Polytope of Type {8,36}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,36}*1152f
if this polytope has a name.
Group : SmallGroup(1152,154279)
Rank : 3
Schlafli Type : {8,36}
Number of vertices, edges, etc : 16, 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 : {4,36}*576b, {8,18}*576c
3-fold quotients : {8,12}*384f
4-fold quotients : {4,36}*288b, {4,36}*288c, {4,18}*288
6-fold quotients : {4,12}*192b, {8,6}*192c
8-fold quotients : {2,36}*144, {4,9}*144, {4,18}*144b, {4,18}*144c
12-fold quotients : {4,12}*96b, {4,12}*96c, {4,6}*96
16-fold quotients : {4,9}*72, {2,18}*72
24-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
32-fold quotients : {2,9}*36
48-fold quotients : {4,3}*24, {2,6}*24
72-fold quotients : {2,4}*16
96-fold quotients : {2,3}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,437)( 2,438)( 3,440)( 4,439)( 5,434)( 6,433)( 7,435)( 8,436)
( 9,445)( 10,446)( 11,448)( 12,447)( 13,442)( 14,441)( 15,443)( 16,444)
( 17,453)( 18,454)( 19,456)( 20,455)( 21,450)( 22,449)( 23,451)( 24,452)
( 25,461)( 26,462)( 27,464)( 28,463)( 29,458)( 30,457)( 31,459)( 32,460)
( 33,469)( 34,470)( 35,472)( 36,471)( 37,466)( 38,465)( 39,467)( 40,468)
( 41,477)( 42,478)( 43,480)( 44,479)( 45,474)( 46,473)( 47,475)( 48,476)
( 49,485)( 50,486)( 51,488)( 52,487)( 53,482)( 54,481)( 55,483)( 56,484)
( 57,493)( 58,494)( 59,496)( 60,495)( 61,490)( 62,489)( 63,491)( 64,492)
( 65,501)( 66,502)( 67,504)( 68,503)( 69,498)( 70,497)( 71,499)( 72,500)
( 73,509)( 74,510)( 75,512)( 76,511)( 77,506)( 78,505)( 79,507)( 80,508)
( 81,517)( 82,518)( 83,520)( 84,519)( 85,514)( 86,513)( 87,515)( 88,516)
( 89,525)( 90,526)( 91,528)( 92,527)( 93,522)( 94,521)( 95,523)( 96,524)
( 97,533)( 98,534)( 99,536)(100,535)(101,530)(102,529)(103,531)(104,532)
(105,541)(106,542)(107,544)(108,543)(109,538)(110,537)(111,539)(112,540)
(113,549)(114,550)(115,552)(116,551)(117,546)(118,545)(119,547)(120,548)
(121,557)(122,558)(123,560)(124,559)(125,554)(126,553)(127,555)(128,556)
(129,565)(130,566)(131,568)(132,567)(133,562)(134,561)(135,563)(136,564)
(137,573)(138,574)(139,576)(140,575)(141,570)(142,569)(143,571)(144,572)
(145,366)(146,365)(147,367)(148,368)(149,361)(150,362)(151,364)(152,363)
(153,374)(154,373)(155,375)(156,376)(157,369)(158,370)(159,372)(160,371)
(161,382)(162,381)(163,383)(164,384)(165,377)(166,378)(167,380)(168,379)
(169,390)(170,389)(171,391)(172,392)(173,385)(174,386)(175,388)(176,387)
(177,398)(178,397)(179,399)(180,400)(181,393)(182,394)(183,396)(184,395)
(185,406)(186,405)(187,407)(188,408)(189,401)(190,402)(191,404)(192,403)
(193,414)(194,413)(195,415)(196,416)(197,409)(198,410)(199,412)(200,411)
(201,422)(202,421)(203,423)(204,424)(205,417)(206,418)(207,420)(208,419)
(209,430)(210,429)(211,431)(212,432)(213,425)(214,426)(215,428)(216,427)
(217,294)(218,293)(219,295)(220,296)(221,289)(222,290)(223,292)(224,291)
