Polytope of Type {12,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*1152b
if this polytope has a name.
Group : SmallGroup(1152,12010)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 24, 288, 48
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
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 : {12,12}*576a, {12,24}*576c, {12,24}*576e
3-fold quotients : {4,24}*384a, {12,8}*384a
4-fold quotients : {6,24}*288a, {12,12}*288a
6-fold quotients : {4,24}*192a, {4,12}*192a, {12,4}*192a, {4,24}*192b, {12,8}*192a, {12,8}*192b
8-fold quotients : {6,12}*144a, {12,6}*144a
9-fold quotients : {4,8}*128a
12-fold quotients : {4,12}*96a, {12,4}*96a, {2,24}*96, {6,8}*96
16-fold quotients : {6,6}*72a
18-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
24-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
36-fold quotients : {4,4}*32, {2,8}*32
48-fold quotients : {2,6}*24, {6,2}*24
72-fold quotients : {2,4}*16, {4,2}*16
96-fold quotients : {2,3}*12, {3,2}*12
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,145)( 2,150)( 3,152)( 4,148)( 5,153)( 6,146)( 7,151)( 8,147)
( 9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)( 16,160)
( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)( 24,164)
( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)( 32,180)
( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)( 40,184)
( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)( 48,197)
( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)( 56,204)
( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)( 64,208)
( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)( 72,212)
( 73,226)( 74,231)( 75,233)( 76,229)( 77,234)( 78,227)( 79,232)( 80,228)
( 81,230)( 82,217)( 83,222)( 84,224)( 85,220)( 86,225)( 87,218)( 88,223)
( 89,219)( 90,221)( 91,244)( 92,249)( 93,251)( 94,247)( 95,252)( 96,245)
( 97,250)( 98,246)( 99,248)(100,235)(101,240)(102,242)(103,238)(104,243)
(105,236)(106,241)(107,237)(108,239)(109,262)(110,267)(111,269)(112,265)
(113,270)(114,263)(115,268)(116,264)(117,266)(118,253)(119,258)(120,260)
(121,256)(122,261)(123,254)(124,259)(125,255)(126,257)(127,280)(128,285)
(129,287)(130,283)(131,288)(132,281)(133,286)(134,282)(135,284)(136,271)
(137,276)(138,278)(139,274)(140,279)(141,272)(142,277)(143,273)(144,275)
(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)(296,435)
(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)(304,448)
(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)(312,452)
(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)(320,468)
(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)(328,472)
(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)(336,485)
(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)(344,492)
(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)(352,496)
(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)(360,500)
(361,514)(362,519)(363,521)(364,517)(365,522)(366,515)(367,520)(368,516)
(369,518)(370,505)(371,510)(372,512)(373,508)(374,513)(375,506)(376,511)
(377,507)(378,509)(379,532)(380,537)(381,539)(382,535)(383,540)(384,533)
(385,538)(386,534)(387,536)(388,523)(389,528)(390,530)(391,526)(392,531)
(393,524)(394,529)(395,525)(396,527)(397,550)(398,555)(399,557)(400,553)
(401,558)(402,551)(403,556)(404,552)(405,554)(406,541)(407,546)(408,548)
(409,544)(410,549)(411,542)(412,547)(413,543)(414,545)(415,568)(416,573)
