Polytope of Type {8,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8}*1152b
if this polytope has a name.
Group : SmallGroup(1152,12921)
Rank : 3
Schlafli Type : {8,8}
Number of vertices, edges, etc : 72, 288, 72
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 12
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 : {8,4}*576a, {4,8}*576b
   4-fold quotients : {4,4}*288
   8-fold quotients : {4,4}*144
   9-fold quotients : {8,8}*128c
   16-fold quotients : {4,4}*72
   18-fold quotients : {8,4}*64a, {4,8}*64b
   36-fold quotients : {4,4}*32, {8,2}*32
   72-fold quotients : {2,4}*16, {4,2}*16
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,289)(  2,291)(  3,290)(  4,293)(  5,292)(  6,294)(  7,297)(  8,296)
(  9,295)( 10,298)( 11,300)( 12,299)( 13,302)( 14,301)( 15,303)( 16,306)
( 17,305)( 18,304)( 19,307)( 20,309)( 21,308)( 22,311)( 23,310)( 24,312)
( 25,315)( 26,314)( 27,313)( 28,316)( 29,318)( 30,317)( 31,320)( 32,319)
( 33,321)( 34,324)( 35,323)( 36,322)( 37,334)( 38,336)( 39,335)( 40,338)
( 41,337)( 42,339)( 43,342)( 44,341)( 45,340)( 46,325)( 47,327)( 48,326)
( 49,329)( 50,328)( 51,330)( 52,333)( 53,332)( 54,331)( 55,352)( 56,354)
( 57,353)( 58,356)( 59,355)( 60,357)( 61,360)( 62,359)( 63,358)( 64,343)
( 65,345)( 66,344)( 67,347)( 68,346)( 69,348)( 70,351)( 71,350)( 72,349)
( 73,379)( 74,381)( 75,380)( 76,383)( 77,382)( 78,384)( 79,387)( 80,386)
( 81,385)( 82,388)( 83,390)( 84,389)( 85,392)( 86,391)( 87,393)( 88,396)
( 89,395)( 90,394)( 91,361)( 92,363)( 93,362)( 94,365)( 95,364)( 96,366)
( 97,369)( 98,368)( 99,367)(100,370)(101,372)(102,371)(103,374)(104,373)
(105,375)(106,378)(107,377)(108,376)(109,424)(110,426)(111,425)(112,428)
(113,427)(114,429)(115,432)(116,431)(117,430)(118,415)(119,417)(120,416)
(121,419)(122,418)(123,420)(124,423)(125,422)(126,421)(127,406)(128,408)
(129,407)(130,410)(131,409)(132,411)(133,414)(134,413)(135,412)(136,397)
(137,399)(138,398)(139,401)(140,400)(141,402)(142,405)(143,404)(144,403)
(145,433)(146,435)(147,434)(148,437)(149,436)(150,438)(151,441)(152,440)
(153,439)(154,442)(155,444)(156,443)(157,446)(158,445)(159,447)(160,450)
(161,449)(162,448)(163,451)(164,453)(165,452)(166,455)(167,454)(168,456)
(169,459)(170,458)(171,457)(172,460)(173,462)(174,461)(175,464)(176,463)
(177,465)(178,468)(179,467)(180,466)(181,478)(182,480)(183,479)(184,482)
(185,481)(186,483)(187,486)(188,485)(189,484)(190,469)(191,471)(192,470)
(193,473)(194,472)(195,474)(196,477)(197,476)(198,475)(199,496)(200,498)
(201,497)(202,500)(203,499)(204,501)(205,504)(206,503)(207,502)(208,487)
(209,489)(210,488)(211,491)(212,490)(213,492)(214,495)(215,494)(216,493)
(217,523)(218,525)(219,524)(220,527)(221,526)(222,528)(223,531)(224,530)
(225,529)(226,532)(227,534)(228,533)(229,536)(230,535)(231,537)(232,540)
