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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}*1152a
Also Known As : {{12,8|2},{8,6|2}}. if this polytope has another name.
Group : SmallGroup(1152,97531)
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, {6,8,6}*576
   3-fold quotients : {12,8,2}*384a, {4,8,6}*384a
   4-fold quotients : {12,2,6}*288, {6,4,6}*288
   6-fold quotients : {12,4,2}*192a, {4,4,6}*192, {2,8,6}*192, {6,8,2}*192
   8-fold quotients : {12,2,3}*144, {6,2,6}*144
   9-fold quotients : {4,8,2}*128a
   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, {2,8,2}*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)( 37,253)( 38,260)( 39,258)( 40,259)
( 41,257)( 42,255)( 43,256)( 44,254)( 45,261)( 46,262)( 47,269)( 48,267)
( 49,268)( 50,266)( 51,264)( 52,265)( 53,263)( 54,270)( 55,271)( 56,278)
( 57,276)( 58,277)( 59,275)( 60,273)( 61,274)( 62,272)( 63,279)( 64,280)
( 65,287)( 66,285)( 67,286)( 68,284)( 69,282)( 70,283)( 71,281)( 72,288)
( 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)(109,181)(110,188)(111,186)(112,187)
(113,185)(114,183)(115,184)(116,182)(117,189)(118,190)(119,197)(120,195)
(121,196)(122,194)(123,192)(124,193)(125,191)(126,198)(127,199)(128,206)
(129,204)(130,205)(131,203)(132,201)(133,202)(134,200)(135,207)(136,208)
(137,215)(138,213)(139,214)(140,212)(141,210)(142,211)(143,209)(144,216)
(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)(325,541)(326,548)(327,546)(328,547)
(329,545)(330,543)(331,544)(332,542)(333,549)(334,550)(335,557)(336,555)
(337,556)(338,554)(339,552)(340,553)(341,551)(342,558)(343,559)(344,566)
(345,564)(346,565)(347,563)(348,561)(349,562)(350,560)(351,567)(352,568)
(353,575)(354,573)(355,574)(356,572)(357,570)(358,571)(359,569)(360,576)
(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)(397,469)(398,476)(399,474)(400,475)
(401,473)(402,471)(403,472)(404,470)(405,477)(406,478)(407,485)(408,483)
(409,484)(410,482)(411,480)(412,481)(413,479)(414,486)(415,487)(416,494)
(417,492)(418,493)(419,491)(420,489)(421,490)(422,488)(423,495)(424,496)
(425,503)(426,501)(427,502)(428,500)(429,498)(430,499)(431,497)(432,504);;
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)
(433,562)(434,560)(435,567)(436,559)(437,566)(438,564)(439,565)(440,563)
(441,561)(442,571)(443,569)(444,576)(445,568)(446,575)(447,573)(448,574)
(449,572)(450,570)(451,544)(452,542)(453,549)(454,541)(455,548)(456,546)
(457,547)(458,545)(459,543)(460,553)(461,551)(462,558)(463,550)(464,557)
(465,555)(466,556)(467,554)(468,552)(469,526)(470,524)(471,531)(472,523)
(473,530)(474,528)(475,529)(476,527)(477,525)(478,535)(479,533)(480,540)
(481,532)(482,539)(483,537)(484,538)(485,536)(486,534)(487,508)(488,506)
(489,513)(490,505)(491,512)(492,510)(493,511)(494,509)(495,507)(496,517)
(497,515)(498,522)(499,514)(500,521)(501,519)(502,520)(503,518)(504,516);;
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)( 19,379)( 20,384)( 21,386)( 22,382)( 23,387)( 24,380)
( 25,385)( 26,381)( 27,383)( 28,388)( 29,393)( 30,395)( 31,391)( 32,396)
( 33,389)( 34,394)( 35,390)( 36,392)( 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)( 55,424)( 56,429)
( 57,431)( 58,427)( 59,432)( 60,425)( 61,430)( 62,426)( 63,428)( 64,415)
( 65,420)( 66,422)( 67,418)( 68,423)( 69,416)( 70,421)( 71,417)( 72,419)
( 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)( 91,307)( 92,312)( 93,314)( 94,310)( 95,315)( 96,308)
( 97,313)( 98,309)( 99,311)(100,316)(101,321)(102,323)(103,319)(104,324)
(105,317)(106,322)(107,318)(108,320)(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)(127,352)(128,357)
(129,359)(130,355)(131,360)(132,353)(133,358)(134,354)(135,356)(136,343)
(137,348)(138,350)(139,346)(140,351)(141,344)(142,349)(143,345)(144,347)
(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)(163,523)(164,528)(165,530)(166,526)(167,531)(168,524)
(169,529)(170,525)(171,527)(172,532)(173,537)(174,539)(175,535)(176,540)
(177,533)(178,538)(179,534)(180,536)(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)(199,568)(200,573)
(201,575)(202,571)(203,576)(204,569)(205,574)(206,570)(207,572)(208,559)
(209,564)(210,566)(211,562)(212,567)(213,560)(214,565)(215,561)(216,563)
(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)(235,451)(236,456)(237,458)(238,454)(239,459)(240,452)
(241,457)(242,453)(243,455)(244,460)(245,465)(246,467)(247,463)(248,468)
