Polytope of Type {8,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,18}*1152a
if this polytope has a name.
Group : SmallGroup(1152,153963)
Rank : 3
Schlafli Type : {8,18}
Number of vertices, edges, etc : 32, 288, 72
Order of s0s1s2 : 36
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {8,9}*576
3-fold quotients : {8,6}*384a
6-fold quotients : {8,3}*192
8-fold quotients : {4,9}*144
16-fold quotients : {4,9}*72
24-fold quotients : {4,3}*48
32-fold quotients : {2,9}*36
48-fold quotients : {4,3}*24
96-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,305)( 2,306)( 3,307)( 4,308)( 5,309)( 6,310)( 7,311)( 8,312)
( 9,320)( 10,319)( 11,318)( 12,317)( 13,316)( 14,315)( 15,314)( 16,313)
( 17,295)( 18,296)( 19,293)( 20,294)( 21,291)( 22,292)( 23,289)( 24,290)
( 25,298)( 26,297)( 27,300)( 28,299)( 29,302)( 30,301)( 31,304)( 32,303)
( 33,337)( 34,338)( 35,339)( 36,340)( 37,341)( 38,342)( 39,343)( 40,344)
( 41,352)( 42,351)( 43,350)( 44,349)( 45,348)( 46,347)( 47,346)( 48,345)
( 49,327)( 50,328)( 51,325)( 52,326)( 53,323)( 54,324)( 55,321)( 56,322)
( 57,330)( 58,329)( 59,332)( 60,331)( 61,334)( 62,333)( 63,336)( 64,335)
( 65,369)( 66,370)( 67,371)( 68,372)( 69,373)( 70,374)( 71,375)( 72,376)
( 73,384)( 74,383)( 75,382)( 76,381)( 77,380)( 78,379)( 79,378)( 80,377)
( 81,359)( 82,360)( 83,357)( 84,358)( 85,355)( 86,356)( 87,353)( 88,354)
( 89,362)( 90,361)( 91,364)( 92,363)( 93,366)( 94,365)( 95,368)( 96,367)
( 97,401)( 98,402)( 99,403)(100,404)(101,405)(102,406)(103,407)(104,408)
(105,416)(106,415)(107,414)(108,413)(109,412)(110,411)(111,410)(112,409)
(113,391)(114,392)(115,389)(116,390)(117,387)(118,388)(119,385)(120,386)
(121,394)(122,393)(123,396)(124,395)(125,398)(126,397)(127,400)(128,399)
(129,433)(130,434)(131,435)(132,436)(133,437)(134,438)(135,439)(136,440)
(137,448)(138,447)(139,446)(140,445)(141,444)(142,443)(143,442)(144,441)
(145,423)(146,424)(147,421)(148,422)(149,419)(150,420)(151,417)(152,418)
(153,426)(154,425)(155,428)(156,427)(157,430)(158,429)(159,432)(160,431)
(161,465)(162,466)(163,467)(164,468)(165,469)(166,470)(167,471)(168,472)
(169,480)(170,479)(171,478)(172,477)(173,476)(174,475)(175,474)(176,473)
(177,455)(178,456)(179,453)(180,454)(181,451)(182,452)(183,449)(184,450)
(185,458)(186,457)(187,460)(188,459)(189,462)(190,461)(191,464)(192,463)
(193,497)(194,498)(195,499)(196,500)(197,501)(198,502)(199,503)(200,504)
(201,512)(202,511)(203,510)(204,509)(205,508)(206,507)(207,506)(208,505)
(209,487)(210,488)(211,485)(212,486)(213,483)(214,484)(215,481)(216,482)
(217,490)(218,489)(219,492)(220,491)(221,494)(222,493)(223,496)(224,495)
(225,529)(226,530)(227,531)(228,532)(229,533)(230,534)(231,535)(232,536)
(233,544)(234,543)(235,542)(236,541)(237,540)(238,539)(239,538)(240,537)
(241,519)(242,520)(243,517)(244,518)(245,515)(246,516)(247,513)(248,514)
(249,522)(250,521)(251,524)(252,523)(253,526)(254,525)(255,528)(256,527)
(257,561)(258,562)(259,563)(260,564)(261,565)(262,566)(263,567)(264,568)
(265,576)(266,575)(267,574)(268,573)(269,572)(270,571)(271,570)(272,569)
(273,551)(274,552)(275,549)(276,550)(277,547)(278,548)(279,545)(280,546)
(281,554)(282,553)(283,556)(284,555)(285,558)(286,557)(287,560)(288,559);;
s1 := ( 3, 4)( 5, 6)( 9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 26)( 18, 25)
( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 33, 65)( 34, 66)
( 35, 68)( 36, 67)( 37, 70)( 38, 69)( 39, 71)( 40, 72)( 41, 80)( 42, 79)
( 43, 77)( 44, 78)( 45, 75)( 46, 76)( 47, 74)( 48, 73)( 49, 90)( 50, 89)
( 51, 91)( 52, 92)( 53, 93)( 54, 94)( 55, 96)( 56, 95)( 57, 82)( 58, 81)
( 59, 83)( 60, 84)( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 97,257)( 98,258)
( 99,260)(100,259)(101,262)(102,261)(103,263)(104,264)(105,272)(106,271)
(107,269)(108,270)(109,267)(110,268)(111,266)(112,265)(113,282)(114,281)
(115,283)(116,284)(117,285)(118,286)(119,288)(120,287)(121,274)(122,273)
(123,275)(124,276)(125,277)(126,278)(127,280)(128,279)(129,225)(130,226)
(131,228)(132,227)(133,230)(134,229)(135,231)(136,232)(137,240)(138,239)
(139,237)(140,238)(141,235)(142,236)(143,234)(144,233)(145,250)(146,249)
(147,251)(148,252)(149,253)(150,254)(151,256)(152,255)(153,242)(154,241)
(155,243)(156,244)(157,245)(158,246)(159,248)(160,247)(161,193)(162,194)
(163,196)(164,195)(165,198)(166,197)(167,199)(168,200)(169,208)(170,207)
(171,205)(172,206)(173,203)(174,204)(175,202)(176,201)(177,218)(178,217)
(179,219)(180,220)(181,221)(182,222)(183,224)(184,223)(185,210)(186,209)
(187,211)(188,212)(189,213)(190,214)(191,216)(192,215)(289,295)(290,296)
(291,294)(292,293)(297,298)(303,304)(305,320)(306,319)(307,317)(308,318)
(309,315)(310,316)(311,314)(312,313)(321,359)(322,360)(323,358)(324,357)
(325,356)(326,355)(327,353)(328,354)(329,362)(330,361)(331,363)(332,364)
(333,365)(334,366)(335,368)(336,367)(337,384)(338,383)(339,381)(340,382)
(341,379)(342,380)(343,378)(344,377)(345,376)(346,375)(347,373)(348,374)
(349,371)(350,372)(351,370)(352,369)(385,551)(386,552)(387,550)(388,549)
(389,548)(390,547)(391,545)(392,546)(393,554)(394,553)(395,555)(396,556)
(397,557)(398,558)(399,560)(400,559)(401,576)(402,575)(403,573)(404,574)
(405,571)(406,572)(407,570)(408,569)(409,568)(410,567)(411,565)(412,566)
(413,563)(414,564)(415,562)(416,561)(417,519)(418,520)(419,518)(420,517)
(421,516)(422,515)(423,513)(424,514)(425,522)(426,521)(427,523)(428,524)
(429,525)(430,526)(431,528)(432,527)(433,544)(434,543)(435,541)(436,542)
(437,539)(438,540)(439,538)(440,537)(441,536)(442,535)(443,533)(444,534)
(445,531)(446,532)(447,530)(448,529)(449,487)(450,488)(451,486)(452,485)
(453,484)(454,483)(455,481)(456,482)(457,490)(458,489)(459,491)(460,492)
(461,493)(462,494)(463,496)(464,495)(465,512)(466,511)(467,509)(468,510)
(469,507)(470,508)(471,506)(472,505)(473,504)(474,503)(475,501)(476,502)
(477,499)(478,500)(479,498)(480,497);;
s2 := ( 1,101)( 2,104)( 3,103)( 4,102)( 5, 97)( 6,100)( 7, 99)( 8, 98)
( 9,128)( 10,125)( 11,126)( 12,127)( 13,124)( 14,121)( 15,122)( 16,123)
( 17,115)( 18,114)( 19,113)( 20,116)( 21,119)( 22,118)( 23,117)( 24,120)
( 25,110)( 26,111)( 27,112)( 28,109)( 29,106)( 30,107)( 31,108)( 32,105)
( 33,165)( 34,168)( 35,167)( 36,166)( 37,161)( 38,164)( 39,163)( 40,162)
( 41,192)( 42,189)( 43,190)( 44,191)( 45,188)( 46,185)( 47,186)( 48,187)
( 49,179)( 50,178)( 51,177)( 52,180)( 53,183)( 54,182)( 55,181)( 56,184)
( 57,174)( 58,175)( 59,176)( 60,173)( 61,170)( 62,171)( 63,172)( 64,169)
( 65,133)( 66,136)( 67,135)( 68,134)( 69,129)( 70,132)( 71,131)( 72,130)
( 73,160)( 74,157)( 75,158)( 76,159)( 77,156)( 78,153)( 79,154)( 80,155)
( 81,147)( 82,146)( 83,145)( 84,148)( 85,151)( 86,150)( 87,149)( 88,152)
( 89,142)( 90,143)( 91,144)( 92,141)( 93,138)( 94,139)( 95,140)( 96,137)
(193,261)(194,264)(195,263)(196,262)(197,257)(198,260)(199,259)(200,258)
(201,288)(202,285)(203,286)(204,287)(205,284)(206,281)(207,282)(208,283)
(209,275)(210,274)(211,273)(212,276)(213,279)(214,278)(215,277)(216,280)
(217,270)(218,271)(219,272)(220,269)(221,266)(222,267)(223,268)(224,265)
(225,229)(226,232)(227,231)(228,230)(233,256)(234,253)(235,254)(236,255)
(237,252)(238,249)(239,250)(240,251)(241,243)(245,247)(289,387)(290,386)
(291,385)(292,388)(293,391)(294,390)(295,389)(296,392)(297,410)(298,411)
(299,412)(300,409)(301,414)(302,415)(303,416)(304,413)(305,405)(306,408)
(307,407)(308,406)(309,401)(310,404)(311,403)(312,402)(313,396)(314,393)
(315,394)(316,395)(317,400)(318,397)(319,398)(320,399)(321,451)(322,450)
(323,449)(324,452)(325,455)(326,454)(327,453)(328,456)(329,474)(330,475)
(331,476)(332,473)(333,478)(334,479)(335,480)(336,477)(337,469)(338,472)
(339,471)(340,470)(341,465)(342,468)(343,467)(344,466)(345,460)(346,457)
(347,458)(348,459)(349,464)(350,461)(351,462)(352,463)(353,419)(354,418)
(355,417)(356,420)(357,423)(358,422)(359,421)(360,424)(361,442)(362,443)
(363,444)(364,441)(365,446)(366,447)(367,448)(368,445)(369,437)(370,440)
(371,439)(372,438)(373,433)(374,436)(375,435)(376,434)(377,428)(378,425)
(379,426)(380,427)(381,432)(382,429)(383,430)(384,431)(481,547)(482,546)
(483,545)(484,548)(485,551)(486,550)(487,549)(488,552)(489,570)(490,571)
(491,572)(492,569)(493,574)(494,575)(495,576)(496,573)(497,565)(498,568)
(499,567)(500,566)(501,561)(502,564)(503,563)(504,562)(505,556)(506,553)
(507,554)(508,555)(509,560)(510,557)(511,558)(512,559)(513,515)(517,519)
(521,538)(522,539)(523,540)(524,537)(525,542)(526,543)(527,544)(528,541)
(529,533)(530,536)(531,535)(532,534);;
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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,305)( 2,306)( 3,307)( 4,308)( 5,309)( 6,310)( 7,311)
( 8,312)( 9,320)( 10,319)( 11,318)( 12,317)( 13,316)( 14,315)( 15,314)
( 16,313)( 17,295)( 18,296)( 19,293)( 20,294)( 21,291)( 22,292)( 23,289)
( 24,290)( 25,298)( 26,297)( 27,300)( 28,299)( 29,302)( 30,301)( 31,304)
( 32,303)( 33,337)( 34,338)( 35,339)( 36,340)( 37,341)( 38,342)( 39,343)
( 40,344)( 41,352)( 42,351)( 43,350)( 44,349)( 45,348)( 46,347)( 47,346)
( 48,345)( 49,327)( 50,328)( 51,325)( 52,326)( 53,323)( 54,324)( 55,321)
( 56,322)( 57,330)( 58,329)( 59,332)( 60,331)( 61,334)( 62,333)( 63,336)
( 64,335)( 65,369)( 66,370)( 67,371)( 68,372)( 69,373)( 70,374)( 71,375)
( 72,376)( 73,384)( 74,383)( 75,382)( 76,381)( 77,380)( 78,379)( 79,378)
( 80,377)( 81,359)( 82,360)( 83,357)( 84,358)( 85,355)( 86,356)( 87,353)
( 88,354)( 89,362)( 90,361)( 91,364)( 92,363)( 93,366)( 94,365)( 95,368)
( 96,367)( 97,401)( 98,402)( 99,403)(100,404)(101,405)(102,406)(103,407)
(104,408)(105,416)(106,415)(107,414)(108,413)(109,412)(110,411)(111,410)
(112,409)(113,391)(114,392)(115,389)(116,390)(117,387)(118,388)(119,385)
(120,386)(121,394)(122,393)(123,396)(124,395)(125,398)(126,397)(127,400)
(128,399)(129,433)(130,434)(131,435)(132,436)(133,437)(134,438)(135,439)
(136,440)(137,448)(138,447)(139,446)(140,445)(141,444)(142,443)(143,442)
(144,441)(145,423)(146,424)(147,421)(148,422)(149,419)(150,420)(151,417)
(152,418)(153,426)(154,425)(155,428)(156,427)(157,430)(158,429)(159,432)
(160,431)(161,465)(162,466)(163,467)(164,468)(165,469)(166,470)(167,471)
(168,472)(169,480)(170,479)(171,478)(172,477)(173,476)(174,475)(175,474)
(176,473)(177,455)(178,456)(179,453)(180,454)(181,451)(182,452)(183,449)
(184,450)(185,458)(186,457)(187,460)(188,459)(189,462)(190,461)(191,464)
(192,463)(193,497)(194,498)(195,499)(196,500)(197,501)(198,502)(199,503)
(200,504)(201,512)(202,511)(203,510)(204,509)(205,508)(206,507)(207,506)
(208,505)(209,487)(210,488)(211,485)(212,486)(213,483)(214,484)(215,481)
(216,482)(217,490)(218,489)(219,492)(220,491)(221,494)(222,493)(223,496)
(224,495)(225,529)(226,530)(227,531)(228,532)(229,533)(230,534)(231,535)
(232,536)(233,544)(234,543)(235,542)(236,541)(237,540)(238,539)(239,538)
(240,537)(241,519)(242,520)(243,517)(244,518)(245,515)(246,516)(247,513)
(248,514)(249,522)(250,521)(251,524)(252,523)(253,526)(254,525)(255,528)
(256,527)(257,561)(258,562)(259,563)(260,564)(261,565)(262,566)(263,567)
(264,568)(265,576)(266,575)(267,574)(268,573)(269,572)(270,571)(271,570)
(272,569)(273,551)(274,552)(275,549)(276,550)(277,547)(278,548)(279,545)
(280,546)(281,554)(282,553)(283,556)(284,555)(285,558)(286,557)(287,560)
(288,559);
s1 := Sym(576)!( 3, 4)( 5, 6)( 9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 26)
( 18, 25)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 33, 65)
( 34, 66)( 35, 68)( 36, 67)( 37, 70)( 38, 69)( 39, 71)( 40, 72)( 41, 80)
( 42, 79)( 43, 77)( 44, 78)( 45, 75)( 46, 76)( 47, 74)( 48, 73)( 49, 90)
( 50, 89)( 51, 91)( 52, 92)( 53, 93)( 54, 94)( 55, 96)( 56, 95)( 57, 82)
( 58, 81)( 59, 83)( 60, 84)( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 97,257)
( 98,258)( 99,260)(100,259)(101,262)(102,261)(103,263)(104,264)(105,272)
(106,271)(107,269)(108,270)(109,267)(110,268)(111,266)(112,265)(113,282)
(114,281)(115,283)(116,284)(117,285)(118,286)(119,288)(120,287)(121,274)
(122,273)(123,275)(124,276)(125,277)(126,278)(127,280)(128,279)(129,225)
(130,226)(131,228)(132,227)(133,230)(134,229)(135,231)(136,232)(137,240)
(138,239)(139,237)(140,238)(141,235)(142,236)(143,234)(144,233)(145,250)
(146,249)(147,251)(148,252)(149,253)(150,254)(151,256)(152,255)(153,242)
(154,241)(155,243)(156,244)(157,245)(158,246)(159,248)(160,247)(161,193)
(162,194)(163,196)(164,195)(165,198)(166,197)(167,199)(168,200)(169,208)
(170,207)(171,205)(172,206)(173,203)(174,204)(175,202)(176,201)(177,218)
(178,217)(179,219)(180,220)(181,221)(182,222)(183,224)(184,223)(185,210)
(186,209)(187,211)(188,212)(189,213)(190,214)(191,216)(192,215)(289,295)
(290,296)(291,294)(292,293)(297,298)(303,304)(305,320)(306,319)(307,317)
(308,318)(309,315)(310,316)(311,314)(312,313)(321,359)(322,360)(323,358)
(324,357)(325,356)(326,355)(327,353)(328,354)(329,362)(330,361)(331,363)
(332,364)(333,365)(334,366)(335,368)(336,367)(337,384)(338,383)(339,381)
(340,382)(341,379)(342,380)(343,378)(344,377)(345,376)(346,375)(347,373)
(348,374)(349,371)(350,372)(351,370)(352,369)(385,551)(386,552)(387,550)
(388,549)(389,548)(390,547)(391,545)(392,546)(393,554)(394,553)(395,555)
(396,556)(397,557)(398,558)(399,560)(400,559)(401,576)(402,575)(403,573)
(404,574)(405,571)(406,572)(407,570)(408,569)(409,568)(410,567)(411,565)
(412,566)(413,563)(414,564)(415,562)(416,561)(417,519)(418,520)(419,518)
(420,517)(421,516)(422,515)(423,513)(424,514)(425,522)(426,521)(427,523)
(428,524)(429,525)(430,526)(431,528)(432,527)(433,544)(434,543)(435,541)
(436,542)(437,539)(438,540)(439,538)(440,537)(441,536)(442,535)(443,533)
(444,534)(445,531)(446,532)(447,530)(448,529)(449,487)(450,488)(451,486)
(452,485)(453,484)(454,483)(455,481)(456,482)(457,490)(458,489)(459,491)
(460,492)(461,493)(462,494)(463,496)(464,495)(465,512)(466,511)(467,509)
(468,510)(469,507)(470,508)(471,506)(472,505)(473,504)(474,503)(475,501)
(476,502)(477,499)(478,500)(479,498)(480,497);
s2 := Sym(576)!( 1,101)( 2,104)( 3,103)( 4,102)( 5, 97)( 6,100)( 7, 99)
( 8, 98)( 9,128)( 10,125)( 11,126)( 12,127)( 13,124)( 14,121)( 15,122)
( 16,123)( 17,115)( 18,114)( 19,113)( 20,116)( 21,119)( 22,118)( 23,117)
( 24,120)( 25,110)( 26,111)( 27,112)( 28,109)( 29,106)( 30,107)( 31,108)
( 32,105)( 33,165)( 34,168)( 35,167)( 36,166)( 37,161)( 38,164)( 39,163)
( 40,162)( 41,192)( 42,189)( 43,190)( 44,191)( 45,188)( 46,185)( 47,186)
( 48,187)( 49,179)( 50,178)( 51,177)( 52,180)( 53,183)( 54,182)( 55,181)
( 56,184)( 57,174)( 58,175)( 59,176)( 60,173)( 61,170)( 62,171)( 63,172)
( 64,169)( 65,133)( 66,136)( 67,135)( 68,134)( 69,129)( 70,132)( 71,131)
( 72,130)( 73,160)( 74,157)( 75,158)( 76,159)( 77,156)( 78,153)( 79,154)
( 80,155)( 81,147)( 82,146)( 83,145)( 84,148)( 85,151)( 86,150)( 87,149)
( 88,152)( 89,142)( 90,143)( 91,144)( 92,141)( 93,138)( 94,139)( 95,140)
( 96,137)(193,261)(194,264)(195,263)(196,262)(197,257)(198,260)(199,259)
(200,258)(201,288)(202,285)(203,286)(204,287)(205,284)(206,281)(207,282)
(208,283)(209,275)(210,274)(211,273)(212,276)(213,279)(214,278)(215,277)
(216,280)(217,270)(218,271)(219,272)(220,269)(221,266)(222,267)(223,268)
(224,265)(225,229)(226,232)(227,231)(228,230)(233,256)(234,253)(235,254)
(236,255)(237,252)(238,249)(239,250)(240,251)(241,243)(245,247)(289,387)
(290,386)(291,385)(292,388)(293,391)(294,390)(295,389)(296,392)(297,410)
(298,411)(299,412)(300,409)(301,414)(302,415)(303,416)(304,413)(305,405)
(306,408)(307,407)(308,406)(309,401)(310,404)(311,403)(312,402)(313,396)
(314,393)(315,394)(316,395)(317,400)(318,397)(319,398)(320,399)(321,451)
(322,450)(323,449)(324,452)(325,455)(326,454)(327,453)(328,456)(329,474)
(330,475)(331,476)(332,473)(333,478)(334,479)(335,480)(336,477)(337,469)
(338,472)(339,471)(340,470)(341,465)(342,468)(343,467)(344,466)(345,460)
(346,457)(347,458)(348,459)(349,464)(350,461)(351,462)(352,463)(353,419)
(354,418)(355,417)(356,420)(357,423)(358,422)(359,421)(360,424)(361,442)
(362,443)(363,444)(364,441)(365,446)(366,447)(367,448)(368,445)(369,437)
(370,440)(371,439)(372,438)(373,433)(374,436)(375,435)(376,434)(377,428)
(378,425)(379,426)(380,427)(381,432)(382,429)(383,430)(384,431)(481,547)
(482,546)(483,545)(484,548)(485,551)(486,550)(487,549)(488,552)(489,570)
(490,571)(491,572)(492,569)(493,574)(494,575)(495,576)(496,573)(497,565)
(498,568)(499,567)(500,566)(501,561)(502,564)(503,563)(504,562)(505,556)
(506,553)(507,554)(508,555)(509,560)(510,557)(511,558)(512,559)(513,515)
(517,519)(521,538)(522,539)(523,540)(524,537)(525,542)(526,543)(527,544)
(528,541)(529,533)(530,536)(531,535)(532,534);
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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s0*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 >;
References : None.
to this polytope