(233,539)(234,538)(235,505)(236,507)(237,506)(238,509)(239,508)(240,510)
(241,513)(242,512)(243,511)(244,514)(245,516)(246,515)(247,518)(248,517)
(249,519)(250,522)(251,521)(252,520)(253,568)(254,570)(255,569)(256,572)
(257,571)(258,573)(259,576)(260,575)(261,574)(262,559)(263,561)(264,560)
(265,563)(266,562)(267,564)(268,567)(269,566)(270,565)(271,550)(272,552)
(273,551)(274,554)(275,553)(276,555)(277,558)(278,557)(279,556)(280,541)
(281,543)(282,542)(283,545)(284,544)(285,546)(286,549)(287,548)(288,547);;
s1 := (  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)( 21, 26)
( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 37, 46)( 38, 51)( 39, 53)( 40, 49)
( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)( 57, 71)
( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73, 91)( 74, 96)
( 75, 98)( 76, 94)( 77, 99)( 78, 92)( 79, 97)( 80, 93)( 81, 95)( 82,100)
( 83,105)( 84,107)( 85,103)( 86,108)( 87,101)( 88,106)( 89,102)( 90,104)
(109,136)(110,141)(111,143)(112,139)(113,144)(114,137)(115,142)(116,138)
(117,140)(118,127)(119,132)(120,134)(121,130)(122,135)(123,128)(124,133)
(125,129)(126,131)(145,181)(146,186)(147,188)(148,184)(149,189)(150,182)
(151,187)(152,183)(153,185)(154,190)(155,195)(156,197)(157,193)(158,198)
(159,191)(160,196)(161,192)(162,194)(163,199)(164,204)(165,206)(166,202)
(167,207)(168,200)(169,205)(170,201)(171,203)(172,208)(173,213)(174,215)
(175,211)(176,216)(177,209)(178,214)(179,210)(180,212)(217,271)(218,276)
(219,278)(220,274)(221,279)(222,272)(223,277)(224,273)(225,275)(226,280)
(227,285)(228,287)(229,283)(230,288)(231,281)(232,286)(233,282)(234,284)
(235,253)(236,258)(237,260)(238,256)(239,261)(240,254)(241,259)(242,255)
(243,257)(244,262)(245,267)(246,269)(247,265)(248,270)(249,263)(250,268)
(251,264)(252,266)(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)
(295,367)(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)
(303,371)(304,376)(305,372)(306,374)(307,379)(308,384)(309,386)(310,382)
(311,387)(312,380)(313,385)(314,381)(315,383)(316,388)(317,393)(318,395)
(319,391)(320,396)(321,389)(322,394)(323,390)(324,392)(325,406)(326,411)
(327,413)(328,409)(329,414)(330,407)(331,412)(332,408)(333,410)(334,397)
(335,402)(336,404)(337,400)(338,405)(339,398)(340,403)(341,399)(342,401)
(343,424)(344,429)(345,431)(346,427)(347,432)(348,425)(349,430)(350,426)
(351,428)(352,415)(353,420)(354,422)(355,418)(356,423)(357,416)(358,421)
(359,417)(360,419)(433,550)(434,555)(435,557)(436,553)(437,558)(438,551)
(439,556)(440,552)(441,554)(442,541)(443,546)(444,548)(445,544)(446,549)
(447,542)(448,547)(449,543)(450,545)(451,568)(452,573)(453,575)(454,571)
(455,576)(456,569)(457,574)(458,570)(459,572)(460,559)(461,564)(462,566)
(463,562)(464,567)(465,560)(466,565)(467,561)(468,563)(469,514)(470,519)
(471,521)(472,517)(473,522)(474,515)(475,520)(476,516)(477,518)(478,505)
(479,510)(480,512)(481,508)(482,513)(483,506)(484,511)(485,507)(486,509)
(487,532)(488,537)(489,539)(490,535)(491,540)(492,533)(493,538)(494,534)
(495,536)(496,523)(497,528)(498,530)(499,526)(500,531)(501,524)(502,529)
(503,525)(504,527);;
s2 := (  1,440)(  2,441)(  3,439)(  4,436)(  5,437)(  6,438)(  7,435)(  8,433)
(  9,434)( 10,449)( 11,450)( 12,448)( 13,445)( 14,446)( 15,447)( 16,444)
( 17,442)( 18,443)( 19,458)( 20,459)( 21,457)( 22,454)( 23,455)( 24,456)
( 25,453)( 26,451)( 27,452)( 28,467)( 29,468)( 30,466)( 31,463)( 32,464)
( 33,465)( 34,462)( 35,460)( 36,461)( 37,476)( 38,477)( 39,475)( 40,472)
( 41,473)( 42,474)( 43,471)( 44,469)( 45,470)( 46,485)( 47,486)( 48,484)
( 49,481)( 50,482)( 51,483)( 52,480)( 53,478)( 54,479)( 55,494)( 56,495)
( 57,493)( 58,490)( 59,491)( 60,492)( 61,489)( 62,487)( 63,488)( 64,503)
( 65,504)( 66,502)( 67,499)( 68,500)( 69,501)( 70,498)( 71,496)( 72,497)
( 73,539)( 74,540)( 75,538)( 76,535)( 77,536)( 78,537)( 79,534)( 80,532)
( 81,533)( 82,530)( 83,531)( 84,529)( 85,526)( 86,527)( 87,528)( 88,525)
( 89,523)( 90,524)( 91,521)( 92,522)( 93,520)( 94,517)( 95,518)( 96,519)
( 97,516)( 98,514)( 99,515)(100,512)(101,513)(102,511)(103,508)(104,509)
(105,510)(106,507)(107,505)(108,506)(109,575)(110,576)(111,574)(112,571)
(113,572)(114,573)(115,570)(116,568)(117,569)(118,566)(119,567)(120,565)
(121,562)(122,563)(123,564)(124,561)(125,559)(126,560)(127,557)(128,558)
(129,556)(130,553)(131,554)(132,555)(133,552)(134,550)(135,551)(136,548)
(137,549)(138,547)(139,544)(140,545)(141,546)(142,543)(143,541)(144,542)
(145,296)(146,297)(147,295)(148,292)(149,293)(150,294)(151,291)(152,289)
(153,290)(154,305)(155,306)(156,304)(157,301)(158,302)(159,303)(160,300)
(161,298)(162,299)(163,314)(164,315)(165,313)(166,310)(167,311)(168,312)
(169,309)(170,307)(171,308)(172,323)(173,324)(174,322)(175,319)(176,320)
(177,321)(178,318)(179,316)(180,317)(181,332)(182,333)(183,331)(184,328)
(185,329)(186,330)(187,327)(188,325)(189,326)(190,341)(191,342)(192,340)
(193,337)(194,338)(195,339)(196,336)(197,334)(198,335)(199,350)(200,351)
(201,349)(202,346)(203,347)(204,348)(205,345)(206,343)(207,344)(208,359)
(209,360)(210,358)(211,355)(212,356)(213,357)(214,354)(215,352)(216,353)
(217,395)(218,396)(219,394)(220,391)(221,392)(222,393)(223,390)(224,388)
(225,389)(226,386)(227,387)(228,385)(229,382)(230,383)(231,384)(232,381)
(233,379)(234,380)(235,377)(236,378)(237,376)(238,373)(239,374)(240,375)
(241,372)(242,370)(243,371)(244,368)(245,369)(246,367)(247,364)(248,365)
(249,366)(250,363)(251,361)(252,362)(253,431)(254,432)(255,430)(256,427)
(257,428)(258,429)(259,426)(260,424)(261,425)(262,422)(263,423)(264,421)
(265,418)(266,419)(267,420)(268,417)(269,415)(270,416)(271,413)(272,414)
(273,412)(274,409)(275,410)(276,411)(277,408)(278,406)(279,407)(280,404)
(281,405)(282,403)(283,400)(284,401)(285,402)(286,399)(287,397)(288,398);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(576)!(  1,289)(  2,291)(  3,290)(  4,293)(  5,292)(  6,294)(  7,297)
(  8,296)(  9,295)( 10,298)( 11,300)( 12,299)( 13,302)( 14,301)( 15,303)
( 16,306)( 17,305)( 18,304)( 19,307)( 20,309)( 21,308)( 22,311)( 23,310)
( 24,312)( 25,315)( 26,314)( 27,313)( 28,316)( 29,318)( 30,317)( 31,320)
( 32,319)( 33,321)( 34,324)( 35,323)( 36,322)( 37,334)( 38,336)( 39,335)
( 40,338)( 41,337)( 42,339)( 43,342)( 44,341)( 45,340)( 46,325)( 47,327)
( 48,326)( 49,329)( 50,328)( 51,330)( 52,333)( 53,332)( 54,331)( 55,352)
( 56,354)( 57,353)( 58,356)( 59,355)( 60,357)( 61,360)( 62,359)( 63,358)
( 64,343)( 65,345)( 66,344)( 67,347)( 68,346)( 69,348)( 70,351)( 71,350)
( 72,349)( 73,379)( 74,381)( 75,380)( 76,383)( 77,382)( 78,384)( 79,387)
( 80,386)( 81,385)( 82,388)( 83,390)( 84,389)( 85,392)( 86,391)( 87,393)
( 88,396)( 89,395)( 90,394)( 91,361)( 92,363)( 93,362)( 94,365)( 95,364)
( 96,366)( 97,369)( 98,368)( 99,367)(100,370)(101,372)(102,371)(103,374)
(104,373)(105,375)(106,378)(107,377)(108,376)(109,424)(110,426)(111,425)
(112,428)(113,427)(114,429)(115,432)(116,431)(117,430)(118,415)(119,417)
(120,416)(121,419)(122,418)(123,420)(124,423)(125,422)(126,421)(127,406)
(128,408)(129,407)(130,410)(131,409)(132,411)(133,414)(134,413)(135,412)
(136,397)(137,399)(138,398)(139,401)(140,400)(141,402)(142,405)(143,404)
(144,403)(145,433)(146,435)(147,434)(148,437)(149,436)(150,438)(151,441)
(152,440)(153,439)(154,442)(155,444)(156,443)(157,446)(158,445)(159,447)
(160,450)(161,449)(162,448)(163,451)(164,453)(165,452)(166,455)(167,454)
(168,456)(169,459)(170,458)(171,457)(172,460)(173,462)(174,461)(175,464)
(176,463)(177,465)(178,468)(179,467)(180,466)(181,478)(182,480)(183,479)
(184,482)(185,481)(186,483)(187,486)(188,485)(189,484)(190,469)(191,471)
(192,470)(193,473)(194,472)(195,474)(196,477)(197,476)(198,475)(199,496)
(200,498)(201,497)(202,500)(203,499)(204,501)(205,504)(206,503)(207,502)
(208,487)(209,489)(210,488)(211,491)(212,490)(213,492)(214,495)(215,494)
(216,493)(217,523)(218,525)(219,524)(220,527)(221,526)(222,528)(223,531)
(224,530)(225,529)(226,532)(227,534)(228,533)(229,536)(230,535)(231,537)
(232,540)(233,539)(234,538)(235,505)(236,507)(237,506)(238,509)(239,508)
(240,510)(241,513)(242,512)(243,511)(244,514)(245,516)(246,515)(247,518)
(248,517)(249,519)(250,522)(251,521)(252,520)(253,568)(254,570)(255,569)
(256,572)(257,571)(258,573)(259,576)(260,575)(261,574)(262,559)(263,561)
(264,560)(265,563)(266,562)(267,564)(268,567)(269,566)(270,565)(271,550)