(249,461)(250,466)(251,462)(252,464)(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)(271,496)(272,501)
(273,503)(274,499)(275,504)(276,497)(277,502)(278,498)(279,500)(280,487)
(281,492)(282,494)(283,490)(284,495)(285,488)(286,493)(287,489)(288,491);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
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)( 37,253)( 38,260)( 39,258)
( 40,259)( 41,257)( 42,255)( 43,256)( 44,254)( 45,261)( 46,262)( 47,269)
( 48,267)( 49,268)( 50,266)( 51,264)( 52,265)( 53,263)( 54,270)( 55,271)
( 56,278)( 57,276)( 58,277)( 59,275)( 60,273)( 61,274)( 62,272)( 63,279)
( 64,280)( 65,287)( 66,285)( 67,286)( 68,284)( 69,282)( 70,283)( 71,281)
( 72,288)( 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)(109,181)(110,188)(111,186)
(112,187)(113,185)(114,183)(115,184)(116,182)(117,189)(118,190)(119,197)
(120,195)(121,196)(122,194)(123,192)(124,193)(125,191)(126,198)(127,199)
(128,206)(129,204)(130,205)(131,203)(132,201)(133,202)(134,200)(135,207)
(136,208)(137,215)(138,213)(139,214)(140,212)(141,210)(142,211)(143,209)
(144,216)(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)(325,541)(326,548)(327,546)
(328,547)(329,545)(330,543)(331,544)(332,542)(333,549)(334,550)(335,557)
(336,555)(337,556)(338,554)(339,552)(340,553)(341,551)(342,558)(343,559)
(344,566)(345,564)(346,565)(347,563)(348,561)(349,562)(350,560)(351,567)
(352,568)(353,575)(354,573)(355,574)(356,572)(357,570)(358,571)(359,569)
(360,576)(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)(397,469)(398,476)(399,474)
(400,475)(401,473)(402,471)(403,472)(404,470)(405,477)(406,478)(407,485)
(408,483)(409,484)(410,482)(411,480)(412,481)(413,479)(414,486)(415,487)
(416,494)(417,492)(418,493)(419,491)(420,489)(421,490)(422,488)(423,495)
(424,496)(425,503)(426,501)(427,502)(428,500)(429,498)(430,499)(431,497)
(432,504);
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)(433,562)(434,560)(435,567)(436,559)(437,566)(438,564)(439,565)
(440,563)(441,561)(442,571)(443,569)(444,576)(445,568)(446,575)(447,573)
(448,574)(449,572)(450,570)(451,544)(452,542)(453,549)(454,541)(455,548)
(456,546)(457,547)(458,545)(459,543)(460,553)(461,551)(462,558)(463,550)
(464,557)(465,555)(466,556)(467,554)(468,552)(469,526)(470,524)(471,531)
(472,523)(473,530)(474,528)(475,529)(476,527)(477,525)(478,535)(479,533)
(480,540)(481,532)(482,539)(483,537)(484,538)(485,536)(486,534)(487,508)
(488,506)(489,513)(490,505)(491,512)(492,510)(493,511)(494,509)(495,507)
(496,517)(497,515)(498,522)(499,514)(500,521)(501,519)(502,520)(503,518)
(504,516);
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)( 19,379)( 20,384)( 21,386)( 22,382)( 23,387)
( 24,380)( 25,385)( 26,381)( 27,383)( 28,388)( 29,393)( 30,395)( 31,391)
( 32,396)( 33,389)( 34,394)( 35,390)( 36,392)( 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)( 55,424)
( 56,429)( 57,431)( 58,427)( 59,432)( 60,425)( 61,430)( 62,426)( 63,428)
( 64,415)( 65,420)( 66,422)( 67,418)( 68,423)( 69,416)( 70,421)( 71,417)
( 72,419)( 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)( 91,307)( 92,312)( 93,314)( 94,310)( 95,315)
( 96,308)( 97,313)( 98,309)( 99,311)(100,316)(101,321)(102,323)(103,319)
(104,324)(105,317)(106,322)(107,318)(108,320)(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)(127,352)
(128,357)(129,359)(130,355)(131,360)(132,353)(133,358)(134,354)(135,356)
(136,343)(137,348)(138,350)(139,346)(140,351)(141,344)(142,349)(143,345)
(144,347)(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)(163,523)(164,528)(165,530)(166,526)(167,531)
(168,524)(169,529)(170,525)(171,527)(172,532)(173,537)(174,539)(175,535)
(176,540)(177,533)(178,538)(179,534)(180,536)(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)(199,568)
(200,573)(201,575)(202,571)(203,576)(204,569)(205,574)(206,570)(207,572)
(208,559)(209,564)(210,566)(211,562)(212,567)(213,560)(214,565)(215,561)
(216,563)(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)(235,451)(236,456)(237,458)(238,454)(239,459)
(240,452)(241,457)(242,453)(243,455)(244,460)(245,465)(246,467)(247,463)
(248,468)(249,461)(250,466)(251,462)(252,464)(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)(271,496)
(272,501)(273,503)(274,499)(275,504)(276,497)(277,502)(278,498)(279,500)
(280,487)(281,492)(282,494)(283,490)(284,495)(285,488)(286,493)(287,489)
(288,491);
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >; 
 
References : None.
to this polytope