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Polytope of Type {12,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98785)
Rank : 4
Schlafli Type : {12,8,6}
Number of vertices, edges, etc : 12, 48, 24, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
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 : {12,4,6}*576
   3-fold quotients : {12,8,2}*384b, {4,8,6}*384b
   4-fold quotients : {12,2,6}*288, {6,4,6}*288
   6-fold quotients : {12,4,2}*192a, {4,4,6}*192
   8-fold quotients : {12,2,3}*144, {6,2,6}*144
   9-fold quotients : {4,8,2}*128b
   12-fold quotients : {12,2,2}*96, {2,4,6}*96a, {4,2,6}*96, {6,4,2}*96a
   16-fold quotients : {3,2,6}*72, {6,2,3}*72
   18-fold quotients : {4,4,2}*64
   24-fold quotients : {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
   32-fold quotients : {3,2,3}*36
   36-fold quotients : {2,4,2}*32, {4,2,2}*32
   48-fold quotients : {2,2,3}*24, {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,217)(  2,224)(  3,222)(  4,223)(  5,221)(  6,219)(  7,220)(  8,218)
(  9,225)( 10,226)( 11,233)( 12,231)( 13,232)( 14,230)( 15,228)( 16,229)
( 17,227)( 18,234)( 19,235)( 20,242)( 21,240)( 22,241)( 23,239)( 24,237)
( 25,238)( 26,236)( 27,243)( 28,244)( 29,251)( 30,249)( 31,250)( 32,248)
( 33,246)( 34,247)( 35,245)( 36,252)( 37,262)( 38,269)( 39,267)( 40,268)
( 41,266)( 42,264)( 43,265)( 44,263)( 45,270)( 46,253)( 47,260)( 48,258)
( 49,259)( 50,257)( 51,255)( 52,256)( 53,254)( 54,261)( 55,280)( 56,287)
( 57,285)( 58,286)( 59,284)( 60,282)( 61,283)( 62,281)( 63,288)( 64,271)
( 65,278)( 66,276)( 67,277)( 68,275)( 69,273)( 70,274)( 71,272)( 72,279)
( 73,145)( 74,152)( 75,150)( 76,151)( 77,149)( 78,147)( 79,148)( 80,146)
( 81,153)( 82,154)( 83,161)( 84,159)( 85,160)( 86,158)( 87,156)( 88,157)
( 89,155)( 90,162)( 91,163)( 92,170)( 93,168)( 94,169)( 95,167)( 96,165)
( 97,166)( 98,164)( 99,171)(100,172)(101,179)(102,177)(103,178)(104,176)
(105,174)(106,175)(107,173)(108,180)(109,190)(110,197)(111,195)(112,196)
(113,194)(114,192)(115,193)(116,191)(117,198)(118,181)(119,188)(120,186)
(121,187)(122,185)(123,183)(124,184)(125,182)(126,189)(127,208)(128,215)
(129,213)(130,214)(131,212)(132,210)(133,211)(134,209)(135,216)(136,199)
(137,206)(138,204)(139,205)(140,203)(141,201)(142,202)(143,200)(144,207)
(289,505)(290,512)(291,510)(292,511)(293,509)(294,507)(295,508)(296,506)
(297,513)(298,514)(299,521)(300,519)(301,520)(302,518)(303,516)(304,517)
(305,515)(306,522)(307,523)(308,530)(309,528)(310,529)(311,527)(312,525)
(313,526)(314,524)(315,531)(316,532)(317,539)(318,537)(319,538)(320,536)
(321,534)(322,535)(323,533)(324,540)(325,550)(326,557)(327,555)(328,556)
(329,554)(330,552)(331,553)(332,551)(333,558)(334,541)(335,548)(336,546)
(337,547)(338,545)(339,543)(340,544)(341,542)(342,549)(343,568)(344,575)
(345,573)(346,574)(347,572)(348,570)(349,571)(350,569)(351,576)(352,559)
(353,566)(354,564)(355,565)(356,563)(357,561)(358,562)(359,560)(360,567)
(361,433)(362,440)(363,438)(364,439)(365,437)(366,435)(367,436)(368,434)
(369,441)(370,442)(371,449)(372,447)(373,448)(374,446)(375,444)(376,445)
(377,443)(378,450)(379,451)(380,458)(381,456)(382,457)(383,455)(384,453)
(385,454)(386,452)(387,459)(388,460)(389,467)(390,465)(391,466)(392,464)
(393,462)(394,463)(395,461)(396,468)(397,478)(398,485)(399,483)(400,484)
(401,482)(402,480)(403,481)(404,479)(405,486)(406,469)(407,476)(408,474)
(409,475)(410,473)(411,471)(412,472)(413,470)(414,477)(415,496)(416,503)
(417,501)(418,502)(419,500)(420,498)(421,499)(422,497)(423,504)(424,487)
(425,494)(426,492)(427,493)(428,491)(429,489)(430,490)(431,488)(432,495);;
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)
(145,238)(146,236)(147,243)(148,235)(149,242)(150,240)(151,241)(152,239)
(153,237)(154,247)(155,245)(156,252)(157,244)(158,251)(159,249)(160,250)
(161,248)(162,246)(163,220)(164,218)(165,225)(166,217)(167,224)(168,222)
(169,223)(170,221)(171,219)(172,229)(173,227)(174,234)(175,226)(176,233)
(177,231)(178,232)(179,230)(180,228)(181,283)(182,281)(183,288)(184,280)
(185,287)(186,285)(187,286)(188,284)(189,282)(190,274)(191,272)(192,279)
(193,271)(194,278)(195,276)(196,277)(197,275)(198,273)(199,265)(200,263)
(201,270)(202,262)(203,269)(204,267)(205,268)(206,266)(207,264)(208,256)
(209,254)(210,261)(211,253)(212,260)(213,258)(214,259)(215,257)(216,255)
(289,400)(290,398)(291,405)(292,397)(293,404)(294,402)(295,403)(296,401)
(297,399)(298,409)(299,407)(300,414)(301,406)(302,413)(303,411)(304,412)
(305,410)(306,408)(307,418)(308,416)(309,423)(310,415)(311,422)(312,420)
(313,421)(314,419)(315,417)(316,427)(317,425)(318,432)(319,424)(320,431)
(321,429)(322,430)(323,428)(324,426)(325,364)(326,362)(327,369)(328,361)
(329,368)(330,366)(331,367)(332,365)(333,363)(334,373)(335,371)(336,378)
(337,370)(338,377)(339,375)(340,376)(341,374)(342,372)(343,382)(344,380)
(345,387)(346,379)(347,386)(348,384)(349,385)(350,383)(351,381)(352,391)
(353,389)(354,396)(355,388)(356,395)(357,393)(358,394)(359,392)(360,390)
(433,571)(434,569)(435,576)(436,568)(437,575)(438,573)(439,574)(440,572)
(441,570)(442,562)(443,560)(444,567)(445,559)(446,566)(447,564)(448,565)
(449,563)(450,561)(451,553)(452,551)(453,558)(454,550)(455,557)(456,555)
(457,556)(458,554)(459,552)(460,544)(461,542)(462,549)(463,541)(464,548)
(465,546)(466,547)(467,545)(468,543)(469,535)(470,533)(471,540)(472,532)
(473,539)(474,537)(475,538)(476,536)(477,534)(478,526)(479,524)(480,531)
(481,523)(482,530)(483,528)(484,529)(485,527)(486,525)(487,517)(488,515)
(489,522)(490,514)(491,521)(492,519)(493,520)(494,518)(495,516)(496,508)
(497,506)(498,513)(499,505)(500,512)(501,510)(502,511)(503,509)(504,507);;
s2 := (  1,361)(  2,366)(  3,368)(  4,364)(  5,369)(  6,362)(  7,367)(  8,363)
(  9,365)( 10,370)( 11,375)( 12,377)( 13,373)( 14,378)( 15,371)( 16,376)
( 17,372)( 18,374)( 19,388)( 20,393)( 21,395)( 22,391)( 23,396)( 24,389)
( 25,394)( 26,390)( 27,392)( 28,379)( 29,384)( 30,386)( 31,382)( 32,387)
( 33,380)( 34,385)( 35,381)( 36,383)( 37,406)( 38,411)( 39,413)( 40,409)
( 41,414)( 42,407)( 43,412)( 44,408)( 45,410)( 46,397)( 47,402)( 48,404)
( 49,400)( 50,405)( 51,398)( 52,403)( 53,399)( 54,401)( 55,415)( 56,420)
( 57,422)( 58,418)( 59,423)( 60,416)( 61,421)( 62,417)( 63,419)( 64,424)
( 65,429)( 66,431)( 67,427)( 68,432)( 69,425)( 70,430)( 71,426)( 72,428)
( 73,289)( 74,294)( 75,296)( 76,292)( 77,297)( 78,290)( 79,295)( 80,291)
( 81,293)( 82,298)( 83,303)( 84,305)( 85,301)( 86,306)( 87,299)( 88,304)
( 89,300)( 90,302)( 91,316)( 92,321)( 93,323)( 94,319)( 95,324)( 96,317)
( 97,322)( 98,318)( 99,320)(100,307)(101,312)(102,314)(103,310)(104,315)
(105,308)(106,313)(107,309)(108,311)(109,334)(110,339)(111,341)(112,337)
(113,342)(114,335)(115,340)(116,336)(117,338)(118,325)(119,330)(120,332)
(121,328)(122,333)(123,326)(124,331)(125,327)(126,329)(127,343)(128,348)
(129,350)(130,346)(131,351)(132,344)(133,349)(134,345)(135,347)(136,352)
(137,357)(138,359)(139,355)(140,360)(141,353)(142,358)(143,354)(144,356)
(145,505)(146,510)(147,512)(148,508)(149,513)(150,506)(151,511)(152,507)
(153,509)(154,514)(155,519)(156,521)(157,517)(158,522)(159,515)(160,520)
(161,516)(162,518)(163,532)(164,537)(165,539)(166,535)(167,540)(168,533)
(169,538)(170,534)(171,536)(172,523)(173,528)(174,530)(175,526)(176,531)
(177,524)(178,529)(179,525)(180,527)(181,550)(182,555)(183,557)(184,553)
(185,558)(186,551)(187,556)(188,552)(189,554)(190,541)(191,546)(192,548)
(193,544)(194,549)(195,542)(196,547)(197,543)(198,545)(199,559)(200,564)
(201,566)(202,562)(203,567)(204,560)(205,565)(206,561)(207,563)(208,568)
(209,573)(210,575)(211,571)(212,576)(213,569)(214,574)(215,570)(216,572)
(217,433)(218,438)(219,440)(220,436)(221,441)(222,434)(223,439)(224,435)
(225,437)(226,442)(227,447)(228,449)(229,445)(230,450)(231,443)(232,448)
(233,444)(234,446)(235,460)(236,465)(237,467)(238,463)(239,468)(240,461)
(241,466)(242,462)(243,464)(244,451)(245,456)(246,458)(247,454)(248,459)
(249,452)(250,457)(251,453)(252,455)(253,478)(254,483)(255,485)(256,481)
(257,486)(258,479)(259,484)(260,480)(261,482)(262,469)(263,474)(264,476)
(265,472)(266,477)(267,470)(268,475)(269,471)(270,473)(271,487)(272,492)
(273,494)(274,490)(275,495)(276,488)(277,493)(278,489)(279,491)(280,496)
(281,501)(282,503)(283,499)(284,504)(285,497)(286,502)(287,498)(288,500);;
s3 := (  1, 77)(  2, 79)(  3, 75)(  4, 80)(  5, 73)(  6, 78)(  7, 74)(  8, 76)
(  9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)( 16, 83)
( 17, 85)( 18, 90)( 19, 95)( 20, 97)( 21, 93)( 22, 98)( 23, 91)( 24, 96)
( 25, 92)( 26, 94)( 27, 99)( 28,104)( 29,106)( 30,102)( 31,107)( 32,100)
( 33,105)( 34,101)( 35,103)( 36,108)( 37,113)( 38,115)( 39,111)( 40,116)
( 41,109)( 42,114)( 43,110)( 44,112)( 45,117)( 46,122)( 47,124)( 48,120)
( 49,125)( 50,118)( 51,123)( 52,119)( 53,121)( 54,126)( 55,131)( 56,133)
( 57,129)( 58,134)( 59,127)( 60,132)( 61,128)( 62,130)( 63,135)( 64,140)
( 65,142)( 66,138)( 67,143)( 68,136)( 69,141)( 70,137)( 71,139)( 72,144)
(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)(152,220)