(272,552)(273,551)(274,554)(275,553)(276,555)(277,558)(278,557)(279,556)
(280,541)(281,543)(282,542)(283,545)(284,544)(285,546)(286,549)(287,548)
(288,547);
s1 := Sym(576)!(  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)
( 21, 26)( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 37, 46)( 38, 51)( 39, 53)
( 40, 49)( 41, 54)( 42, 47)( 43, 52)( 44, 48)( 45, 50)( 55, 64)( 56, 69)
( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73, 91)
( 74, 96)( 75, 98)( 76, 94)( 77, 99)( 78, 92)( 79, 97)( 80, 93)( 81, 95)
( 82,100)( 83,105)( 84,107)( 85,103)( 86,108)( 87,101)( 88,106)( 89,102)
( 90,104)(109,136)(110,141)(111,143)(112,139)(113,144)(114,137)(115,142)
(116,138)(117,140)(118,127)(119,132)(120,134)(121,130)(122,135)(123,128)
(124,133)(125,129)(126,131)(145,181)(146,186)(147,188)(148,184)(149,189)
(150,182)(151,187)(152,183)(153,185)(154,190)(155,195)(156,197)(157,193)
(158,198)(159,191)(160,196)(161,192)(162,194)(163,199)(164,204)(165,206)
(166,202)(167,207)(168,200)(169,205)(170,201)(171,203)(172,208)(173,213)
(174,215)(175,211)(176,216)(177,209)(178,214)(179,210)(180,212)(217,271)
(218,276)(219,278)(220,274)(221,279)(222,272)(223,277)(224,273)(225,275)
(226,280)(227,285)(228,287)(229,283)(230,288)(231,281)(232,286)(233,282)
(234,284)(235,253)(236,258)(237,260)(238,256)(239,261)(240,254)(241,259)
(242,255)(243,257)(244,262)(245,267)(246,269)(247,265)(248,270)(249,263)
(250,268)(251,264)(252,266)(289,361)(290,366)(291,368)(292,364)(293,369)
(294,362)(295,367)(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)
(302,378)(303,371)(304,376)(305,372)(306,374)(307,379)(308,384)(309,386)
(310,382)(311,387)(312,380)(313,385)(314,381)(315,383)(316,388)(317,393)
(318,395)(319,391)(320,396)(321,389)(322,394)(323,390)(324,392)(325,406)
(326,411)(327,413)(328,409)(329,414)(330,407)(331,412)(332,408)(333,410)
(334,397)(335,402)(336,404)(337,400)(338,405)(339,398)(340,403)(341,399)
(342,401)(343,424)(344,429)(345,431)(346,427)(347,432)(348,425)(349,430)
(350,426)(351,428)(352,415)(353,420)(354,422)(355,418)(356,423)(357,416)
(358,421)(359,417)(360,419)(433,550)(434,555)(435,557)(436,553)(437,558)
(438,551)(439,556)(440,552)(441,554)(442,541)(443,546)(444,548)(445,544)
(446,549)(447,542)(448,547)(449,543)(450,545)(451,568)(452,573)(453,575)
(454,571)(455,576)(456,569)(457,574)(458,570)(459,572)(460,559)(461,564)
(462,566)(463,562)(464,567)(465,560)(466,565)(467,561)(468,563)(469,514)
(470,519)(471,521)(472,517)(473,522)(474,515)(475,520)(476,516)(477,518)
(478,505)(479,510)(480,512)(481,508)(482,513)(483,506)(484,511)(485,507)
(486,509)(487,532)(488,537)(489,539)(490,535)(491,540)(492,533)(493,538)
(494,534)(495,536)(496,523)(497,528)(498,530)(499,526)(500,531)(501,524)