(417,575)(418,571)(419,576)(420,569)(421,574)(422,570)(423,572)(424,559)
(425,564)(426,566)(427,562)(428,567)(429,560)(430,565)(431,561)(432,563);;
s1 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 11)( 13, 17)( 14, 16)( 15, 18)
( 19, 20)( 22, 26)( 23, 25)( 24, 27)( 28, 29)( 31, 35)( 32, 34)( 33, 36)
( 37, 38)( 40, 44)( 41, 43)( 42, 45)( 46, 47)( 49, 53)( 50, 52)( 51, 54)
( 55, 56)( 58, 62)( 59, 61)( 60, 63)( 64, 65)( 67, 71)( 68, 70)( 69, 72)
( 73, 92)( 74, 91)( 75, 93)( 76, 98)( 77, 97)( 78, 99)( 79, 95)( 80, 94)
( 81, 96)( 82,101)( 83,100)( 84,102)( 85,107)( 86,106)( 87,108)( 88,104)
( 89,103)( 90,105)(109,128)(110,127)(111,129)(112,134)(113,133)(114,135)
(115,131)(116,130)(117,132)(118,137)(119,136)(120,138)(121,143)(122,142)
(123,144)(124,140)(125,139)(126,141)(145,182)(146,181)(147,183)(148,188)
(149,187)(150,189)(151,185)(152,184)(153,186)(154,191)(155,190)(156,192)
(157,197)(158,196)(159,198)(160,194)(161,193)(162,195)(163,200)(164,199)
(165,201)(166,206)(167,205)(168,207)(169,203)(170,202)(171,204)(172,209)
(173,208)(174,210)(175,215)(176,214)(177,216)(178,212)(179,211)(180,213)
(217,272)(218,271)(219,273)(220,278)(221,277)(222,279)(223,275)(224,274)
(225,276)(226,281)(227,280)(228,282)(229,287)(230,286)(231,288)(232,284)
(233,283)(234,285)(235,254)(236,253)(237,255)(238,260)(239,259)(240,261)
(241,257)(242,256)(243,258)(244,263)(245,262)(246,264)(247,269)(248,268)
(249,270)(250,266)(251,265)(252,267)(289,362)(290,361)(291,363)(292,368)
(293,367)(294,369)(295,365)(296,364)(297,366)(298,371)(299,370)(300,372)
(301,377)(302,376)(303,378)(304,374)(305,373)(306,375)(307,380)(308,379)
(309,381)(310,386)(311,385)(312,387)(313,383)(314,382)(315,384)(316,389)
(317,388)(318,390)(319,395)(320,394)(321,396)(322,392)(323,391)(324,393)
(325,398)(326,397)(327,399)(328,404)(329,403)(330,405)(331,401)(332,400)
(333,402)(334,407)(335,406)(336,408)(337,413)(338,412)(339,414)(340,410)
(341,409)(342,411)(343,416)(344,415)(345,417)(346,422)(347,421)(348,423)
(349,419)(350,418)(351,420)(352,425)(353,424)(354,426)(355,431)(356,430)
(357,432)(358,428)(359,427)(360,429)(433,551)(434,550)(435,552)(436,557)
(437,556)(438,558)(439,554)(440,553)(441,555)(442,542)(443,541)(444,543)
(445,548)(446,547)(447,549)(448,545)(449,544)(450,546)(451,569)(452,568)
(453,570)(454,575)(455,574)(456,576)(457,572)(458,571)(459,573)(460,560)
(461,559)(462,561)(463,566)(464,565)(465,567)(466,563)(467,562)(468,564)
(469,515)(470,514)(471,516)(472,521)(473,520)(474,522)(475,518)(476,517)
(477,519)(478,506)(479,505)(480,507)(481,512)(482,511)(483,513)(484,509)
(485,508)(486,510)(487,533)(488,532)(489,534)(490,539)(491,538)(492,540)
(493,536)(494,535)(495,537)(496,524)(497,523)(498,525)(499,530)(500,529)
(501,531)(502,527)(503,526)(504,528);;
s2 := ( 1,433)( 2,440)( 3,438)( 4,439)( 5,437)( 6,435)( 7,436)( 8,434)
( 9,441)( 10,442)( 11,449)( 12,447)( 13,448)( 14,446)( 15,444)( 16,445)
( 17,443)( 18,450)( 19,451)( 20,458)( 21,456)( 22,457)( 23,455)( 24,453)
( 25,454)( 26,452)( 27,459)( 28,460)( 29,467)( 30,465)( 31,466)( 32,464)
( 33,462)( 34,463)( 35,461)( 36,468)( 37,478)( 38,485)( 39,483)( 40,484)
( 41,482)( 42,480)( 43,481)( 44,479)( 45,486)( 46,469)( 47,476)( 48,474)
( 49,475)( 50,473)( 51,471)( 52,472)( 53,470)( 54,477)( 55,496)( 56,503)
( 57,501)( 58,502)( 59,500)( 60,498)( 61,499)( 62,497)( 63,504)( 64,487)
( 65,494)( 66,492)( 67,493)( 68,491)( 69,489)( 70,490)( 71,488)( 72,495)
( 73,532)( 74,539)( 75,537)( 76,538)( 77,536)( 78,534)( 79,535)( 80,533)
( 81,540)( 82,523)( 83,530)( 84,528)( 85,529)( 86,527)( 87,525)( 88,526)
( 89,524)( 90,531)( 91,514)( 92,521)( 93,519)( 94,520)( 95,518)( 96,516)
( 97,517)( 98,515)( 99,522)(100,505)(101,512)(102,510)(103,511)(104,509)
(105,507)(106,508)(107,506)(108,513)(109,559)(110,566)(111,564)(112,565)
(113,563)(114,561)(115,562)(116,560)(117,567)(118,568)(119,575)(120,573)
(121,574)(122,572)(123,570)(124,571)(125,569)(126,576)(127,541)(128,548)
(129,546)(130,547)(131,545)(132,543)(133,544)(134,542)(135,549)(136,550)
(137,557)(138,555)(139,556)(140,554)(141,552)(142,553)(143,551)(144,558)
(145,289)(146,296)(147,294)(148,295)(149,293)(150,291)(151,292)(152,290)
(153,297)(154,298)(155,305)(156,303)(157,304)(158,302)(159,300)(160,301)
(161,299)(162,306)(163,307)(164,314)(165,312)(166,313)(167,311)(168,309)
(169,310)(170,308)(171,315)(172,316)(173,323)(174,321)(175,322)(176,320)
(177,318)(178,319)(179,317)(180,324)(181,334)(182,341)(183,339)(184,340)
(185,338)(186,336)(187,337)(188,335)(189,342)(190,325)(191,332)(192,330)
(193,331)(194,329)(195,327)(196,328)(197,326)(198,333)(199,352)(200,359)
(201,357)(202,358)(203,356)(204,354)(205,355)(206,353)(207,360)(208,343)
(209,350)(210,348)(211,349)(212,347)(213,345)(214,346)(215,344)(216,351)
(217,388)(218,395)(219,393)(220,394)(221,392)(222,390)(223,391)(224,389)
(225,396)(226,379)(227,386)(228,384)(229,385)(230,383)(231,381)(232,382)
(233,380)(234,387)(235,370)(236,377)(237,375)(238,376)(239,374)(240,372)
(241,373)(242,371)(243,378)(244,361)(245,368)(246,366)(247,367)(248,365)
(249,363)(250,364)(251,362)(252,369)(253,415)(254,422)(255,420)(256,421)
(257,419)(258,417)(259,418)(260,416)(261,423)(262,424)(263,431)(264,429)
(265,430)(266,428)(267,426)(268,427)(269,425)(270,432)(271,397)(272,404)
(273,402)(274,403)(275,401)(276,399)(277,400)(278,398)(279,405)(280,406)
(281,413)(282,411)(283,412)(284,410)(285,408)(286,409)(287,407)(288,414);;
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*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*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,
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)!( 1,145)( 2,150)( 3,152)( 4,148)( 5,153)( 6,146)( 7,151)
( 8,147)( 9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)
( 16,160)( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)
( 24,164)( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)
( 32,180)( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)
( 40,184)( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)
( 48,197)( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)
( 56,204)( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)
( 64,208)( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)
( 72,212)( 73,226)( 74,231)( 75,233)( 76,229)( 77,234)( 78,227)( 79,232)
( 80,228)( 81,230)( 82,217)( 83,222)( 84,224)( 85,220)( 86,225)( 87,218)
( 88,223)( 89,219)( 90,221)( 91,244)( 92,249)( 93,251)( 94,247)( 95,252)
( 96,245)( 97,250)( 98,246)( 99,248)(100,235)(101,240)(102,242)(103,238)
(104,243)(105,236)(106,241)(107,237)(108,239)(109,262)(110,267)(111,269)
(112,265)(113,270)(114,263)(115,268)(116,264)(117,266)(118,253)(119,258)
(120,260)(121,256)(122,261)(123,254)(124,259)(125,255)(126,257)(127,280)
(128,285)(129,287)(130,283)(131,288)(132,281)(133,286)(134,282)(135,284)
(136,271)(137,276)(138,278)(139,274)(140,279)(141,272)(142,277)(143,273)
(144,275)(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)
(296,435)(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)
(304,448)(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)
(312,452)(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)
(320,468)(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)
(328,472)(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)
(336,485)(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)
(344,492)(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)
(352,496)(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)
(360,500)(361,514)(362,519)(363,521)(364,517)(365,522)(366,515)(367,520)
(368,516)(369,518)(370,505)(371,510)(372,512)(373,508)(374,513)(375,506)
(376,511)(377,507)(378,509)(379,532)(380,537)(381,539)(382,535)(383,540)
(384,533)(385,538)(386,534)(387,536)(388,523)(389,528)(390,530)(391,526)
(392,531)(393,524)(394,529)(395,525)(396,527)(397,550)(398,555)(399,557)
(400,553)(401,558)(402,551)(403,556)(404,552)(405,554)(406,541)(407,546)
(408,548)(409,544)(410,549)(411,542)(412,547)(413,543)(414,545)(415,568)
(416,573)(417,575)(418,571)(419,576)(420,569)(421,574)(422,570)(423,572)
(424,559)(425,564)(426,566)(427,562)(428,567)(429,560)(430,565)(431,561)
(432,563);
s1 := Sym(576)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)( 10, 11)( 13, 17)( 14, 16)
( 15, 18)( 19, 20)( 22, 26)( 23, 25)( 24, 27)( 28, 29)( 31, 35)( 32, 34)
( 33, 36)( 37, 38)( 40, 44)( 41, 43)( 42, 45)( 46, 47)( 49, 53)( 50, 52)
( 51, 54)( 55, 56)( 58, 62)( 59, 61)( 60, 63)( 64, 65)( 67, 71)( 68, 70)
( 69, 72)( 73, 92)( 74, 91)( 75, 93)( 76, 98)( 77, 97)( 78, 99)( 79, 95)
( 80, 94)( 81, 96)( 82,101)( 83,100)( 84,102)( 85,107)( 86,106)( 87,108)
( 88,104)( 89,103)( 90,105)(109,128)(110,127)(111,129)(112,134)(113,133)
(114,135)(115,131)(116,130)(117,132)(118,137)(119,136)(120,138)(121,143)
(122,142)(123,144)(124,140)(125,139)(126,141)(145,182)(146,181)(147,183)
(148,188)(149,187)(150,189)(151,185)(152,184)(153,186)(154,191)(155,190)
(156,192)(157,197)(158,196)(159,198)(160,194)(161,193)(162,195)(163,200)
(164,199)(165,201)(166,206)(167,205)(168,207)(169,203)(170,202)(171,204)
(172,209)(173,208)(174,210)(175,215)(176,214)(177,216)(178,212)(179,211)
(180,213)(217,272)(218,271)(219,273)(220,278)(221,277)(222,279)(223,275)
(224,274)(225,276)(226,281)(227,280)(228,282)(229,287)(230,286)(231,288)
(232,284)(233,283)(234,285)(235,254)(236,253)(237,255)(238,260)(239,259)
(240,261)(241,257)(242,256)(243,258)(244,263)(245,262)(246,264)(247,269)
(248,268)(249,270)(250,266)(251,265)(252,267)(289,362)(290,361)(291,363)
(292,368)(293,367)(294,369)(295,365)(296,364)(297,366)(298,371)(299,370)
(300,372)(301,377)(302,376)(303,378)(304,374)(305,373)(306,375)(307,380)
(308,379)(309,381)(310,386)(311,385)(312,387)(313,383)(314,382)(315,384)
(316,389)(317,388)(318,390)(319,395)(320,394)(321,396)(322,392)(323,391)
(324,393)(325,398)(326,397)(327,399)(328,404)(329,403)(330,405)(331,401)
(332,400)(333,402)(334,407)(335,406)(336,408)(337,413)(338,412)(339,414)
(340,410)(341,409)(342,411)(343,416)(344,415)(345,417)(346,422)(347,421)
(348,423)(349,419)(350,418)(351,420)(352,425)(353,424)(354,426)(355,431)
(356,430)(357,432)(358,428)(359,427)(360,429)(433,551)(434,550)(435,552)
(436,557)(437,556)(438,558)(439,554)(440,553)(441,555)(442,542)(443,541)
(444,543)(445,548)(446,547)(447,549)(448,545)(449,544)(450,546)(451,569)
(452,568)(453,570)(454,575)(455,574)(456,576)(457,572)(458,571)(459,573)
(460,560)(461,559)(462,561)(463,566)(464,565)(465,567)(466,563)(467,562)
(468,564)(469,515)(470,514)(471,516)(472,521)(473,520)(474,522)(475,518)
(476,517)(477,519)(478,506)(479,505)(480,507)(481,512)(482,511)(483,513)
(484,509)(485,508)(486,510)(487,533)(488,532)(489,534)(490,539)(491,538)
(492,540)(493,536)(494,535)(495,537)(496,524)(497,523)(498,525)(499,530)
(500,529)(501,531)(502,527)(503,526)(504,528);
s2 := Sym(576)!( 1,433)( 2,440)( 3,438)( 4,439)( 5,437)( 6,435)( 7,436)
( 8,434)( 9,441)( 10,442)( 11,449)( 12,447)( 13,448)( 14,446)( 15,444)
( 16,445)( 17,443)( 18,450)( 19,451)( 20,458)( 21,456)( 22,457)( 23,455)
( 24,453)( 25,454)( 26,452)( 27,459)( 28,460)( 29,467)( 30,465)( 31,466)
( 32,464)( 33,462)( 34,463)( 35,461)( 36,468)( 37,478)( 38,485)( 39,483)
( 40,484)( 41,482)( 42,480)( 43,481)( 44,479)( 45,486)( 46,469)( 47,476)
( 48,474)( 49,475)( 50,473)( 51,471)( 52,472)( 53,470)( 54,477)( 55,496)
( 56,503)( 57,501)( 58,502)( 59,500)( 60,498)( 61,499)( 62,497)( 63,504)
( 64,487)( 65,494)( 66,492)( 67,493)( 68,491)( 69,489)( 70,490)( 71,488)
( 72,495)( 73,532)( 74,539)( 75,537)( 76,538)( 77,536)( 78,534)( 79,535)
( 80,533)( 81,540)( 82,523)( 83,530)( 84,528)( 85,529)( 86,527)( 87,525)
( 88,526)( 89,524)( 90,531)( 91,514)( 92,521)( 93,519)( 94,520)( 95,518)
( 96,516)( 97,517)( 98,515)( 99,522)(100,505)(101,512)(102,510)(103,511)
(104,509)(105,507)(106,508)(107,506)(108,513)(109,559)(110,566)(111,564)
(112,565)(113,563)(114,561)(115,562)(116,560)(117,567)(118,568)(119,575)
(120,573)(121,574)(122,572)(123,570)(124,571)(125,569)(126,576)(127,541)
(128,548)(129,546)(130,547)(131,545)(132,543)(133,544)(134,542)(135,549)
(136,550)(137,557)(138,555)(139,556)(140,554)(141,552)(142,553)(143,551)
(144,558)(145,289)(146,296)(147,294)(148,295)(149,293)(150,291)(151,292)
(152,290)(153,297)(154,298)(155,305)(156,303)(157,304)(158,302)(159,300)
(160,301)(161,299)(162,306)(163,307)(164,314)(165,312)(166,313)(167,311)
(168,309)(169,310)(170,308)(171,315)(172,316)(173,323)(174,321)(175,322)
(176,320)(177,318)(178,319)(179,317)(180,324)(181,334)(182,341)(183,339)
(184,340)(185,338)(186,336)(187,337)(188,335)(189,342)(190,325)(191,332)
(192,330)(193,331)(194,329)(195,327)(196,328)(197,326)(198,333)(199,352)
(200,359)(201,357)(202,358)(203,356)(204,354)(205,355)(206,353)(207,360)
(208,343)(209,350)(210,348)(211,349)(212,347)(213,345)(214,346)(215,344)
(216,351)(217,388)(218,395)(219,393)(220,394)(221,392)(222,390)(223,391)
(224,389)(225,396)(226,379)(227,386)(228,384)(229,385)(230,383)(231,381)
(232,382)(233,380)(234,387)(235,370)(236,377)(237,375)(238,376)(239,374)
(240,372)(241,373)(242,371)(243,378)(244,361)(245,368)(246,366)(247,367)
(248,365)(249,363)(250,364)(251,362)(252,369)(253,415)(254,422)(255,420)
(256,421)(257,419)(258,417)(259,418)(260,416)(261,423)(262,424)(263,431)
(264,429)(265,430)(266,428)(267,426)(268,427)(269,425)(270,432)(271,397)
(272,404)(273,402)(274,403)(275,401)(276,399)(277,400)(278,398)(279,405)
(280,406)(281,413)(282,411)(283,412)(284,410)(285,408)(286,409)(287,407)
(288,414);
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*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*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,
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