(235,383)(236,384)(237,377)(238,378)(239,379)(240,380)
(241,391)(242,392)(243,389)(244,390)(245,387)(246,388)(247,385)(248,386)
(249,397)(250,398)(251,399)(252,400)(253,393)(254,394)(255,395)(256,396)
(257,407)(258,408)(259,405)(260,406)(261,403)(262,404)(263,401)(264,402)
(265,413)(266,414)(267,415)(268,416)(269,409)(270,410)(271,411)(272,412)
(273,423)(274,424)(275,421)(276,422)(277,419)(278,420)(279,417)(280,418)
(281,429)(282,430)(283,431)(284,432)(285,425)(286,426)(287,427)(288,428);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 3, 4)( 5, 6)( 9, 14)( 10, 13)( 11, 15)( 12, 16)( 17, 33)
( 18, 34)( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 39)( 24, 40)( 25, 46)
( 26, 45)( 27, 47)( 28, 48)( 29, 42)( 30, 41)( 31, 43)( 32, 44)( 49,129)
( 50,130)( 51,132)( 52,131)( 53,134)( 54,133)( 55,135)( 56,136)( 57,142)
( 58,141)( 59,143)( 60,144)( 61,138)( 62,137)( 63,139)( 64,140)( 65,113)
( 66,114)( 67,116)( 68,115)( 69,118)( 70,117)( 71,119)( 72,120)( 73,126)
( 74,125)( 75,127)( 76,128)( 77,122)( 78,121)( 79,123)( 80,124)( 81, 97)
( 82, 98)( 83,100)( 84, 99)( 85,102)( 86,101)( 87,103)( 88,104)( 89,110)
( 90,109)( 91,111)( 92,112)( 93,106)( 94,105)( 95,107)( 96,108)(147,148)
(149,150)(153,158)(154,157)(155,159)(156,160)(161,177)(162,178)(163,180)
(164,179)(165,182)(166,181)(167,183)(168,184)(169,190)(170,189)(171,191)
(172,192)(173,186)(174,185)(175,187)(176,188)(193,273)(194,274)(195,276)
(196,275)(197,278)(198,277)(199,279)(200,280)(201,286)(202,285)(203,287)
(204,288)(205,282)(206,281)(207,283)(208,284)(209,257)(210,258)(211,260)
(212,259)(213,262)(214,261)(215,263)(216,264)(217,270)(218,269)(219,271)
(220,272)(221,266)(222,265)(223,267)(224,268)(225,241)(226,242)(227,244)
(228,243)(229,246)(230,245)(231,247)(232,248)(233,254)(234,253)(235,255)
(236,256)(237,250)(238,249)(239,251)(240,252)(291,292)(293,294)(297,302)
(298,301)(299,303)(300,304)(305,321)(306,322)(307,324)(308,323)(309,326)
(310,325)(311,327)(312,328)(313,334)(314,333)(315,335)(316,336)(317,330)
(318,329)(319,331)(320,332)(337,417)(338,418)(339,420)(340,419)(341,422)
(342,421)(343,423)(344,424)(345,430)(346,429)(347,431)(348,432)(349,426)
(350,425)(351,427)(352,428)(353,401)(354,402)(355,404)(356,403)(357,406)
(358,405)(359,407)(360,408)(361,414)(362,413)(363,415)(364,416)(365,410)
(366,409)(367,411)(368,412)(369,385)(370,386)(371,388)(372,387)(373,390)
(374,389)(375,391)(376,392)(377,398)(378,397)(379,399)(380,400)(381,394)
(382,393)(383,395)(384,396)(435,436)(437,438)(441,446)(442,445)(443,447)
(444,448)(449,465)(450,466)(451,468)(452,467)(453,470)(454,469)(455,471)
(456,472)(457,478)(458,477)(459,479)(460,480)(461,474)(462,473)(463,475)
(464,476)(481,561)(482,562)(483,564)(484,563)(485,566)(486,565)(487,567)
(488,568)(489,574)(490,573)(491,575)(492,576)(493,570)(494,569)(495,571)