(502,529)(503,525)(504,527);
s2 := Sym(576)!(  1,440)(  2,441)(  3,439)(  4,436)(  5,437)(  6,438)(  7,435)
(  8,433)(  9,434)( 10,449)( 11,450)( 12,448)( 13,445)( 14,446)( 15,447)
( 16,444)( 17,442)( 18,443)( 19,458)( 20,459)( 21,457)( 22,454)( 23,455)
( 24,456)( 25,453)( 26,451)( 27,452)( 28,467)( 29,468)( 30,466)( 31,463)
( 32,464)( 33,465)( 34,462)( 35,460)( 36,461)( 37,476)( 38,477)( 39,475)
( 40,472)( 41,473)( 42,474)( 43,471)( 44,469)( 45,470)( 46,485)( 47,486)
( 48,484)( 49,481)( 50,482)( 51,483)( 52,480)( 53,478)( 54,479)( 55,494)
( 56,495)( 57,493)( 58,490)( 59,491)( 60,492)( 61,489)( 62,487)( 63,488)
( 64,503)( 65,504)( 66,502)( 67,499)( 68,500)( 69,501)( 70,498)( 71,496)
( 72,497)( 73,539)( 74,540)( 75,538)( 76,535)( 77,536)( 78,537)( 79,534)
( 80,532)( 81,533)( 82,530)( 83,531)( 84,529)( 85,526)( 86,527)( 87,528)
( 88,525)( 89,523)( 90,524)( 91,521)( 92,522)( 93,520)( 94,517)( 95,518)
( 96,519)( 97,516)( 98,514)( 99,515)(100,512)(101,513)(102,511)(103,508)
(104,509)(105,510)(106,507)(107,505)(108,506)(109,575)(110,576)(111,574)
(112,571)(113,572)(114,573)(115,570)(116,568)(117,569)(118,566)(119,567)
(120,565)(121,562)(122,563)(123,564)(124,561)(125,559)(126,560)(127,557)
(128,558)(129,556)(130,553)(131,554)(132,555)(133,552)(134,550)(135,551)
(136,548)(137,549)(138,547)(139,544)(140,545)(141,546)(142,543)(143,541)
(144,542)(145,296)(146,297)(147,295)(148,292)(149,293)(150,294)(151,291)
(152,289)(153,290)(154,305)(155,306)(156,304)(157,301)(158,302)(159,303)
(160,300)(161,298)(162,299)(163,314)(164,315)(165,313)(166,310)(167,311)
(168,312)(169,309)(170,307)(171,308)(172,323)(173,324)(174,322)(175,319)
(176,320)(177,321)(178,318)(179,316)(180,317)(181,332)(182,333)(183,331)
(184,328)(185,329)(186,330)(187,327)(188,325)(189,326)(190,341)(191,342)
(192,340)(193,337)(194,338)(195,339)(196,336)(197,334)(198,335)(199,350)
(200,351)(201,349)(202,346)(203,347)(204,348)(205,345)(206,343)(207,344)
(208,359)(209,360)(210,358)(211,355)(212,356)(213,357)(214,354)(215,352)
(216,353)(217,395)(218,396)(219,394)(220,391)(221,392)(222,393)(223,390)
(224,388)(225,389)(226,386)(227,387)(228,385)(229,382)(230,383)(231,384)
(232,381)(233,379)(234,380)(235,377)(236,378)(237,376)(238,373)(239,374)
(240,375)(241,372)(242,370)(243,371)(244,368)(245,369)(246,367)(247,364)
(248,365)(249,366)(250,363)(251,361)(252,362)(253,431)(254,432)(255,430)
(256,427)(257,428)(258,429)(259,426)(260,424)(261,425)(262,422)(263,423)
(264,421)(265,418)(266,419)(267,420)(268,417)(269,415)(270,416)(271,413)
(272,414)(273,412)(274,409)(275,410)(276,411)(277,408)(278,406)(279,407)
(280,404)(281,405)(282,403)(283,400)(284,401)(285,402)(286,399)(287,397)
(288,398);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2 >;

References : None.
to this polytope