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Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,12018)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 48, 288, 72
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
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 : {4,12}*576, {8,12}*576a, {8,12}*576b
   4-fold quotients : {8,6}*288, {4,12}*288
   8-fold quotients : {4,6}*144
   9-fold quotients : {8,4}*128a
   16-fold quotients : {4,6}*72
   18-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   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)( 38, 42)( 39, 44)( 41, 45)( 47, 51)
( 48, 53)( 50, 54)( 56, 60)( 57, 62)( 59, 63)( 65, 69)( 66, 71)( 68, 72)
( 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)(109,127)(110,132)(111,134)(112,130)(113,135)(114,128)
(115,133)(116,129)(117,131)(118,136)(119,141)(120,143)(121,139)(122,144)
(123,137)(124,142)(125,138)(126,140)(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)
(325,397)(326,402)(327,404)(328,400)(329,405)(330,398)(331,403)(332,399)
(333,401)(334,406)(335,411)(336,413)(337,409)(338,414)(339,407)(340,412)
(341,408)(342,410)(343,415)(344,420)(345,422)(346,418)(347,423)(348,416)
(349,421)(350,417)(351,419)(352,424)(353,429)(354,431)(355,427)(356,432)
(357,425)(358,430)(359,426)(360,428)(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 := (  1,152)(  2,151)(  3,153)(  4,149)(  5,148)(  6,150)(  7,146)(  8,145)
(  9,147)( 10,161)( 11,160)( 12,162)( 13,158)( 14,157)( 15,159)( 16,155)
( 17,154)( 18,156)( 19,170)( 20,169)( 21,171)( 22,167)( 23,166)( 24,168)
( 25,164)( 26,163)( 27,165)( 28,179)( 29,178)( 30,180)( 31,176)( 32,175)
( 33,177)( 34,173)( 35,172)( 36,174)( 37,188)( 38,187)( 39,189)( 40,185)
( 41,184)( 42,186)( 43,182)( 44,181)( 45,183)( 46,197)( 47,196)( 48,198)
( 49,194)( 50,193)( 51,195)( 52,191)( 53,190)( 54,192)( 55,206)( 56,205)
( 57,207)( 58,203)( 59,202)( 60,204)( 61,200)( 62,199)( 63,201)( 64,215)
( 65,214)( 66,216)( 67,212)( 68,211)( 69,213)( 70,209)( 71,208)( 72,210)
( 73,233)( 74,232)( 75,234)( 76,230)( 77,229)( 78,231)( 79,227)( 80,226)
( 81,228)( 82,224)( 83,223)( 84,225)( 85,221)( 86,220)( 87,222)( 88,218)
( 89,217)( 90,219)( 91,251)( 92,250)( 93,252)( 94,248)( 95,247)( 96,249)
( 97,245)( 98,244)( 99,246)(100,242)(101,241)(102,243)(103,239)(104,238)
(105,240)(106,236)(107,235)(108,237)(109,269)(110,268)(111,270)(112,266)
(113,265)(114,267)(115,263)(116,262)(117,264)(118,260)(119,259)(120,261)
(121,257)(122,256)(123,258)(124,254)(125,253)(126,255)(127,287)(128,286)
(129,288)(130,284)(131,283)(132,285)(133,281)(134,280)(135,282)(136,278)
(137,277)(138,279)(139,275)(140,274)(141,276)(142,272)(143,271)(144,273)
(289,440)(290,439)(291,441)(292,437)(293,436)(294,438)(295,434)(296,433)
(297,435)(298,449)(299,448)(300,450)(301,446)(302,445)(303,447)(304,443)
(305,442)(306,444)(307,458)(308,457)(309,459)(310,455)(311,454)(312,456)
(313,452)(314,451)(315,453)(316,467)(317,466)(318,468)(319,464)(320,463)
(321,465)(322,461)(323,460)(324,462)(325,476)(326,475)(327,477)(328,473)
(329,472)(330,474)(331,470)(332,469)(333,471)(334,485)(335,484)(336,486)
(337,482)(338,481)(339,483)(340,479)(341,478)(342,480)(343,494)(344,493)
(345,495)(346,491)(347,490)(348,492)(349,488)(350,487)(351,489)(352,503)
(353,502)(354,504)(355,500)(356,499)(357,501)(358,497)(359,496)(360,498)
(361,521)(362,520)(363,522)(364,518)(365,517)(366,519)(367,515)(368,514)
(369,516)(370,512)(371,511)(372,513)(373,509)(374,508)(375,510)(376,506)
(377,505)(378,507)(379,539)(380,538)(381,540)(382,536)(383,535)(384,537)
(385,533)(386,532)(387,534)(388,530)(389,529)(390,531)(391,527)(392,526)
(393,528)(394,524)(395,523)(396,525)(397,557)(398,556)(399,558)(400,554)
(401,553)(402,555)(403,551)(404,550)(405,552)(406,548)(407,547)(408,549)
(409,545)(410,544)(411,546)(412,542)(413,541)(414,543)(415,575)(416,574)
(417,576)(418,572)(419,571)(420,573)(421,569)(422,568)(423,570)(424,566)
(425,565)(426,567)(427,563)(428,562)(429,564)(430,560)(431,559)(432,561);;
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*s0*s1*s2*s0*s1*s2*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 ];;
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)( 38, 42)( 39, 44)( 41, 45)
( 47, 51)( 48, 53)( 50, 54)( 56, 60)( 57, 62)( 59, 63)( 65, 69)( 66, 71)
( 68, 72)( 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)(109,127)(110,132)(111,134)(112,130)(113,135)
(114,128)(115,133)(116,129)(117,131)(118,136)(119,141)(120,143)(121,139)
(122,144)(123,137)(124,142)(125,138)(126,140)(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)(325,397)(326,402)(327,404)(328,400)(329,405)(330,398)(331,403)
(332,399)(333,401)(334,406)(335,411)(336,413)(337,409)(338,414)(339,407)
(340,412)(341,408)(342,410)(343,415)(344,420)(345,422)(346,418)(347,423)
(348,416)(349,421)(350,417)(351,419)(352,424)(353,429)(354,431)(355,427)
(356,432)(357,425)(358,430)(359,426)(360,428)(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)!(  1,152)(  2,151)(  3,153)(  4,149)(  5,148)(  6,150)(  7,146)
(  8,145)(  9,147)( 10,161)( 11,160)( 12,162)( 13,158)( 14,157)( 15,159)
( 16,155)( 17,154)( 18,156)( 19,170)( 20,169)( 21,171)( 22,167)( 23,166)
( 24,168)( 25,164)( 26,163)( 27,165)( 28,179)( 29,178)( 30,180)( 31,176)
( 32,175)( 33,177)( 34,173)( 35,172)( 36,174)( 37,188)( 38,187)( 39,189)
( 40,185)( 41,184)( 42,186)( 43,182)( 44,181)( 45,183)( 46,197)( 47,196)
( 48,198)( 49,194)( 50,193)( 51,195)( 52,191)( 53,190)( 54,192)( 55,206)
( 56,205)( 57,207)( 58,203)( 59,202)( 60,204)( 61,200)( 62,199)( 63,201)
( 64,215)( 65,214)( 66,216)( 67,212)( 68,211)( 69,213)( 70,209)( 71,208)
( 72,210)( 73,233)( 74,232)( 75,234)( 76,230)( 77,229)( 78,231)( 79,227)
( 80,226)( 81,228)( 82,224)( 83,223)( 84,225)( 85,221)( 86,220)( 87,222)
( 88,218)( 89,217)( 90,219)( 91,251)( 92,250)( 93,252)( 94,248)( 95,247)
( 96,249)( 97,245)( 98,244)( 99,246)(100,242)(101,241)(102,243)(103,239)
(104,238)(105,240)(106,236)(107,235)(108,237)(109,269)(110,268)(111,270)
(112,266)(113,265)(114,267)(115,263)(116,262)(117,264)(118,260)(119,259)
(120,261)(121,257)(122,256)(123,258)(124,254)(125,253)(126,255)(127,287)
(128,286)(129,288)(130,284)(131,283)(132,285)(133,281)(134,280)(135,282)
(136,278)(137,277)(138,279)(139,275)(140,274)(141,276)(142,272)(143,271)
(144,273)(289,440)(290,439)(291,441)(292,437)(293,436)(294,438)(295,434)
(296,433)(297,435)(298,449)(299,448)(300,450)(301,446)(302,445)(303,447)
(304,443)(305,442)(306,444)(307,458)(308,457)(309,459)(310,455)(311,454)
(312,456)(313,452)(314,451)(315,453)(316,467)(317,466)(318,468)(319,464)
(320,463)(321,465)(322,461)(323,460)(324,462)(325,476)(326,475)(327,477)
(328,473)(329,472)(330,474)(331,470)(332,469)(333,471)(334,485)(335,484)
(336,486)(337,482)(338,481)(339,483)(340,479)(341,478)(342,480)(343,494)
(344,493)(345,495)(346,491)(347,490)(348,492)(349,488)(350,487)(351,489)
(352,503)(353,502)(354,504)(355,500)(356,499)(357,501)(358,497)(359,496)
(360,498)(361,521)(362,520)(363,522)(364,518)(365,517)(366,519)(367,515)
(368,514)(369,516)(370,512)(371,511)(372,513)(373,509)(374,508)(375,510)
(376,506)(377,505)(378,507)(379,539)(380,538)(381,540)(382,536)(383,535)
(384,537)(385,533)(386,532)(387,534)(388,530)(389,529)(390,531)(391,527)
(392,526)(393,528)(394,524)(395,523)(396,525)(397,557)(398,556)(399,558)
(400,554)(401,553)(402,555)(403,551)(404,550)(405,552)(406,548)(407,547)
(408,549)(409,545)(410,544)(411,546)(412,542)(413,541)(414,543)(415,575)
(416,574)(417,576)(418,572)(419,571)(420,573)(421,569)(422,568)(423,570)
(424,566)(425,565)(426,567)(427,563)(428,562)(429,564)(430,560)(431,559)
(432,561);
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*s0*s1*s2*s0*s1*s2*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 >; 
 
References : None.
to this polytope