(496,572)(497,545)(498,546)(499,548)(500,547)(501,550)(502,549)(503,551)
(504,552)(505,558)(506,557)(507,559)(508,560)(509,554)(510,553)(511,555)
(512,556)(513,529)(514,530)(515,532)(516,531)(517,534)(518,533)(519,535)
(520,536)(521,542)(522,541)(523,543)(524,544)(525,538)(526,537)(527,539)
(528,540);
s1 := Sym(576)!( 1,193)( 2,196)( 3,195)( 4,194)( 5,205)( 6,208)( 7,207)
( 8,206)( 9,203)( 10,202)( 11,201)( 12,204)( 13,197)( 14,200)( 15,199)
( 16,198)( 17,225)( 18,228)( 19,227)( 20,226)( 21,237)( 22,240)( 23,239)
( 24,238)( 25,235)( 26,234)( 27,233)( 28,236)( 29,229)( 30,232)( 31,231)
( 32,230)( 33,209)( 34,212)( 35,211)( 36,210)( 37,221)( 38,224)( 39,223)
( 40,222)( 41,219)( 42,218)( 43,217)( 44,220)( 45,213)( 46,216)( 47,215)
( 48,214)( 49,145)( 50,148)( 51,147)( 52,146)( 53,157)( 54,160)( 55,159)
( 56,158)( 57,155)( 58,154)( 59,153)( 60,156)( 61,149)( 62,152)( 63,151)
( 64,150)( 65,177)( 66,180)( 67,179)( 68,178)( 69,189)( 70,192)( 71,191)
( 72,190)( 73,187)( 74,186)( 75,185)( 76,188)( 77,181)( 78,184)( 79,183)
( 80,182)( 81,161)( 82,164)( 83,163)( 84,162)( 85,173)( 86,176)( 87,175)
( 88,174)( 89,171)( 90,170)( 91,169)( 92,172)( 93,165)( 94,168)( 95,167)
( 96,166)( 97,273)( 98,276)( 99,275)(100,274)(101,285)(102,288)(103,287)
(104,286)(105,283)(106,282)(107,281)(108,284)(109,277)(110,280)(111,279)
(112,278)(113,257)(114,260)(115,259)(116,258)(117,269)(118,272)(119,271)
(120,270)(121,267)(122,266)(123,265)(124,268)(125,261)(126,264)(127,263)
(128,262)(129,241)(130,244)(131,243)(132,242)(133,253)(134,256)(135,255)
(136,254)(137,251)(138,250)(139,249)(140,252)(141,245)(142,248)(143,247)
(144,246)(289,481)(290,484)(291,483)(292,482)(293,493)(294,496)(295,495)
(296,494)(297,491)(298,490)(299,489)(300,492)(301,485)(302,488)(303,487)
(304,486)(305,513)(306,516)(307,515)(308,514)(309,525)(310,528)(311,527)
(312,526)(313,523)(314,522)(315,521)(316,524)(317,517)(318,520)(319,519)
(320,518)(321,497)(322,500)(323,499)(324,498)(325,509)(326,512)(327,511)
(328,510)(329,507)(330,506)(331,505)(332,508)(333,501)(334,504)(335,503)
(336,502)(337,433)(338,436)(339,435)(340,434)(341,445)(342,448)(343,447)
(344,446)(345,443)(346,442)(347,441)(348,444)(349,437)(350,440)(351,439)
(352,438)(353,465)(354,468)(355,467)(356,466)(357,477)(358,480)(359,479)
(360,478)(361,475)(362,474)(363,473)(364,476)(365,469)(366,472)(367,471)
(368,470)(369,449)(370,452)(371,451)(372,450)(373,461)(374,464)(375,463)
(376,462)(377,459)(378,458)(379,457)(380,460)(381,453)(382,456)(383,455)
(384,454)(385,561)(386,564)(387,563)(388,562)(389,573)(390,576)(391,575)
(392,574)(393,571)(394,570)(395,569)(396,572)(397,565)(398,568)(399,567)
(400,566)(401,545)(402,548)(403,547)(404,546)(405,557)(406,560)(407,559)
(408,558)(409,555)(410,554)(411,553)(412,556)(413,549)(414,552)(415,551)
(416,550)(417,529)(418,532)(419,531)(420,530)(421,541)(422,544)(423,543)