(225,302)(226,301)(227,303)(228,304)(229,297)(230,298)(231,300)(232,299)
(233,310)(234,309)(235,311)(236,312)(237,305)(238,306)(239,308)(240,307)
(241,318)(242,317)(243,319)(244,320)(245,313)(246,314)(247,316)(248,315)
(249,326)(250,325)(251,327)(252,328)(253,321)(254,322)(255,324)(256,323)
(257,334)(258,333)(259,335)(260,336)(261,329)(262,330)(263,332)(264,331)
(265,342)(266,341)(267,343)(268,344)(269,337)(270,338)(271,340)(272,339)
(273,350)(274,349)(275,351)(276,352)(277,345)(278,346)(279,348)(280,347)
(281,358)(282,357)(283,359)(284,360)(285,353)(286,354)(287,356)(288,355);;
s1 := ( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)
( 14, 24)( 15, 21)( 16, 22)( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 71)
( 30, 72)( 31, 69)( 32, 70)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)
( 38, 64)( 39, 61)( 40, 62)( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 45, 55)
( 46, 56)( 47, 53)( 48, 54)( 75, 76)( 77, 79)( 78, 80)( 81, 89)( 82, 90)
( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97,137)( 98,138)
( 99,140)(100,139)(101,143)(102,144)(103,141)(104,142)(105,129)(106,130)
(107,132)(108,131)(109,135)(110,136)(111,133)(112,134)(113,121)(114,122)
(115,124)(116,123)(117,127)(118,128)(119,125)(120,126)(145,217)(146,218)
(147,220)(148,219)(149,223)(150,224)(151,221)(152,222)(153,233)(154,234)
(155,236)(156,235)(157,239)(158,240)(159,237)(160,238)(161,225)(162,226)
(163,228)(164,227)(165,231)(166,232)(167,229)(168,230)(169,281)(170,282)
(171,284)(172,283)(173,287)(174,288)(175,285)(176,286)(177,273)(178,274)
(179,276)(180,275)(181,279)(182,280)(183,277)(184,278)(185,265)(186,266)
(187,268)(188,267)(189,271)(190,272)(191,269)(192,270)(193,257)(194,258)
(195,260)(196,259)(197,263)(198,264)(199,261)(200,262)(201,249)(202,250)
(203,252)(204,251)(205,255)(206,256)(207,253)(208,254)(209,241)(210,242)
(211,244)(212,243)(213,247)(214,248)(215,245)(216,246)(289,361)(290,362)
(291,364)(292,363)(293,367)(294,368)(295,365)(296,366)(297,377)(298,378)
(299,380)(300,379)(301,383)(302,384)(303,381)(304,382)(305,369)(306,370)
(307,372)(308,371)(309,375)(310,376)(311,373)(312,374)(313,425)(314,426)
(315,428)(316,427)(317,431)(318,432)(319,429)(320,430)(321,417)(322,418)
(323,420)(324,419)(325,423)(326,424)(327,421)(328,422)(329,409)(330,410)
(331,412)(332,411)(333,415)(334,416)(335,413)(336,414)(337,401)(338,402)
(339,404)(340,403)(341,407)(342,408)(343,405)(344,406)(345,393)(346,394)
(347,396)(348,395)(349,399)(350,400)(351,397)(352,398)(353,385)(354,386)
(355,388)(356,387)(357,391)(358,392)(359,389)(360,390)(435,436)(437,439)
(438,440)(441,449)(442,450)(443,452)(444,451)(445,455)(446,456)(447,453)
(448,454)(457,497)(458,498)(459,500)(460,499)(461,503)(462,504)(463,501)
(464,502)(465,489)(466,490)(467,492)(468,491)(469,495)(470,496)(471,493)
(472,494)(473,481)(474,482)(475,484)(476,483)(477,487)(478,488)(479,485)
(480,486)(507,508)(509,511)(510,512)(513,521)(514,522)(515,524)(516,523)
(517,527)(518,528)(519,525)(520,526)(529,569)(530,570)(531,572)(532,571)
(533,575)(534,576)(535,573)(536,574)(537,561)(538,562)(539,564)(540,563)
(541,567)(542,568)(543,565)(544,566)(545,553)(546,554)(547,556)(548,555)
(549,559)(550,560)(551,557)(552,558);;
s2 := ( 1,313)( 2,314)( 3,319)( 4,320)( 5,318)( 6,317)( 7,315)( 8,316)
( 9,329)( 10,330)( 11,335)( 12,336)( 13,334)( 14,333)( 15,331)( 16,332)
( 17,321)( 18,322)( 19,327)( 20,328)( 21,326)( 22,325)( 23,323)( 24,324)
( 25,289)( 26,290)( 27,295)( 28,296)( 29,294)( 30,293)( 31,291)( 32,292)
( 33,305)( 34,306)( 35,311)( 36,312)( 37,310)( 38,309)( 39,307)( 40,308)
( 41,297)( 42,298)( 43,303)( 44,304)( 45,302)( 46,301)( 47,299)( 48,300)
( 49,353)( 50,354)( 51,359)( 52,360)( 53,358)( 54,357)( 55,355)( 56,356)
( 57,345)( 58,346)( 59,351)( 60,352)( 61,350)( 62,349)( 63,347)( 64,348)
( 65,337)( 66,338)( 67,343)( 68,344)( 69,342)( 70,341)( 71,339)( 72,340)
( 73,385)( 74,386)( 75,391)( 76,392)( 77,390)( 78,389)( 79,387)( 80,388)
( 81,401)( 82,402)( 83,407)( 84,408)( 85,406)( 86,405)( 87,403)( 88,404)
( 89,393)( 90,394)( 91,399)( 92,400)( 93,398)( 94,397)( 95,395)( 96,396)
( 97,361)( 98,362)( 99,367)(100,368)(101,366)(102,365)(103,363)(104,364)
(105,377)(106,378)(107,383)(108,384)(109,382)(110,381)(111,379)(112,380)
(113,369)(114,370)(115,375)(116,376)(117,374)(118,373)(119,371)(120,372)
(121,425)(122,426)(123,431)(124,432)(125,430)(126,429)(127,427)(128,428)
(129,417)(130,418)(131,423)(132,424)(133,422)(134,421)(135,419)(136,420)
(137,409)(138,410)(139,415)(140,416)(141,414)(142,413)(143,411)(144,412)
(145,530)(146,529)(147,536)(148,535)(149,533)(150,534)(151,532)(152,531)
(153,546)(154,545)(155,552)(156,551)(157,549)(158,550)(159,548)(160,547)
(161,538)(162,537)(163,544)(164,543)(165,541)(166,542)(167,540)(168,539)
(169,506)(170,505)(171,512)(172,511)(173,509)(174,510)(175,508)(176,507)
(177,522)(178,521)(179,528)(180,527)(181,525)(182,526)(183,524)(184,523)
(185,514)(186,513)(187,520)(188,519)(189,517)(190,518)(191,516)(192,515)
(193,570)(194,569)(195,576)(196,575)(197,573)(198,574)(199,572)(200,571)
(201,562)(202,561)(203,568)(204,567)(205,565)(206,566)(207,564)(208,563)
(209,554)(210,553)(211,560)(212,559)(213,557)(214,558)(215,556)(216,555)
(217,458)(218,457)(219,464)(220,463)(221,461)(222,462)(223,460)(224,459)
(225,474)(226,473)(227,480)(228,479)(229,477)(230,478)(231,476)(232,475)
(233,466)(234,465)(235,472)(236,471)(237,469)(238,470)(239,468)(240,467)
(241,434)(242,433)(243,440)(244,439)(245,437)(246,438)(247,436)(248,435)
(249,450)(250,449)(251,456)(252,455)(253,453)(254,454)(255,452)(256,451)
(257,442)(258,441)(259,448)(260,447)(261,445)(262,446)(263,444)(264,443)
(265,498)(266,497)(267,504)(268,503)(269,501)(270,502)(271,500)(272,499)
(273,490)(274,489)(275,496)(276,495)(277,493)(278,494)(279,492)(280,491)
(281,482)(282,481)(283,488)(284,487)(285,485)(286,486)(287,484)(288,483);;
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*s0*s1*s2*s1*s2*s0*s1*s0*s1,
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*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)!( 1,437)( 2,438)( 3,440)( 4,439)( 5,434)( 6,433)( 7,435)
( 8,436)( 9,445)( 10,446)( 11,448)( 12,447)( 13,442)( 14,441)( 15,443)
( 16,444)( 17,453)( 18,454)( 19,456)( 20,455)( 21,450)( 22,449)( 23,451)
( 24,452)( 25,461)( 26,462)( 27,464)( 28,463)( 29,458)( 30,457)( 31,459)
( 32,460)( 33,469)( 34,470)( 35,472)( 36,471)( 37,466)( 38,465)( 39,467)
( 40,468)( 41,477)( 42,478)( 43,480)( 44,479)( 45,474)( 46,473)( 47,475)
( 48,476)( 49,485)( 50,486)( 51,488)( 52,487)( 53,482)( 54,481)( 55,483)
( 56,484)( 57,493)( 58,494)( 59,496)( 60,495)( 61,490)( 62,489)( 63,491)
( 64,492)( 65,501)( 66,502)( 67,504)( 68,503)( 69,498)( 70,497)( 71,499)
( 72,500)( 73,509)( 74,510)( 75,512)( 76,511)( 77,506)( 78,505)( 79,507)
( 80,508)( 81,517)( 82,518)( 83,520)( 84,519)( 85,514)( 86,513)( 87,515)
( 88,516)( 89,525)( 90,526)( 91,528)( 92,527)( 93,522)( 94,521)( 95,523)
( 96,524)( 97,533)( 98,534)( 99,536)(100,535)(101,530)(102,529)(103,531)
(104,532)(105,541)(106,542)(107,544)(108,543)(109,538)(110,537)(111,539)
(112,540)(113,549)(114,550)(115,552)(116,551)(117,546)(118,545)(119,547)
(120,548)(121,557)(122,558)(123,560)(124,559)(125,554)(126,553)(127,555)
(128,556)(129,565)(130,566)(131,568)(132,567)(133,562)(134,561)(135,563)
(136,564)(137,573)(138,574)(139,576)(140,575)(141,570)(142,569)(143,571)
(144,572)(145,366)(146,365)(147,367)(148,368)(149,361)(150,362)(151,364)
(152,363)(153,374)(154,373)(155,375)(156,376)(157,369)(158,370)(159,372)
(160,371)(161,382)(162,381)(163,383)(164,384)(165,377)(166,378)(167,380)
(168,379)(169,390)(170,389)(171,391)(172,392)(173,385)(174,386)(175,388)
(176,387)(177,398)(178,397)(179,399)(180,400)(181,393)(182,394)(183,396)
(184,395)(185,406)(186,405)(187,407)(188,408)(189,401)(190,402)(191,404)
(192,403)(193,414)(194,413)(195,415)(196,416)(197,409)(198,410)(199,412)
(200,411)(201,422)(202,421)(203,423)(204,424)(205,417)(206,418)(207,420)
(208,419)(209,430)(210,429)(211,431)(212,432)(213,425)(214,426)(215,428)
(216,427)(217,294)(218,293)(219,295)(220,296)(221,289)(222,290)(223,292)
(224,291)(225,302)(226,301)(227,303)(228,304)(229,297)(230,298)(231,300)
(232,299)(233,310)(234,309)(235,311)(236,312)(237,305)(238,306)(239,308)
(240,307)(241,318)(242,317)(243,319)(244,320)(245,313)(246,314)(247,316)
(248,315)(249,326)(250,325)(251,327)(252,328)(253,321)(254,322)(255,324)
(256,323)(257,334)(258,333)(259,335)(260,336)(261,329)(262,330)(263,332)
(264,331)(265,342)(266,341)(267,343)(268,344)(269,337)(270,338)(271,340)
(272,339)(273,350)(274,349)(275,351)(276,352)(277,345)(278,346)(279,348)
(280,347)(281,358)(282,357)(283,359)(284,360)(285,353)(286,354)(287,356)
(288,355);
s1 := Sym(576)!( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)
( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 25, 65)( 26, 66)( 27, 68)( 28, 67)
( 29, 71)( 30, 72)( 31, 69)( 32, 70)( 33, 57)( 34, 58)( 35, 60)( 36, 59)
( 37, 63)( 38, 64)( 39, 61)( 40, 62)( 41, 49)( 42, 50)( 43, 52)( 44, 51)
( 45, 55)( 46, 56)( 47, 53)( 48, 54)( 75, 76)( 77, 79)( 78, 80)( 81, 89)
( 82, 90)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97,137)
( 98,138)( 99,140)(100,139)(101,143)(102,144)(103,141)(104,142)(105,129)
(106,130)(107,132)(108,131)(109,135)(110,136)(111,133)(112,134)(113,121)
(114,122)(115,124)(116,123)(117,127)(118,128)(119,125)(120,126)(145,217)
(146,218)(147,220)(148,219)(149,223)(150,224)(151,221)(152,222)(153,233)
(154,234)(155,236)(156,235)(157,239)(158,240)(159,237)(160,238)(161,225)
(162,226)(163,228)(164,227)(165,231)(166,232)(167,229)(168,230)(169,281)
(170,282)(171,284)(172,283)(173,287)(174,288)(175,285)(176,286)(177,273)
(178,274)(179,276)(180,275)(181,279)(182,280)(183,277)(184,278)(185,265)
(186,266)(187,268)(188,267)(189,271)(190,272)(191,269)(192,270)(193,257)
(194,258)(195,260)(196,259)(197,263)(198,264)(199,261)(200,262)(201,249)
(202,250)(203,252)(204,251)(205,255)(206,256)(207,253)(208,254)(209,241)
(210,242)(211,244)(212,243)(213,247)(214,248)(215,245)(216,246)(289,361)
(290,362)(291,364)(292,363)(293,367)(294,368)(295,365)(296,366)(297,377)
(298,378)(299,380)(300,379)(301,383)(302,384)(303,381)(304,382)(305,369)
(306,370)(307,372)(308,371)(309,375)(310,376)(311,373)(312,374)(313,425)
(314,426)(315,428)(316,427)(317,431)(318,432)(319,429)(320,430)(321,417)
(322,418)(323,420)(324,419)(325,423)(326,424)(327,421)(328,422)(329,409)
(330,410)(331,412)(332,411)(333,415)(334,416)(335,413)(336,414)(337,401)
(338,402)(339,404)(340,403)(341,407)(342,408)(343,405)(344,406)(345,393)
(346,394)(347,396)(348,395)(349,399)(350,400)(351,397)(352,398)(353,385)
(354,386)(355,388)(356,387)(357,391)(358,392)(359,389)(360,390)(435,436)
(437,439)(438,440)(441,449)(442,450)(443,452)(444,451)(445,455)(446,456)
(447,453)(448,454)(457,497)(458,498)(459,500)(460,499)(461,503)(462,504)
(463,501)(464,502)(465,489)(466,490)(467,492)(468,491)(469,495)(470,496)
(471,493)(472,494)(473,481)(474,482)(475,484)(476,483)(477,487)(478,488)
(479,485)(480,486)(507,508)(509,511)(510,512)(513,521)(514,522)(515,524)
(516,523)(517,527)(518,528)(519,525)(520,526)(529,569)(530,570)(531,572)
(532,571)(533,575)(534,576)(535,573)(536,574)(537,561)(538,562)(539,564)
(540,563)(541,567)(542,568)(543,565)(544,566)(545,553)(546,554)(547,556)
(548,555)(549,559)(550,560)(551,557)(552,558);
s2 := Sym(576)!( 1,313)( 2,314)( 3,319)( 4,320)( 5,318)( 6,317)( 7,315)
( 8,316)( 9,329)( 10,330)( 11,335)( 12,336)( 13,334)( 14,333)( 15,331)
( 16,332)( 17,321)( 18,322)( 19,327)( 20,328)( 21,326)( 22,325)( 23,323)
( 24,324)( 25,289)( 26,290)( 27,295)( 28,296)( 29,294)( 30,293)( 31,291)
( 32,292)( 33,305)( 34,306)( 35,311)( 36,312)( 37,310)( 38,309)( 39,307)
( 40,308)( 41,297)( 42,298)( 43,303)( 44,304)( 45,302)( 46,301)( 47,299)
( 48,300)( 49,353)( 50,354)( 51,359)( 52,360)( 53,358)( 54,357)( 55,355)
( 56,356)( 57,345)( 58,346)( 59,351)( 60,352)( 61,350)( 62,349)( 63,347)
( 64,348)( 65,337)( 66,338)( 67,343)( 68,344)( 69,342)( 70,341)( 71,339)
( 72,340)( 73,385)( 74,386)( 75,391)( 76,392)( 77,390)( 78,389)( 79,387)
( 80,388)( 81,401)( 82,402)( 83,407)( 84,408)( 85,406)( 86,405)( 87,403)
( 88,404)( 89,393)( 90,394)( 91,399)( 92,400)( 93,398)( 94,397)( 95,395)
( 96,396)( 97,361)( 98,362)( 99,367)(100,368)(101,366)(102,365)(103,363)
(104,364)(105,377)(106,378)(107,383)(108,384)(109,382)(110,381)(111,379)
(112,380)(113,369)(114,370)(115,375)(116,376)(117,374)(118,373)(119,371)
(120,372)(121,425)(122,426)(123,431)(124,432)(125,430)(126,429)(127,427)
(128,428)(129,417)(130,418)(131,423)(132,424)(133,422)(134,421)(135,419)
(136,420)(137,409)(138,410)(139,415)(140,416)(141,414)(142,413)(143,411)
(144,412)(145,530)(146,529)(147,536)(148,535)(149,533)(150,534)(151,532)
(152,531)(153,546)(154,545)(155,552)(156,551)(157,549)(158,550)(159,548)
(160,547)(161,538)(162,537)(163,544)(164,543)(165,541)(166,542)(167,540)
(168,539)(169,506)(170,505)(171,512)(172,511)(173,509)(174,510)(175,508)
(176,507)(177,522)(178,521)(179,528)(180,527)(181,525)(182,526)(183,524)
(184,523)(185,514)(186,513)(187,520)(188,519)(189,517)(190,518)(191,516)
(192,515)(193,570)(194,569)(195,576)(196,575)(197,573)(198,574)(199,572)
(200,571)(201,562)(202,561)(203,568)(204,567)(205,565)(206,566)(207,564)
(208,563)(209,554)(210,553)(211,560)(212,559)(213,557)(214,558)(215,556)
(216,555)(217,458)(218,457)(219,464)(220,463)(221,461)(222,462)(223,460)
(224,459)(225,474)(226,473)(227,480)(228,479)(229,477)(230,478)(231,476)
(232,475)(233,466)(234,465)(235,472)(236,471)(237,469)(238,470)(239,468)
(240,467)(241,434)(242,433)(243,440)(244,439)(245,437)(246,438)(247,436)
(248,435)(249,450)(250,449)(251,456)(252,455)(253,453)(254,454)(255,452)
(256,451)(257,442)(258,441)(259,448)(260,447)(261,445)(262,446)(263,444)
(264,443)(265,498)(266,497)(267,504)(268,503)(269,501)(270,502)(271,500)
(272,499)(273,490)(274,489)(275,496)(276,495)(277,493)(278,494)(279,492)
(280,491)(281,482)(282,481)(283,488)(284,487)(285,485)(286,486)(287,484)
(288,483);
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*s0*s1*s2*s1*s2*s0*s1*s0*s1,
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*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