Polytope of Type {36,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,8}*1152f
if this polytope has a name.
Group : SmallGroup(1152,154279)
Rank : 3
Schlafli Type : {36,8}
Number of vertices, edges, etc : 72, 288, 16
Order of s0s1s2 : 36
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
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 : {36,4}*576b, {18,8}*576c
3-fold quotients : {12,8}*384f
4-fold quotients : {36,4}*288b, {36,4}*288c, {18,4}*288
6-fold quotients : {12,4}*192b, {6,8}*192c
8-fold quotients : {36,2}*144, {9,4}*144, {18,4}*144b, {18,4}*144c
12-fold quotients : {12,4}*96b, {12,4}*96c, {6,4}*96
16-fold quotients : {9,4}*72, {18,2}*72
24-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
32-fold quotients : {9,2}*36
48-fold quotients : {3,4}*24, {6,2}*24
72-fold quotients : {4,2}*16
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 := ( 1,289)( 2,290)( 3,292)( 4,291)( 5,295)( 6,296)( 7,293)( 8,294)
( 9,305)( 10,306)( 11,308)( 12,307)( 13,311)( 14,312)( 15,309)( 16,310)
( 17,297)( 18,298)( 19,300)( 20,299)( 21,303)( 22,304)( 23,301)( 24,302)
( 25,353)( 26,354)( 27,356)( 28,355)( 29,359)( 30,360)( 31,357)( 32,358)
( 33,345)( 34,346)( 35,348)( 36,347)( 37,351)( 38,352)( 39,349)( 40,350)
( 41,337)( 42,338)( 43,340)( 44,339)( 45,343)( 46,344)( 47,341)( 48,342)
( 49,329)( 50,330)( 51,332)( 52,331)( 53,335)( 54,336)( 55,333)( 56,334)
( 57,321)( 58,322)( 59,324)( 60,323)( 61,327)( 62,328)( 63,325)( 64,326)
( 65,313)( 66,314)( 67,316)( 68,315)( 69,319)( 70,320)( 71,317)( 72,318)
( 73,361)( 74,362)( 75,364)( 76,363)( 77,367)( 78,368)( 79,365)( 80,366)
( 81,377)( 82,378)( 83,380)( 84,379)( 85,383)( 86,384)( 87,381)( 88,382)
( 89,369)( 90,370)( 91,372)( 92,371)( 93,375)( 94,376)( 95,373)( 96,374)
( 97,425)( 98,426)( 99,428)(100,427)(101,431)(102,432)(103,429)(104,430)
(105,417)(106,418)(107,420)(108,419)(109,423)(110,424)(111,421)(112,422)
(113,409)(114,410)(115,412)(116,411)(117,415)(118,416)(119,413)(120,414)
(121,401)(122,402)(123,404)(124,403)(125,407)(126,408)(127,405)(128,406)
(129,393)(130,394)(131,396)(132,395)(133,399)(134,400)(135,397)(136,398)
(137,385)(138,386)(139,388)(140,387)(141,391)(142,392)(143,389)(144,390)
(145,506)(146,505)(147,507)(148,508)(149,512)(150,511)(151,510)(152,509)
(153,522)(154,521)(155,523)(156,524)(157,528)(158,527)(159,526)(160,525)
(161,514)(162,513)(163,515)(164,516)(165,520)(166,519)(167,518)(168,517)
(169,570)(170,569)(171,571)(172,572)(173,576)(174,575)(175,574)(176,573)
(177,562)(178,561)(179,563)(180,564)(181,568)(182,567)(183,566)(184,565)
(185,554)(186,553)(187,555)(188,556)(189,560)(190,559)(191,558)(192,557)
(193,546)(194,545)(195,547)(196,548)(197,552)(198,551)(199,550)(200,549)
(201,538)(202,537)(203,539)(204,540)(205,544)(206,543)(207,542)(208,541)
(209,530)(210,529)(211,531)(212,532)(213,536)(214,535)(215,534)(216,533)
(217,434)(218,433)(219,435)(220,436)(221,440)(222,439)(223,438)(224,437)
(225,450)(226,449)(227,451)(228,452)(229,456)(230,455)(231,454)(232,453)
(233,442)(234,441)(235,443)(236,444)(237,448)(238,447)(239,446)(240,445)
(241,498)(242,497)(243,499)(244,500)(245,504)(246,503)(247,502)(248,501)
(249,490)(250,489)(251,491)(252,492)(253,496)(254,495)(255,494)(256,493)
(257,482)(258,481)(259,483)(260,484)(261,488)(262,487)(263,486)(264,485)
(265,474)(266,473)(267,475)(268,476)(269,480)(270,479)(271,478)(272,477)
(273,466)(274,465)(275,467)(276,468)(277,472)(278,471)(279,470)(280,469)
(281,458)(282,457)(283,459)(284,460)(285,464)(286,463)(287,462)(288,461);;
s1 := ( 1, 25)( 2, 26)( 3, 31)( 4, 32)( 5, 30)( 6, 29)( 7, 27)( 8, 28)
( 9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)( 16, 44)
( 17, 33)( 18, 34)( 19, 39)( 20, 40)( 21, 38)( 22, 37)( 23, 35)( 24, 36)
( 49, 65)( 50, 66)( 51, 71)( 52, 72)( 53, 70)( 54, 69)( 55, 67)( 56, 68)
( 59, 63)( 60, 64)( 61, 62)( 73, 97)( 74, 98)( 75,103)( 76,104)( 77,102)
( 78,101)( 79, 99)( 80,100)( 81,113)( 82,114)( 83,119)( 84,120)( 85,118)
( 86,117)( 87,115)( 88,116)( 89,105)( 90,106)( 91,111)( 92,112)( 93,110)
( 94,109)( 95,107)( 96,108)(121,137)(122,138)(123,143)(124,144)(125,142)
(126,141)(127,139)(128,140)(131,135)(132,136)(133,134)(145,241)(146,242)
(147,247)(148,248)(149,246)(150,245)(151,243)(152,244)(153,257)(154,258)
(155,263)(156,264)(157,262)(158,261)(159,259)(160,260)(161,249)(162,250)
(163,255)(164,256)(165,254)(166,253)(167,251)(168,252)(169,217)(170,218)
(171,223)(172,224)(173,222)(174,221)(175,219)(176,220)(177,233)(178,234)
(179,239)(180,240)(181,238)(182,237)(183,235)(184,236)(185,225)(186,226)
(187,231)(188,232)(189,230)(190,229)(191,227)(192,228)(193,281)(194,282)
(195,287)(196,288)(197,286)(198,285)(199,283)(200,284)(201,273)(202,274)
(203,279)(204,280)(205,278)(206,277)(207,275)(208,276)(209,265)(210,266)
(211,271)(212,272)(213,270)(214,269)(215,267)(216,268)(289,385)(290,386)
(291,391)(292,392)(293,390)(294,389)(295,387)(296,388)(297,401)(298,402)
(299,407)(300,408)(301,406)(302,405)(303,403)(304,404)(305,393)(306,394)
(307,399)(308,400)(309,398)(310,397)(311,395)(312,396)(313,361)(314,362)
(315,367)(316,368)(317,366)(318,365)(319,363)(320,364)(321,377)(322,378)
(323,383)(324,384)(325,382)(326,381)(327,379)(328,380)(329,369)(330,370)
(331,375)(332,376)(333,374)(334,373)(335,371)(336,372)(337,425)(338,426)
(339,431)(340,432)(341,430)(342,429)(343,427)(344,428)(345,417)(346,418)
(347,423)(348,424)(349,422)(350,421)(351,419)(352,420)(353,409)(354,410)
(355,415)(356,416)(357,414)(358,413)(359,411)(360,412)(433,457)(434,458)
(435,463)(436,464)(437,462)(438,461)(439,459)(440,460)(441,473)(442,474)
(443,479)(444,480)(445,478)(446,477)(447,475)(448,476)(449,465)(450,466)
(451,471)(452,472)(453,470)(454,469)(455,467)(456,468)(481,497)(482,498)
(483,503)(484,504)(485,502)(486,501)(487,499)(488,500)(491,495)(492,496)
(493,494)(505,529)(506,530)(507,535)(508,536)(509,534)(510,533)(511,531)
(512,532)(513,545)(514,546)(515,551)(516,552)(517,550)(518,549)(519,547)
(520,548)(521,537)(522,538)(523,543)(524,544)(525,542)(526,541)(527,539)
(528,540)(553,569)(554,570)(555,575)(556,576)(557,574)(558,573)(559,571)
(560,572)(563,567)(564,568)(565,566);;
s2 := ( 1,435)( 2,436)( 3,434)( 4,433)( 5,439)( 6,440)( 7,438)( 8,437)
( 9,443)( 10,444)( 11,442)( 12,441)( 13,447)( 14,448)( 15,446)( 16,445)
( 17,451)( 18,452)( 19,450)( 20,449)( 21,455)( 22,456)( 23,454)( 24,453)
( 25,459)( 26,460)( 27,458)( 28,457)( 29,463)( 30,464)( 31,462)( 32,461)
( 33,467)( 34,468)( 35,466)( 36,465)( 37,471)( 38,472)( 39,470)( 40,469)
( 41,475)( 42,476)( 43,474)( 44,473)( 45,479)( 46,480)( 47,478)( 48,477)
( 49,483)( 50,484)( 51,482)( 52,481)( 53,487)( 54,488)( 55,486)( 56,485)
( 57,491)( 58,492)( 59,490)( 60,489)( 61,495)( 62,496)( 63,494)( 64,493)
( 65,499)( 66,500)( 67,498)( 68,497)( 69,503)( 70,504)( 71,502)( 72,501)
( 73,507)( 74,508)( 75,506)( 76,505)( 77,511)( 78,512)( 79,510)( 80,509)
( 81,515)( 82,516)( 83,514)( 84,513)( 85,519)( 86,520)( 87,518)( 88,517)
( 89,523)( 90,524)( 91,522)( 92,521)( 93,527)( 94,528)( 95,526)( 96,525)
( 97,531)( 98,532)( 99,530)(100,529)(101,535)(102,536)(103,534)(104,533)
(105,539)(106,540)(107,538)(108,537)(109,543)(110,544)(111,542)(112,541)
(113,547)(114,548)(115,546)(116,545)(117,551)(118,552)(119,550)(120,549)
(121,555)(122,556)(123,554)(124,553)(125,559)(126,560)(127,558)(128,557)
(129,563)(130,564)(131,562)(132,561)(133,567)(134,568)(135,566)(136,565)
(137,571)(138,572)(139,570)(140,569)(141,575)(142,576)(143,574)(144,573)
(145,364)(146,363)(147,361)(148,362)(149,368)(150,367)(151,365)(152,366)
(153,372)(154,371)(155,369)(156,370)(157,376)(158,375)(159,373)(160,374)
(161,380)(162,379)(163,377)(164,378)(165,384)(166,383)(167,381)(168,382)
(169,388)(170,387)(171,385)(172,386)(173,392)(174,391)(175,389)(176,390)
(177,396)(178,395)(179,393)(180,394)(181,400)(182,399)(183,397)(184,398)
(185,404)(186,403)(187,401)(188,402)(189,408)(190,407)(191,405)(192,406)
(193,412)(194,411)(195,409)(196,410)(197,416)(198,415)(199,413)(200,414)
(201,420)(202,419)(203,417)(204,418)(205,424)(206,423)(207,421)(208,422)
(209,428)(210,427)(211,425)(212,426)(213,432)(214,431)(215,429)(216,430)
(217,292)(218,291)(219,289)(220,290)(221,296)(222,295)(223,293)(224,294)
(225,300)(226,299)(227,297)(228,298)(229,304)(230,303)(231,301)(232,302)
(233,308)(234,307)(235,305)(236,306)(237,312)(238,311)(239,309)(240,310)
(241,316)(242,315)(243,313)(244,314)(245,320)(246,319)(247,317)(248,318)
(249,324)(250,323)(251,321)(252,322)(253,328)(254,327)(255,325)(256,326)
(257,332)(258,331)(259,329)(260,330)(261,336)(262,335)(263,333)(264,334)
(265,340)(266,339)(267,337)(268,338)(269,344)(270,343)(271,341)(272,342)
(273,348)(274,347)(275,345)(276,346)(277,352)(278,351)(279,349)(280,350)
(281,356)(282,355)(283,353)(284,354)(285,360)(286,359)(287,357)(288,358);;
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*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*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)!( 1,289)( 2,290)( 3,292)( 4,291)( 5,295)( 6,296)( 7,293)
( 8,294)( 9,305)( 10,306)( 11,308)( 12,307)( 13,311)( 14,312)( 15,309)
( 16,310)( 17,297)( 18,298)( 19,300)( 20,299)( 21,303)( 22,304)( 23,301)
( 24,302)( 25,353)( 26,354)( 27,356)( 28,355)( 29,359)( 30,360)( 31,357)
( 32,358)( 33,345)( 34,346)( 35,348)( 36,347)( 37,351)( 38,352)( 39,349)
( 40,350)( 41,337)( 42,338)( 43,340)( 44,339)( 45,343)( 46,344)( 47,341)
( 48,342)( 49,329)( 50,330)( 51,332)( 52,331)( 53,335)( 54,336)( 55,333)
( 56,334)( 57,321)( 58,322)( 59,324)( 60,323)( 61,327)( 62,328)( 63,325)
( 64,326)( 65,313)( 66,314)( 67,316)( 68,315)( 69,319)( 70,320)( 71,317)
( 72,318)( 73,361)( 74,362)( 75,364)( 76,363)( 77,367)( 78,368)( 79,365)
( 80,366)( 81,377)( 82,378)( 83,380)( 84,379)( 85,383)( 86,384)( 87,381)
( 88,382)( 89,369)( 90,370)( 91,372)( 92,371)( 93,375)( 94,376)( 95,373)
( 96,374)( 97,425)( 98,426)( 99,428)(100,427)(101,431)(102,432)(103,429)
(104,430)(105,417)(106,418)(107,420)(108,419)(109,423)(110,424)(111,421)
(112,422)(113,409)(114,410)(115,412)(116,411)(117,415)(118,416)(119,413)
(120,414)(121,401)(122,402)(123,404)(124,403)(125,407)(126,408)(127,405)
(128,406)(129,393)(130,394)(131,396)(132,395)(133,399)(134,400)(135,397)
(136,398)(137,385)(138,386)(139,388)(140,387)(141,391)(142,392)(143,389)
(144,390)(145,506)(146,505)(147,507)(148,508)(149,512)(150,511)(151,510)
(152,509)(153,522)(154,521)(155,523)(156,524)(157,528)(158,527)(159,526)
(160,525)(161,514)(162,513)(163,515)(164,516)(165,520)(166,519)(167,518)
(168,517)(169,570)(170,569)(171,571)(172,572)(173,576)(174,575)(175,574)
(176,573)(177,562)(178,561)(179,563)(180,564)(181,568)(182,567)(183,566)
(184,565)(185,554)(186,553)(187,555)(188,556)(189,560)(190,559)(191,558)
(192,557)(193,546)(194,545)(195,547)(196,548)(197,552)(198,551)(199,550)
(200,549)(201,538)(202,537)(203,539)(204,540)(205,544)(206,543)(207,542)
(208,541)(209,530)(210,529)(211,531)(212,532)(213,536)(214,535)(215,534)
(216,533)(217,434)(218,433)(219,435)(220,436)(221,440)(222,439)(223,438)
(224,437)(225,450)(226,449)(227,451)(228,452)(229,456)(230,455)(231,454)
(232,453)(233,442)(234,441)(235,443)(236,444)(237,448)(238,447)(239,446)
(240,445)(241,498)(242,497)(243,499)(244,500)(245,504)(246,503)(247,502)
(248,501)(249,490)(250,489)(251,491)(252,492)(253,496)(254,495)(255,494)
(256,493)(257,482)(258,481)(259,483)(260,484)(261,488)(262,487)(263,486)
(264,485)(265,474)(266,473)(267,475)(268,476)(269,480)(270,479)(271,478)
(272,477)(273,466)(274,465)(275,467)(276,468)(277,472)(278,471)(279,470)
(280,469)(281,458)(282,457)(283,459)(284,460)(285,464)(286,463)(287,462)
(288,461);
s1 := Sym(576)!( 1, 25)( 2, 26)( 3, 31)( 4, 32)( 5, 30)( 6, 29)( 7, 27)
( 8, 28)( 9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)
( 16, 44)( 17, 33)( 18, 34)( 19, 39)( 20, 40)( 21, 38)( 22, 37)( 23, 35)
( 24, 36)( 49, 65)( 50, 66)( 51, 71)( 52, 72)( 53, 70)( 54, 69)( 55, 67)
( 56, 68)( 59, 63)( 60, 64)( 61, 62)( 73, 97)( 74, 98)( 75,103)( 76,104)
( 77,102)( 78,101)( 79, 99)( 80,100)( 81,113)( 82,114)( 83,119)( 84,120)
( 85,118)( 86,117)( 87,115)( 88,116)( 89,105)( 90,106)( 91,111)( 92,112)
( 93,110)( 94,109)( 95,107)( 96,108)(121,137)(122,138)(123,143)(124,144)
(125,142)(126,141)(127,139)(128,140)(131,135)(132,136)(133,134)(145,241)
(146,242)(147,247)(148,248)(149,246)(150,245)(151,243)(152,244)(153,257)
(154,258)(155,263)(156,264)(157,262)(158,261)(159,259)(160,260)(161,249)
(162,250)(163,255)(164,256)(165,254)(166,253)(167,251)(168,252)(169,217)
(170,218)(171,223)(172,224)(173,222)(174,221)(175,219)(176,220)(177,233)
(178,234)(179,239)(180,240)(181,238)(182,237)(183,235)(184,236)(185,225)
(186,226)(187,231)(188,232)(189,230)(190,229)(191,227)(192,228)(193,281)
(194,282)(195,287)(196,288)(197,286)(198,285)(199,283)(200,284)(201,273)
(202,274)(203,279)(204,280)(205,278)(206,277)(207,275)(208,276)(209,265)
(210,266)(211,271)(212,272)(213,270)(214,269)(215,267)(216,268)(289,385)
(290,386)(291,391)(292,392)(293,390)(294,389)(295,387)(296,388)(297,401)
(298,402)(299,407)(300,408)(301,406)(302,405)(303,403)(304,404)(305,393)
(306,394)(307,399)(308,400)(309,398)(310,397)(311,395)(312,396)(313,361)
(314,362)(315,367)(316,368)(317,366)(318,365)(319,363)(320,364)(321,377)
(322,378)(323,383)(324,384)(325,382)(326,381)(327,379)(328,380)(329,369)
(330,370)(331,375)(332,376)(333,374)(334,373)(335,371)(336,372)(337,425)
(338,426)(339,431)(340,432)(341,430)(342,429)(343,427)(344,428)(345,417)
(346,418)(347,423)(348,424)(349,422)(350,421)(351,419)(352,420)(353,409)
(354,410)(355,415)(356,416)(357,414)(358,413)(359,411)(360,412)(433,457)
(434,458)(435,463)(436,464)(437,462)(438,461)(439,459)(440,460)(441,473)
(442,474)(443,479)(444,480)(445,478)(446,477)(447,475)(448,476)(449,465)
(450,466)(451,471)(452,472)(453,470)(454,469)(455,467)(456,468)(481,497)
(482,498)(483,503)(484,504)(485,502)(486,501)(487,499)(488,500)(491,495)
(492,496)(493,494)(505,529)(506,530)(507,535)(508,536)(509,534)(510,533)
(511,531)(512,532)(513,545)(514,546)(515,551)(516,552)(517,550)(518,549)
(519,547)(520,548)(521,537)(522,538)(523,543)(524,544)(525,542)(526,541)
(527,539)(528,540)(553,569)(554,570)(555,575)(556,576)(557,574)(558,573)
(559,571)(560,572)(563,567)(564,568)(565,566);
s2 := Sym(576)!( 1,435)( 2,436)( 3,434)( 4,433)( 5,439)( 6,440)( 7,438)
( 8,437)( 9,443)( 10,444)( 11,442)( 12,441)( 13,447)( 14,448)( 15,446)
( 16,445)( 17,451)( 18,452)( 19,450)( 20,449)( 21,455)( 22,456)( 23,454)
( 24,453)( 25,459)( 26,460)( 27,458)( 28,457)( 29,463)( 30,464)( 31,462)
( 32,461)( 33,467)( 34,468)( 35,466)( 36,465)( 37,471)( 38,472)( 39,470)
( 40,469)( 41,475)( 42,476)( 43,474)( 44,473)( 45,479)( 46,480)( 47,478)
( 48,477)( 49,483)( 50,484)( 51,482)( 52,481)( 53,487)( 54,488)( 55,486)
( 56,485)( 57,491)( 58,492)( 59,490)( 60,489)( 61,495)( 62,496)( 63,494)
( 64,493)( 65,499)( 66,500)( 67,498)( 68,497)( 69,503)( 70,504)( 71,502)
( 72,501)( 73,507)( 74,508)( 75,506)( 76,505)( 77,511)( 78,512)( 79,510)
( 80,509)( 81,515)( 82,516)( 83,514)( 84,513)( 85,519)( 86,520)( 87,518)
( 88,517)( 89,523)( 90,524)( 91,522)( 92,521)( 93,527)( 94,528)( 95,526)
( 96,525)( 97,531)( 98,532)( 99,530)(100,529)(101,535)(102,536)(103,534)
(104,533)(105,539)(106,540)(107,538)(108,537)(109,543)(110,544)(111,542)
(112,541)(113,547)(114,548)(115,546)(116,545)(117,551)(118,552)(119,550)
(120,549)(121,555)(122,556)(123,554)(124,553)(125,559)(126,560)(127,558)
(128,557)(129,563)(130,564)(131,562)(132,561)(133,567)(134,568)(135,566)
(136,565)(137,571)(138,572)(139,570)(140,569)(141,575)(142,576)(143,574)
(144,573)(145,364)(146,363)(147,361)(148,362)(149,368)(150,367)(151,365)
(152,366)(153,372)(154,371)(155,369)(156,370)(157,376)(158,375)(159,373)
(160,374)(161,380)(162,379)(163,377)(164,378)(165,384)(166,383)(167,381)
(168,382)(169,388)(170,387)(171,385)(172,386)(173,392)(174,391)(175,389)
(176,390)(177,396)(178,395)(179,393)(180,394)(181,400)(182,399)(183,397)
(184,398)(185,404)(186,403)(187,401)(188,402)(189,408)(190,407)(191,405)
(192,406)(193,412)(194,411)(195,409)(196,410)(197,416)(198,415)(199,413)
(200,414)(201,420)(202,419)(203,417)(204,418)(205,424)(206,423)(207,421)
(208,422)(209,428)(210,427)(211,425)(212,426)(213,432)(214,431)(215,429)
(216,430)(217,292)(218,291)(219,289)(220,290)(221,296)(222,295)(223,293)
(224,294)(225,300)(226,299)(227,297)(228,298)(229,304)(230,303)(231,301)
(232,302)(233,308)(234,307)(235,305)(236,306)(237,312)(238,311)(239,309)
(240,310)(241,316)(242,315)(243,313)(244,314)(245,320)(246,319)(247,317)
(248,318)(249,324)(250,323)(251,321)(252,322)(253,328)(254,327)(255,325)
(256,326)(257,332)(258,331)(259,329)(260,330)(261,336)(262,335)(263,333)
(264,334)(265,340)(266,339)(267,337)(268,338)(269,344)(270,343)(271,341)
(272,342)(273,348)(274,347)(275,345)(276,346)(277,352)(278,351)(279,349)
(280,350)(281,356)(282,355)(283,353)(284,354)(285,360)(286,359)(287,357)
(288,358);
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*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*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