(424,542)(425,539)(426,538)(427,537)(428,540)(429,533)(430,536)(431,535)
(432,534);
s2 := Sym(576)!( 1,439)( 2,440)( 3,437)( 4,438)( 5,435)( 6,436)( 7,433)
( 8,434)( 9,445)( 10,446)( 11,447)( 12,448)( 13,441)( 14,442)( 15,443)
( 16,444)( 17,455)( 18,456)( 19,453)( 20,454)( 21,451)( 22,452)( 23,449)
( 24,450)( 25,461)( 26,462)( 27,463)( 28,464)( 29,457)( 30,458)( 31,459)
( 32,460)( 33,471)( 34,472)( 35,469)( 36,470)( 37,467)( 38,468)( 39,465)
( 40,466)( 41,477)( 42,478)( 43,479)( 44,480)( 45,473)( 46,474)( 47,475)
( 48,476)( 49,487)( 50,488)( 51,485)( 52,486)( 53,483)( 54,484)( 55,481)
( 56,482)( 57,493)( 58,494)( 59,495)( 60,496)( 61,489)( 62,490)( 63,491)
( 64,492)( 65,503)( 66,504)( 67,501)( 68,502)( 69,499)( 70,500)( 71,497)
( 72,498)( 73,509)( 74,510)( 75,511)( 76,512)( 77,505)( 78,506)( 79,507)
( 80,508)( 81,519)( 82,520)( 83,517)( 84,518)( 85,515)( 86,516)( 87,513)
( 88,514)( 89,525)( 90,526)( 91,527)( 92,528)( 93,521)( 94,522)( 95,523)
( 96,524)( 97,535)( 98,536)( 99,533)(100,534)(101,531)(102,532)(103,529)
(104,530)(105,541)(106,542)(107,543)(108,544)(109,537)(110,538)(111,539)
(112,540)(113,551)(114,552)(115,549)(116,550)(117,547)(118,548)(119,545)
(120,546)(121,557)(122,558)(123,559)(124,560)(125,553)(126,554)(127,555)
(128,556)(129,567)(130,568)(131,565)(132,566)(133,563)(134,564)(135,561)
(136,562)(137,573)(138,574)(139,575)(140,576)(141,569)(142,570)(143,571)
(144,572)(145,295)(146,296)(147,293)(148,294)(149,291)(150,292)(151,289)
(152,290)(153,301)(154,302)(155,303)(156,304)(157,297)(158,298)(159,299)
(160,300)(161,311)(162,312)(163,309)(164,310)(165,307)(166,308)(167,305)
(168,306)(169,317)(170,318)(171,319)(172,320)(173,313)(174,314)(175,315)
(176,316)(177,327)(178,328)(179,325)(180,326)(181,323)(182,324)(183,321)
(184,322)(185,333)(186,334)(187,335)(188,336)(189,329)(190,330)(191,331)
(192,332)(193,343)(194,344)(195,341)(196,342)(197,339)(198,340)(199,337)
(200,338)(201,349)(202,350)(203,351)(204,352)(205,345)(206,346)(207,347)
(208,348)(209,359)(210,360)(211,357)(212,358)(213,355)(214,356)(215,353)
(216,354)(217,365)(218,366)(219,367)(220,368)(221,361)(222,362)(223,363)
(224,364)(225,375)(226,376)(227,373)(228,374)(229,371)(230,372)(231,369)
(232,370)(233,381)(234,382)(235,383)(236,384)(237,377)(238,378)(239,379)
(240,380)(241,391)(242,392)(243,389)(244,390)(245,387)(246,388)(247,385)
(248,386)(249,397)(250,398)(251,399)(252,400)(253,393)(254,394)(255,395)
(256,396)(257,407)(258,408)(259,405)(260,406)(261,403)(262,404)(263,401)
(264,402)(265,413)(266,414)(267,415)(268,416)(269,409)(270,410)(271,411)
(272,412)(273,423)(274,424)(275,421)(276,422)(277,419)(278,420)(279,417)
(280,418)(281,429)(282,430)(283,431)(284,432)(285,425)(286,426)(287,427)
(288,428);
poly := sub<Sym(576)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope