Polytope of Type {24,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*1152c
if this polytope has a name.
Group : SmallGroup(1152,12921)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 72, 288, 24
Order of s0s1s2 : 8
Order of s0s1s2s1 : 6
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 : {12,8}*576a, {24,4}*576a
4-fold quotients : {6,8}*288, {12,4}*288
8-fold quotients : {6,4}*144
9-fold quotients : {8,8}*128b
16-fold quotients : {6,4}*72
18-fold quotients : {4,8}*64a, {8,4}*64a
36-fold quotients : {4,4}*32, {2,8}*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 := ( 1,145)( 2,147)( 3,146)( 4,151)( 5,153)( 6,152)( 7,148)( 8,150)
( 9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)( 16,157)
( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)( 24,170)
( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)( 32,180)
( 33,179)( 34,175)( 35,177)( 36,176)( 37,190)( 38,192)( 39,191)( 40,196)
( 41,198)( 42,197)( 43,193)( 44,195)( 45,194)( 46,181)( 47,183)( 48,182)
( 49,187)( 50,189)( 51,188)( 52,184)( 53,186)( 54,185)( 55,208)( 56,210)
( 57,209)( 58,214)( 59,216)( 60,215)( 61,211)( 62,213)( 63,212)( 64,199)
( 65,201)( 66,200)( 67,205)( 68,207)( 69,206)( 70,202)( 71,204)( 72,203)
( 73,226)( 74,228)( 75,227)( 76,232)( 77,234)( 78,233)( 79,229)( 80,231)
( 81,230)( 82,217)( 83,219)( 84,218)( 85,223)( 86,225)( 87,224)( 88,220)
( 89,222)( 90,221)( 91,244)( 92,246)( 93,245)( 94,250)( 95,252)( 96,251)
( 97,247)( 98,249)( 99,248)(100,235)(101,237)(102,236)(103,241)(104,243)
(105,242)(106,238)(107,240)(108,239)(109,253)(110,255)(111,254)(112,259)
(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)(120,263)
(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)(128,273)
(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)(136,280)
(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)(144,284)
(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)(296,438)
(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)(304,445)
(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)(312,458)
(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)(320,468)
(321,467)(322,463)(323,465)(324,464)(325,478)(326,480)(327,479)(328,484)
(329,486)(330,485)(331,481)(332,483)(333,482)(334,469)(335,471)(336,470)
(337,475)(338,477)(339,476)(340,472)(341,474)(342,473)(343,496)(344,498)
(345,497)(346,502)(347,504)(348,503)(349,499)(350,501)(351,500)(352,487)
(353,489)(354,488)(355,493)(356,495)(357,494)(358,490)(359,492)(360,491)
(361,514)(362,516)(363,515)(364,520)(365,522)(366,521)(367,517)(368,519)
(369,518)(370,505)(371,507)(372,506)(373,511)(374,513)(375,512)(376,508)
(377,510)(378,509)(379,532)(380,534)(381,533)(382,538)(383,540)(384,539)
(385,535)(386,537)(387,536)(388,523)(389,525)(390,524)(391,529)(392,531)
(393,530)(394,526)(395,528)(396,527)(397,541)(398,543)(399,542)(400,547)
(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)(408,551)
(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)(416,561)
(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)(424,568)
(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)(432,572);;
s1 := ( 1, 76)( 2, 74)( 3, 81)( 4, 73)( 5, 80)( 6, 78)( 7, 79)( 8, 77)
( 9, 75)( 10, 85)( 11, 83)( 12, 90)( 13, 82)( 14, 89)( 15, 87)( 16, 88)
( 17, 86)( 18, 84)( 19, 94)( 20, 92)( 21, 99)( 22, 91)( 23, 98)( 24, 96)
( 25, 97)( 26, 95)( 27, 93)( 28,103)( 29,101)( 30,108)( 31,100)( 32,107)
( 33,105)( 34,106)( 35,104)( 36,102)( 37,121)( 38,119)( 39,126)( 40,118)
( 41,125)( 42,123)( 43,124)( 44,122)( 45,120)( 46,112)( 47,110)( 48,117)
( 49,109)( 50,116)( 51,114)( 52,115)( 53,113)( 54,111)( 55,139)( 56,137)
( 57,144)( 58,136)( 59,143)( 60,141)( 61,142)( 62,140)( 63,138)( 64,130)
( 65,128)( 66,135)( 67,127)( 68,134)( 69,132)( 70,133)( 71,131)( 72,129)
(145,256)(146,254)(147,261)(148,253)(149,260)(150,258)(151,259)(152,257)
(153,255)(154,265)(155,263)(156,270)(157,262)(158,269)(159,267)(160,268)
(161,266)(162,264)(163,274)(164,272)(165,279)(166,271)(167,278)(168,276)
(169,277)(170,275)(171,273)(172,283)(173,281)(174,288)(175,280)(176,287)
(177,285)(178,286)(179,284)(180,282)(181,220)(182,218)(183,225)(184,217)
(185,224)(186,222)(187,223)(188,221)(189,219)(190,229)(191,227)(192,234)
(193,226)(194,233)(195,231)(196,232)(197,230)(198,228)(199,238)(200,236)
(201,243)(202,235)(203,242)(204,240)(205,241)(206,239)(207,237)(208,247)
(209,245)(210,252)(211,244)(212,251)(213,249)(214,250)(215,248)(216,246)
(289,310)(290,308)(291,315)(292,307)(293,314)(294,312)(295,313)(296,311)
(297,309)(298,319)(299,317)(300,324)(301,316)(302,323)(303,321)(304,322)
(305,320)(306,318)(325,355)(326,353)(327,360)(328,352)(329,359)(330,357)
(331,358)(332,356)(333,354)(334,346)(335,344)(336,351)(337,343)(338,350)
(339,348)(340,349)(341,347)(342,345)(361,364)(363,369)(365,368)(370,373)
(372,378)(374,377)(379,382)(381,387)(383,386)(388,391)(390,396)(392,395)
(397,409)(398,407)(399,414)(400,406)(401,413)(402,411)(403,412)(404,410)
(405,408)(415,427)(416,425)(417,432)(418,424)(419,431)(420,429)(421,430)
(422,428)(423,426)(433,499)(434,497)(435,504)(436,496)(437,503)(438,501)
(439,502)(440,500)(441,498)(442,490)(443,488)(444,495)(445,487)(446,494)
(447,492)(448,493)(449,491)(450,489)(451,481)(452,479)(453,486)(454,478)
(455,485)(456,483)(457,484)(458,482)(459,480)(460,472)(461,470)(462,477)
(463,469)(464,476)(465,474)(466,475)(467,473)(468,471)(505,553)(506,551)
(507,558)(508,550)(509,557)(510,555)(511,556)(512,554)(513,552)(514,544)
(515,542)(516,549)(517,541)(518,548)(519,546)(520,547)(521,545)(522,543)
(523,571)(524,569)(525,576)(526,568)(527,575)(528,573)(529,574)(530,572)
(531,570)(532,562)(533,560)(534,567)(535,559)(536,566)(537,564)(538,565)
(539,563)(540,561);;
s2 := ( 1,433)( 2,434)( 3,435)( 4,441)( 5,439)( 6,440)( 7,437)( 8,438)
( 9,436)( 10,442)( 11,443)( 12,444)( 13,450)( 14,448)( 15,449)( 16,446)
( 17,447)( 18,445)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)( 24,458)
( 25,455)( 26,456)( 27,454)( 28,460)( 29,461)( 30,462)( 31,468)( 32,466)
( 33,467)( 34,464)( 35,465)( 36,463)( 37,469)( 38,470)( 39,471)( 40,477)
( 41,475)( 42,476)( 43,473)( 44,474)( 45,472)( 46,478)( 47,479)( 48,480)
( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,487)( 56,488)
( 57,489)( 58,495)( 59,493)( 60,494)( 61,491)( 62,492)( 63,490)( 64,496)
( 65,497)( 66,498)( 67,504)( 68,502)( 69,503)( 70,500)( 71,501)( 72,499)
( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)( 80,537)
( 81,535)( 82,523)( 83,524)( 84,525)( 85,531)( 86,529)( 87,530)( 88,527)
( 89,528)( 90,526)( 91,514)( 92,515)( 93,516)( 94,522)( 95,520)( 96,521)
( 97,518)( 98,519)( 99,517)(100,505)(101,506)(102,507)(103,513)(104,511)
