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# Polytope of Type {12,24}

Atlas Canonical Name : {12,24}*1152a
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 : 12
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}*576b, {12,24}*576d, {12,24}*576f
3-fold quotients : {4,24}*384a
4-fold quotients : {6,24}*288b, {12,12}*288b
6-fold quotients : {4,24}*192a, {4,12}*192a, {4,24}*192b
8-fold quotients : {6,12}*144b, {12,6}*144c
9-fold quotients : {4,8}*128a
12-fold quotients : {4,12}*96a, {2,24}*96
16-fold quotients : {6,6}*72b
18-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
24-fold quotients : {2,12}*48, {4,6}*48a
32-fold quotients : {6,3}*36
36-fold quotients : {4,4}*32, {2,8}*32
48-fold quotients : {2,6}*24
72-fold quotients : {2,4}*16, {4,2}*16
96-fold quotients : {2,3}*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 := (  1,289)(  2,291)(  3,290)(  4,295)(  5,297)(  6,296)(  7,292)(  8,294)
(  9,293)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)( 16,301)
( 17,303)( 18,302)( 19,307)( 20,309)( 21,308)( 22,313)( 23,315)( 24,314)
( 25,310)( 26,312)( 27,311)( 28,316)( 29,318)( 30,317)( 31,322)( 32,324)
( 33,323)( 34,319)( 35,321)( 36,320)( 37,334)( 38,336)( 39,335)( 40,340)
( 41,342)( 42,341)( 43,337)( 44,339)( 45,338)( 46,325)( 47,327)( 48,326)
( 49,331)( 50,333)( 51,332)( 52,328)( 53,330)( 54,329)( 55,352)( 56,354)
( 57,353)( 58,358)( 59,360)( 60,359)( 61,355)( 62,357)( 63,356)( 64,343)
( 65,345)( 66,344)( 67,349)( 68,351)( 69,350)( 70,346)( 71,348)( 72,347)
( 73,379)( 74,381)( 75,380)( 76,385)( 77,387)( 78,386)( 79,382)( 80,384)
( 81,383)( 82,388)( 83,390)( 84,389)( 85,394)( 86,396)( 87,395)( 88,391)
( 89,393)( 90,392)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)( 96,368)
( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)(104,378)
(105,377)(106,373)(107,375)(108,374)(109,424)(110,426)(111,425)(112,430)
(113,432)(114,431)(115,427)(116,429)(117,428)(118,415)(119,417)(120,416)
(121,421)(122,423)(123,422)(124,418)(125,420)(126,419)(127,406)(128,408)
(129,407)(130,412)(131,414)(132,413)(133,409)(134,411)(135,410)(136,397)
(137,399)(138,398)(139,403)(140,405)(141,404)(142,400)(143,402)(144,401)
(145,433)(146,435)(147,434)(148,439)(149,441)(150,440)(151,436)(152,438)
(153,437)(154,442)(155,444)(156,443)(157,448)(158,450)(159,449)(160,445)
(161,447)(162,446)(163,451)(164,453)(165,452)(166,457)(167,459)(168,458)
(169,454)(170,456)(171,455)(172,460)(173,462)(174,461)(175,466)(176,468)
(177,467)(178,463)(179,465)(180,464)(181,478)(182,480)(183,479)(184,484)
(185,486)(186,485)(187,481)(188,483)(189,482)(190,469)(191,471)(192,470)
(193,475)(194,477)(195,476)(196,472)(197,474)(198,473)(199,496)(200,498)
(201,497)(202,502)(203,504)(204,503)(205,499)(206,501)(207,500)(208,487)
(209,489)(210,488)(211,493)(212,495)(213,494)(214,490)(215,492)(216,491)
(217,523)(218,525)(219,524)(220,529)(221,531)(222,530)(223,526)(224,528)
(225,527)(226,532)(227,534)(228,533)(229,538)(230,540)(231,539)(232,535)
(233,537)(234,536)(235,505)(236,507)(237,506)(238,511)(239,513)(240,512)
(241,508)(242,510)(243,509)(244,514)(245,516)(246,515)(247,520)(248,522)
(249,521)(250,517)(251,519)(252,518)(253,568)(254,570)(255,569)(256,574)
(257,576)(258,575)(259,571)(260,573)(261,572)(262,559)(263,561)(264,560)
(265,565)(266,567)(267,566)(268,562)(269,564)(270,563)(271,550)(272,552)
(273,551)(274,556)(275,558)(276,557)(277,553)(278,555)(279,554)(280,541)
(281,543)(282,542)(283,547)(284,549)(285,548)(286,544)(287,546)(288,545);;
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,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*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*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)!(  1,289)(  2,291)(  3,290)(  4,295)(  5,297)(  6,296)(  7,292)
(  8,294)(  9,293)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)
( 16,301)( 17,303)( 18,302)( 19,307)( 20,309)( 21,308)( 22,313)( 23,315)
( 24,314)( 25,310)( 26,312)( 27,311)( 28,316)( 29,318)( 30,317)( 31,322)
( 32,324)( 33,323)( 34,319)( 35,321)( 36,320)( 37,334)( 38,336)( 39,335)
( 40,340)( 41,342)( 42,341)( 43,337)( 44,339)( 45,338)( 46,325)( 47,327)
( 48,326)( 49,331)( 50,333)( 51,332)( 52,328)( 53,330)( 54,329)( 55,352)
( 56,354)( 57,353)( 58,358)( 59,360)( 60,359)( 61,355)( 62,357)( 63,356)
( 64,343)( 65,345)( 66,344)( 67,349)( 68,351)( 69,350)( 70,346)( 71,348)
( 72,347)( 73,379)( 74,381)( 75,380)( 76,385)( 77,387)( 78,386)( 79,382)
( 80,384)( 81,383)( 82,388)( 83,390)( 84,389)( 85,394)( 86,396)( 87,395)
( 88,391)( 89,393)( 90,392)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)
( 96,368)( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)
(104,378)(105,377)(106,373)(107,375)(108,374)(109,424)(110,426)(111,425)
(112,430)(113,432)(114,431)(115,427)(116,429)(117,428)(118,415)(119,417)
(120,416)(121,421)(122,423)(123,422)(124,418)(125,420)(126,419)(127,406)
(128,408)(129,407)(130,412)(131,414)(132,413)(133,409)(134,411)(135,410)
(136,397)(137,399)(138,398)(139,403)(140,405)(141,404)(142,400)(143,402)
(144,401)(145,433)(146,435)(147,434)(148,439)(149,441)(150,440)(151,436)
(152,438)(153,437)(154,442)(155,444)(156,443)(157,448)(158,450)(159,449)
(160,445)(161,447)(162,446)(163,451)(164,453)(165,452)(166,457)(167,459)
(168,458)(169,454)(170,456)(171,455)(172,460)(173,462)(174,461)(175,466)
(176,468)(177,467)(178,463)(179,465)(180,464)(181,478)(182,480)(183,479)
(184,484)(185,486)(186,485)(187,481)(188,483)(189,482)(190,469)(191,471)
(192,470)(193,475)(194,477)(195,476)(196,472)(197,474)(198,473)(199,496)
(200,498)(201,497)(202,502)(203,504)(204,503)(205,499)(206,501)(207,500)
(208,487)(209,489)(210,488)(211,493)(212,495)(213,494)(214,490)(215,492)
(216,491)(217,523)(218,525)(219,524)(220,529)(221,531)(222,530)(223,526)
(224,528)(225,527)(226,532)(227,534)(228,533)(229,538)(230,540)(231,539)
(232,535)(233,537)(234,536)(235,505)(236,507)(237,506)(238,511)(239,513)
(240,512)(241,508)(242,510)(243,509)(244,514)(245,516)(246,515)(247,520)
(248,522)(249,521)(250,517)(251,519)(252,518)(253,568)(254,570)(255,569)
(256,574)(257,576)(258,575)(259,571)(260,573)(261,572)(262,559)(263,561)
(264,560)(265,565)(266,567)(267,566)(268,562)(269,564)(270,563)(271,550)
(272,552)(273,551)(274,556)(275,558)(276,557)(277,553)(278,555)(279,554)
(280,541)(281,543)(282,542)(283,547)(284,549)(285,548)(286,544)(287,546)
(288,545);
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,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*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*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