(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)(160,227)
(161,229)(162,234)(163,239)(164,241)(165,237)(166,242)(167,235)(168,240)
(169,236)(170,238)(171,243)(172,248)(173,250)(174,246)(175,251)(176,244)
(177,249)(178,245)(179,247)(180,252)(181,257)(182,259)(183,255)(184,260)
(185,253)(186,258)(187,254)(188,256)(189,261)(190,266)(191,268)(192,264)
(193,269)(194,262)(195,267)(196,263)(197,265)(198,270)(199,275)(200,277)
(201,273)(202,278)(203,271)(204,276)(205,272)(206,274)(207,279)(208,284)
(209,286)(210,282)(211,287)(212,280)(213,285)(214,281)(215,283)(216,288)
(289,365)(290,367)(291,363)(292,368)(293,361)(294,366)(295,362)(296,364)
(297,369)(298,374)(299,376)(300,372)(301,377)(302,370)(303,375)(304,371)
(305,373)(306,378)(307,383)(308,385)(309,381)(310,386)(311,379)(312,384)
(313,380)(314,382)(315,387)(316,392)(317,394)(318,390)(319,395)(320,388)
(321,393)(322,389)(323,391)(324,396)(325,401)(326,403)(327,399)(328,404)
(329,397)(330,402)(331,398)(332,400)(333,405)(334,410)(335,412)(336,408)
(337,413)(338,406)(339,411)(340,407)(341,409)(342,414)(343,419)(344,421)
(345,417)(346,422)(347,415)(348,420)(349,416)(350,418)(351,423)(352,428)
(353,430)(354,426)(355,431)(356,424)(357,429)(358,425)(359,427)(360,432)
(433,509)(434,511)(435,507)(436,512)(437,505)(438,510)(439,506)(440,508)
(441,513)(442,518)(443,520)(444,516)(445,521)(446,514)(447,519)(448,515)
(449,517)(450,522)(451,527)(452,529)(453,525)(454,530)(455,523)(456,528)
(457,524)(458,526)(459,531)(460,536)(461,538)(462,534)(463,539)(464,532)
(465,537)(466,533)(467,535)(468,540)(469,545)(470,547)(471,543)(472,548)
(473,541)(474,546)(475,542)(476,544)(477,549)(478,554)(479,556)(480,552)
(481,557)(482,550)(483,555)(484,551)(485,553)(486,558)(487,563)(488,565)
(489,561)(490,566)(491,559)(492,564)(493,560)(494,562)(495,567)(496,572)
(497,574)(498,570)(499,575)(500,568)(501,573)(502,569)(503,571)(504,576);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(576)!(  1,217)(  2,224)(  3,222)(  4,223)(  5,221)(  6,219)(  7,220)
(  8,218)(  9,225)( 10,226)( 11,233)( 12,231)( 13,232)( 14,230)( 15,228)
( 16,229)( 17,227)( 18,234)( 19,235)( 20,242)( 21,240)( 22,241)( 23,239)
( 24,237)( 25,238)( 26,236)( 27,243)( 28,244)( 29,251)( 30,249)( 31,250)
( 32,248)( 33,246)( 34,247)( 35,245)( 36,252)( 37,262)( 38,269)( 39,267)
( 40,268)( 41,266)( 42,264)( 43,265)( 44,263)( 45,270)( 46,253)( 47,260)
( 48,258)( 49,259)( 50,257)( 51,255)( 52,256)( 53,254)( 54,261)( 55,280)
( 56,287)( 57,285)( 58,286)( 59,284)( 60,282)( 61,283)( 62,281)( 63,288)
( 64,271)( 65,278)( 66,276)( 67,277)( 68,275)( 69,273)( 70,274)( 71,272)
( 72,279)( 73,145)( 74,152)( 75,150)( 76,151)( 77,149)( 78,147)( 79,148)
( 80,146)( 81,153)( 82,154)( 83,161)( 84,159)( 85,160)( 86,158)( 87,156)
( 88,157)( 89,155)( 90,162)( 91,163)( 92,170)( 93,168)( 94,169)( 95,167)
( 96,165)( 97,166)( 98,164)( 99,171)(100,172)(101,179)(102,177)(103,178)
(104,176)(105,174)(106,175)(107,173)(108,180)(109,190)(110,197)(111,195)
(112,196)(113,194)(114,192)(115,193)(116,191)(117,198)(118,181)(119,188)
(120,186)(121,187)(122,185)(123,183)(124,184)(125,182)(126,189)(127,208)
(128,215)(129,213)(130,214)(131,212)(132,210)(133,211)(134,209)(135,216)
(136,199)(137,206)(138,204)(139,205)(140,203)(141,201)(142,202)(143,200)
(144,207)(289,505)(290,512)(291,510)(292,511)(293,509)(294,507)(295,508)
(296,506)(297,513)(298,514)(299,521)(300,519)(301,520)(302,518)(303,516)
(304,517)(305,515)(306,522)(307,523)(308,530)(309,528)(310,529)(311,527)
(312,525)(313,526)(314,524)(315,531)(316,532)(317,539)(318,537)(319,538)
(320,536)(321,534)(322,535)(323,533)(324,540)(325,550)(326,557)(327,555)
(328,556)(329,554)(330,552)(331,553)(332,551)(333,558)(334,541)(335,548)
(336,546)(337,547)(338,545)(339,543)(340,544)(341,542)(342,549)(343,568)
(344,575)(345,573)(346,574)(347,572)(348,570)(349,571)(350,569)(351,576)
(352,559)(353,566)(354,564)(355,565)(356,563)(357,561)(358,562)(359,560)
(360,567)(361,433)(362,440)(363,438)(364,439)(365,437)(366,435)(367,436)
(368,434)(369,441)(370,442)(371,449)(372,447)(373,448)(374,446)(375,444)
(376,445)(377,443)(378,450)(379,451)(380,458)(381,456)(382,457)(383,455)
(384,453)(385,454)(386,452)(387,459)(388,460)(389,467)(390,465)(391,466)
(392,464)(393,462)(394,463)(395,461)(396,468)(397,478)(398,485)(399,483)
(400,484)(401,482)(402,480)(403,481)(404,479)(405,486)(406,469)(407,476)
(408,474)(409,475)(410,473)(411,471)(412,472)(413,470)(414,477)(415,496)
(416,503)(417,501)(418,502)(419,500)(420,498)(421,499)(422,497)(423,504)
(424,487)(425,494)(426,492)(427,493)(428,491)(429,489)(430,490)(431,488)
(432,495);
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)(145,238)(146,236)(147,243)(148,235)(149,242)(150,240)(151,241)
(152,239)(153,237)(154,247)(155,245)(156,252)(157,244)(158,251)(159,249)
(160,250)(161,248)(162,246)(163,220)(164,218)(165,225)(166,217)(167,224)
(168,222)(169,223)(170,221)(171,219)(172,229)(173,227)(174,234)(175,226)
(176,233)(177,231)(178,232)(179,230)(180,228)(181,283)(182,281)(183,288)
(184,280)(185,287)(186,285)(187,286)(188,284)(189,282)(190,274)(191,272)
(192,279)(193,271)(194,278)(195,276)(196,277)(197,275)(198,273)(199,265)
(200,263)(201,270)(202,262)(203,269)(204,267)(205,268)(206,266)(207,264)
(208,256)(209,254)(210,261)(211,253)(212,260)(213,258)(214,259)(215,257)
(216,255)(289,400)(290,398)(291,405)(292,397)(293,404)(294,402)(295,403)
(296,401)(297,399)(298,409)(299,407)(300,414)(301,406)(302,413)(303,411)
(304,412)(305,410)(306,408)(307,418)(308,416)(309,423)(310,415)(311,422)
(312,420)(313,421)(314,419)(315,417)(316,427)(317,425)(318,432)(319,424)
(320,431)(321,429)(322,430)(323,428)(324,426)(325,364)(326,362)(327,369)
(328,361)(329,368)(330,366)(331,367)(332,365)(333,363)(334,373)(335,371)
(336,378)(337,370)(338,377)(339,375)(340,376)(341,374)(342,372)(343,382)
(344,380)(345,387)(346,379)(347,386)(348,384)(349,385)(350,383)(351,381)
(352,391)(353,389)(354,396)(355,388)(356,395)(357,393)(358,394)(359,392)
(360,390)(433,571)(434,569)(435,576)(436,568)(437,575)(438,573)(439,574)
(440,572)(441,570)(442,562)(443,560)(444,567)(445,559)(446,566)(447,564)
(448,565)(449,563)(450,561)(451,553)(452,551)(453,558)(454,550)(455,557)
(456,555)(457,556)(458,554)(459,552)(460,544)(461,542)(462,549)(463,541)
(464,548)(465,546)(466,547)(467,545)(468,543)(469,535)(470,533)(471,540)
(472,532)(473,539)(474,537)(475,538)(476,536)(477,534)(478,526)(479,524)
(480,531)(481,523)(482,530)(483,528)(484,529)(485,527)(486,525)(487,517)
(488,515)(489,522)(490,514)(491,521)(492,519)(493,520)(494,518)(495,516)
(496,508)(497,506)(498,513)(499,505)(500,512)(501,510)(502,511)(503,509)
(504,507);
s2 := Sym(576)!(  1,361)(  2,366)(  3,368)(  4,364)(  5,369)(  6,362)(  7,367)
(  8,363)(  9,365)( 10,370)( 11,375)( 12,377)( 13,373)( 14,378)( 15,371)
( 16,376)( 17,372)( 18,374)( 19,388)( 20,393)( 21,395)( 22,391)( 23,396)
( 24,389)( 25,394)( 26,390)( 27,392)( 28,379)( 29,384)( 30,386)( 31,382)
( 32,387)( 33,380)( 34,385)( 35,381)( 36,383)( 37,406)( 38,411)( 39,413)
( 40,409)( 41,414)( 42,407)( 43,412)( 44,408)( 45,410)( 46,397)( 47,402)
( 48,404)( 49,400)( 50,405)( 51,398)( 52,403)( 53,399)( 54,401)( 55,415)
( 56,420)( 57,422)( 58,418)( 59,423)( 60,416)( 61,421)( 62,417)( 63,419)
( 64,424)( 65,429)( 66,431)( 67,427)( 68,432)( 69,425)( 70,430)( 71,426)
( 72,428)( 73,289)( 74,294)( 75,296)( 76,292)( 77,297)( 78,290)( 79,295)
( 80,291)( 81,293)( 82,298)( 83,303)( 84,305)( 85,301)( 86,306)( 87,299)
( 88,304)( 89,300)( 90,302)( 91,316)( 92,321)( 93,323)( 94,319)( 95,324)
( 96,317)( 97,322)( 98,318)( 99,320)(100,307)(101,312)(102,314)(103,310)
(104,315)(105,308)(106,313)(107,309)(108,311)(109,334)(110,339)(111,341)
(112,337)(113,342)(114,335)(115,340)(116,336)(117,338)(118,325)(119,330)
(120,332)(121,328)(122,333)(123,326)(124,331)(125,327)(126,329)(127,343)
(128,348)(129,350)(130,346)(131,351)(132,344)(133,349)(134,345)(135,347)
(136,352)(137,357)(138,359)(139,355)(140,360)(141,353)(142,358)(143,354)
(144,356)(145,505)(146,510)(147,512)(148,508)(149,513)(150,506)(151,511)
(152,507)(153,509)(154,514)(155,519)(156,521)(157,517)(158,522)(159,515)
(160,520)(161,516)(162,518)(163,532)(164,537)(165,539)(166,535)(167,540)
(168,533)(169,538)(170,534)(171,536)(172,523)(173,528)(174,530)(175,526)
(176,531)(177,524)(178,529)(179,525)(180,527)(181,550)(182,555)(183,557)
(184,553)(185,558)(186,551)(187,556)(188,552)(189,554)(190,541)(191,546)
(192,548)(193,544)(194,549)(195,542)(196,547)(197,543)(198,545)(199,559)
(200,564)(201,566)(202,562)(203,567)(204,560)(205,565)(206,561)(207,563)
(208,568)(209,573)(210,575)(211,571)(212,576)(213,569)(214,574)(215,570)
(216,572)(217,433)(218,438)(219,440)(220,436)(221,441)(222,434)(223,439)
(224,435)(225,437)(226,442)(227,447)(228,449)(229,445)(230,450)(231,443)
(232,448)(233,444)(234,446)(235,460)(236,465)(237,467)(238,463)(239,468)
(240,461)(241,466)(242,462)(243,464)(244,451)(245,456)(246,458)(247,454)
(248,459)(249,452)(250,457)(251,453)(252,455)(253,478)(254,483)(255,485)
(256,481)(257,486)(258,479)(259,484)(260,480)(261,482)(262,469)(263,474)
(264,476)(265,472)(266,477)(267,470)(268,475)(269,471)(270,473)(271,487)
(272,492)(273,494)(274,490)(275,495)(276,488)(277,493)(278,489)(279,491)
(280,496)(281,501)(282,503)(283,499)(284,504)(285,497)(286,502)(287,498)
(288,500);
s3 := Sym(576)!(  1, 77)(  2, 79)(  3, 75)(  4, 80)(  5, 73)(  6, 78)(  7, 74)
(  8, 76)(  9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)
( 16, 83)( 17, 85)( 18, 90)( 19, 95)( 20, 97)( 21, 93)( 22, 98)( 23, 91)
( 24, 96)( 25, 92)( 26, 94)( 27, 99)( 28,104)( 29,106)( 30,102)( 31,107)
( 32,100)( 33,105)( 34,101)( 35,103)( 36,108)( 37,113)( 38,115)( 39,111)
( 40,116)( 41,109)( 42,114)( 43,110)( 44,112)( 45,117)( 46,122)( 47,124)
( 48,120)( 49,125)( 50,118)( 51,123)( 52,119)( 53,121)( 54,126)( 55,131)
( 56,133)( 57,129)( 58,134)( 59,127)( 60,132)( 61,128)( 62,130)( 63,135)
( 64,140)( 65,142)( 66,138)( 67,143)( 68,136)( 69,141)( 70,137)( 71,139)
( 72,144)(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)
(152,220)(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)
(160,227)(161,229)(162,234)(163,239)(164,241)(165,237)(166,242)(167,235)
(168,240)(169,236)(170,238)(171,243)(172,248)(173,250)(174,246)(175,251)
(176,244)(177,249)(178,245)(179,247)(180,252)(181,257)(182,259)(183,255)
(184,260)(185,253)(186,258)(187,254)(188,256)(189,261)(190,266)(191,268)
(192,264)(193,269)(194,262)(195,267)(196,263)(197,265)(198,270)(199,275)
(200,277)(201,273)(202,278)(203,271)(204,276)(205,272)(206,274)(207,279)
(208,284)(209,286)(210,282)(211,287)(212,280)(213,285)(214,281)(215,283)
(216,288)(289,365)(290,367)(291,363)(292,368)(293,361)(294,366)(295,362)
(296,364)(297,369)(298,374)(299,376)(300,372)(301,377)(302,370)(303,375)
(304,371)(305,373)(306,378)(307,383)(308,385)(309,381)(310,386)(311,379)
(312,384)(313,380)(314,382)(315,387)(316,392)(317,394)(318,390)(319,395)
(320,388)(321,393)(322,389)(323,391)(324,396)(325,401)(326,403)(327,399)
(328,404)(329,397)(330,402)(331,398)(332,400)(333,405)(334,410)(335,412)
(336,408)(337,413)(338,406)(339,411)(340,407)(341,409)(342,414)(343,419)
(344,421)(345,417)(346,422)(347,415)(348,420)(349,416)(350,418)(351,423)
(352,428)(353,430)(354,426)(355,431)(356,424)(357,429)(358,425)(359,427)
(360,432)(433,509)(434,511)(435,507)(436,512)(437,505)(438,510)(439,506)
(440,508)(441,513)(442,518)(443,520)(444,516)(445,521)(446,514)(447,519)
(448,515)(449,517)(450,522)(451,527)(452,529)(453,525)(454,530)(455,523)
(456,528)(457,524)(458,526)(459,531)(460,536)(461,538)(462,534)(463,539)
(464,532)(465,537)(466,533)(467,535)(468,540)(469,545)(470,547)(471,543)
(472,548)(473,541)(474,546)(475,542)(476,544)(477,549)(478,554)(479,556)
(480,552)(481,557)(482,550)(483,555)(484,551)(485,553)(486,558)(487,563)
(488,565)(489,561)(490,566)(491,559)(492,564)(493,560)(494,562)(495,567)
(496,572)(497,574)(498,570)(499,575)(500,568)(501,573)(502,569)(503,571)
(504,576);
poly := sub<Sym(576)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >; 
 
References : None.
to this polytope