(105,512)(106,509)(107,510)(108,508)(109,568)(110,569)(111,570)(112,576)
(113,574)(114,575)(115,572)(116,573)(117,571)(118,559)(119,560)(120,561)
(121,567)(122,565)(123,566)(124,563)(125,564)(126,562)(127,550)(128,551)
(129,552)(130,558)(131,556)(132,557)(133,554)(134,555)(135,553)(136,541)
(137,542)(138,543)(139,549)(140,547)(141,548)(142,545)(143,546)(144,544)
(145,289)(146,290)(147,291)(148,297)(149,295)(150,296)(151,293)(152,294)
(153,292)(154,298)(155,299)(156,300)(157,306)(158,304)(159,305)(160,302)
(161,303)(162,301)(163,307)(164,308)(165,309)(166,315)(167,313)(168,314)
(169,311)(170,312)(171,310)(172,316)(173,317)(174,318)(175,324)(176,322)
(177,323)(178,320)(179,321)(180,319)(181,325)(182,326)(183,327)(184,333)
(185,331)(186,332)(187,329)(188,330)(189,328)(190,334)(191,335)(192,336)
(193,342)(194,340)(195,341)(196,338)(197,339)(198,337)(199,343)(200,344)
(201,345)(202,351)(203,349)(204,350)(205,347)(206,348)(207,346)(208,352)
(209,353)(210,354)(211,360)(212,358)(213,359)(214,356)(215,357)(216,355)
(217,388)(218,389)(219,390)(220,396)(221,394)(222,395)(223,392)(224,393)
(225,391)(226,379)(227,380)(228,381)(229,387)(230,385)(231,386)(232,383)
(233,384)(234,382)(235,370)(236,371)(237,372)(238,378)(239,376)(240,377)
(241,374)(242,375)(243,373)(244,361)(245,362)(246,363)(247,369)(248,367)
(249,368)(250,365)(251,366)(252,364)(253,424)(254,425)(255,426)(256,432)
(257,430)(258,431)(259,428)(260,429)(261,427)(262,415)(263,416)(264,417)
(265,423)(266,421)(267,422)(268,419)(269,420)(270,418)(271,406)(272,407)
(273,408)(274,414)(275,412)(276,413)(277,410)(278,411)(279,409)(280,397)
(281,398)(282,399)(283,405)(284,403)(285,404)(286,401)(287,402)(288,400);;
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*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,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,145)( 2,147)( 3,146)( 4,151)( 5,153)( 6,152)( 7,148)
( 8,150)( 9,149)( 10,154)( 11,156)( 12,155)( 13,160)( 14,162)( 15,161)
( 16,157)( 17,159)( 18,158)( 19,163)( 20,165)( 21,164)( 22,169)( 23,171)
( 24,170)( 25,166)( 26,168)( 27,167)( 28,172)( 29,174)( 30,173)( 31,178)
( 32,180)( 33,179)( 34,175)( 35,177)( 36,176)( 37,190)( 38,192)( 39,191)
( 40,196)( 41,198)( 42,197)( 43,193)( 44,195)( 45,194)( 46,181)( 47,183)
( 48,182)( 49,187)( 50,189)( 51,188)( 52,184)( 53,186)( 54,185)( 55,208)
( 56,210)( 57,209)( 58,214)( 59,216)( 60,215)( 61,211)( 62,213)( 63,212)
( 64,199)( 65,201)( 66,200)( 67,205)( 68,207)( 69,206)( 70,202)( 71,204)
( 72,203)( 73,226)( 74,228)( 75,227)( 76,232)( 77,234)( 78,233)( 79,229)
( 80,231)( 81,230)( 82,217)( 83,219)( 84,218)( 85,223)( 86,225)( 87,224)
( 88,220)( 89,222)( 90,221)( 91,244)( 92,246)( 93,245)( 94,250)( 95,252)
( 96,251)( 97,247)( 98,249)( 99,248)(100,235)(101,237)(102,236)(103,241)
(104,243)(105,242)(106,238)(107,240)(108,239)(109,253)(110,255)(111,254)
(112,259)(113,261)(114,260)(115,256)(116,258)(117,257)(118,262)(119,264)
(120,263)(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,271)
(128,273)(129,272)(130,277)(131,279)(132,278)(133,274)(134,276)(135,275)
(136,280)(137,282)(138,281)(139,286)(140,288)(141,287)(142,283)(143,285)
(144,284)(289,433)(290,435)(291,434)(292,439)(293,441)(294,440)(295,436)
(296,438)(297,437)(298,442)(299,444)(300,443)(301,448)(302,450)(303,449)
