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