(304,445)(305,447)(306,446)(307,451)(308,453)(309,452)(310,457)(311,459)
(312,458)(313,454)(314,456)(315,455)(316,460)(317,462)(318,461)(319,466)
(320,468)(321,467)(322,463)(323,465)(324,464)(325,478)(326,480)(327,479)
(328,484)(329,486)(330,485)(331,481)(332,483)(333,482)(334,469)(335,471)
(336,470)(337,475)(338,477)(339,476)(340,472)(341,474)(342,473)(343,496)
(344,498)(345,497)(346,502)(347,504)(348,503)(349,499)(350,501)(351,500)
(352,487)(353,489)(354,488)(355,493)(356,495)(357,494)(358,490)(359,492)
(360,491)(361,514)(362,516)(363,515)(364,520)(365,522)(366,521)(367,517)
(368,519)(369,518)(370,505)(371,507)(372,506)(373,511)(374,513)(375,512)
(376,508)(377,510)(378,509)(379,532)(380,534)(381,533)(382,538)(383,540)
(384,539)(385,535)(386,537)(387,536)(388,523)(389,525)(390,524)(391,529)
(392,531)(393,530)(394,526)(395,528)(396,527)(397,541)(398,543)(399,542)
(400,547)(401,549)(402,548)(403,544)(404,546)(405,545)(406,550)(407,552)
(408,551)(409,556)(410,558)(411,557)(412,553)(413,555)(414,554)(415,559)
(416,561)(417,560)(418,565)(419,567)(420,566)(421,562)(422,564)(423,563)
(424,568)(425,570)(426,569)(427,574)(428,576)(429,575)(430,571)(431,573)
(432,572);
s1 := Sym(576)!( 1, 76)( 2, 74)( 3, 81)( 4, 73)( 5, 80)( 6, 78)( 7, 79)
( 8, 77)( 9, 75)( 10, 85)( 11, 83)( 12, 90)( 13, 82)( 14, 89)( 15, 87)
( 16, 88)( 17, 86)( 18, 84)( 19, 94)( 20, 92)( 21, 99)( 22, 91)( 23, 98)
( 24, 96)( 25, 97)( 26, 95)( 27, 93)( 28,103)( 29,101)( 30,108)( 31,100)
( 32,107)( 33,105)( 34,106)( 35,104)( 36,102)( 37,121)( 38,119)( 39,126)
( 40,118)( 41,125)( 42,123)( 43,124)( 44,122)( 45,120)( 46,112)( 47,110)
( 48,117)( 49,109)( 50,116)( 51,114)( 52,115)( 53,113)( 54,111)( 55,139)
( 56,137)( 57,144)( 58,136)( 59,143)( 60,141)( 61,142)( 62,140)( 63,138)
( 64,130)( 65,128)( 66,135)( 67,127)( 68,134)( 69,132)( 70,133)( 71,131)
( 72,129)(145,256)(146,254)(147,261)(148,253)(149,260)(150,258)(151,259)
(152,257)(153,255)(154,265)(155,263)(156,270)(157,262)(158,269)(159,267)
(160,268)(161,266)(162,264)(163,274)(164,272)(165,279)(166,271)(167,278)
(168,276)(169,277)(170,275)(171,273)(172,283)(173,281)(174,288)(175,280)
(176,287)(177,285)(178,286)(179,284)(180,282)(181,220)(182,218)(183,225)
(184,217)(185,224)(186,222)(187,223)(188,221)(189,219)(190,229)(191,227)
(192,234)(193,226)(194,233)(195,231)(196,232)(197,230)(198,228)(199,238)
(200,236)(201,243)(202,235)(203,242)(204,240)(205,241)(206,239)(207,237)
(208,247)(209,245)(210,252)(211,244)(212,251)(213,249)(214,250)(215,248)
(216,246)(289,310)(290,308)(291,315)(292,307)(293,314)(294,312)(295,313)
(296,311)(297,309)(298,319)(299,317)(300,324)(301,316)(302,323)(303,321)
(304,322)(305,320)(306,318)(325,355)(326,353)(327,360)(328,352)(329,359)
(330,357)(331,358)(332,356)(333,354)(334,346)(335,344)(336,351)(337,343)
(338,350)(339,348)(340,349)(341,347)(342,345)(361,364)(363,369)(365,368)
(370,373)(372,378)(374,377)(379,382)(381,387)(383,386)(388,391)(390,396)
(392,395)(397,409)(398,407)(399,414)(400,406)(401,413)(402,411)(403,412)
(404,410)(405,408)(415,427)(416,425)(417,432)(418,424)(419,431)(420,429)
(421,430)(422,428)(423,426)(433,499)(434,497)(435,504)(436,496)(437,503)
(438,501)(439,502)(440,500)(441,498)(442,490)(443,488)(444,495)(445,487)
(446,494)(447,492)(448,493)(449,491)(450,489)(451,481)(452,479)(453,486)
(454,478)(455,485)(456,483)(457,484)(458,482)(459,480)(460,472)(461,470)
(462,477)(463,469)(464,476)(465,474)(466,475)(467,473)(468,471)(505,553)
(506,551)(507,558)(508,550)(509,557)(510,555)(511,556)(512,554)(513,552)
(514,544)(515,542)(516,549)(517,541)(518,548)(519,546)(520,547)(521,545)
(522,543)(523,571)(524,569)(525,576)(526,568)(527,575)(528,573)(529,574)
(530,572)(531,570)(532,562)(533,560)(534,567)(535,559)(536,566)(537,564)
(538,565)(539,563)(540,561);
s2 := Sym(576)!( 1,433)( 2,434)( 3,435)( 4,441)( 5,439)( 6,440)( 7,437)
( 8,438)( 9,436)( 10,442)( 11,443)( 12,444)( 13,450)( 14,448)( 15,449)
( 16,446)( 17,447)( 18,445)( 19,451)( 20,452)( 21,453)( 22,459)( 23,457)
( 24,458)( 25,455)( 26,456)( 27,454)( 28,460)( 29,461)( 30,462)( 31,468)
( 32,466)( 33,467)( 34,464)( 35,465)( 36,463)( 37,469)( 38,470)( 39,471)
( 40,477)( 41,475)( 42,476)( 43,473)( 44,474)( 45,472)( 46,478)( 47,479)
( 48,480)( 49,486)( 50,484)( 51,485)( 52,482)( 53,483)( 54,481)( 55,487)
( 56,488)( 57,489)( 58,495)( 59,493)( 60,494)( 61,491)( 62,492)( 63,490)
( 64,496)( 65,497)( 66,498)( 67,504)( 68,502)( 69,503)( 70,500)( 71,501)
( 72,499)( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)
( 80,537)( 81,535)( 82,523)( 83,524)( 84,525)( 85,531)( 86,529)( 87,530)
( 88,527)( 89,528)( 90,526)( 91,514)( 92,515)( 93,516)( 94,522)( 95,520)
( 96,521)( 97,518)( 98,519)( 99,517)(100,505)(101,506)(102,507)(103,513)
(104,511)(105,512)(106,509)(107,510)(108,508)(109,568)(110,569)(111,570)
(112,576)(113,574)(114,575)(115,572)(116,573)(117,571)(118,559)(119,560)
(120,561)(121,567)(122,565)(123,566)(124,563)(125,564)(126,562)(127,550)
(128,551)(129,552)(130,558)(131,556)(132,557)(133,554)(134,555)(135,553)
(136,541)(137,542)(138,543)(139,549)(140,547)(141,548)(142,545)(143,546)
(144,544)(145,289)(146,290)(147,291)(148,297)(149,295)(150,296)(151,293)
(152,294)(153,292)(154,298)(155,299)(156,300)(157,306)(158,304)(159,305)
(160,302)(161,303)(162,301)(163,307)(164,308)(165,309)(166,315)(167,313)
(168,314)(169,311)(170,312)(171,310)(172,316)(173,317)(174,318)(175,324)
(176,322)(177,323)(178,320)(179,321)(180,319)(181,325)(182,326)(183,327)
(184,333)(185,331)(186,332)(187,329)(188,330)(189,328)(190,334)(191,335)
(192,336)(193,342)(194,340)(195,341)(196,338)(197,339)(198,337)(199,343)
(200,344)(201,345)(202,351)(203,349)(204,350)(205,347)(206,348)(207,346)
(208,352)(209,353)(210,354)(211,360)(212,358)(213,359)(214,356)(215,357)
(216,355)(217,388)(218,389)(219,390)(220,396)(221,394)(222,395)(223,392)
(224,393)(225,391)(226,379)(227,380)(228,381)(229,387)(230,385)(231,386)
(232,383)(233,384)(234,382)(235,370)(236,371)(237,372)(238,378)(239,376)
(240,377)(241,374)(242,375)(243,373)(244,361)(245,362)(246,363)(247,369)
(248,367)(249,368)(250,365)(251,366)(252,364)(253,424)(254,425)(255,426)
(256,432)(257,430)(258,431)(259,428)(260,429)(261,427)(262,415)(263,416)
(264,417)(265,423)(266,421)(267,422)(268,419)(269,420)(270,418)(271,406)
(272,407)(273,408)(274,414)(275,412)(276,413)(277,410)(278,411)(279,409)
(280,397)(281,398)(282,399)(283,405)(284,403)(285,404)(286,401)(287,402)
(288,400);
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*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,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope