Polytope of Type {12,6,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,8}*1152b
Also Known As : {{12,6|2},{6,8|2}}. if this polytope has another name.
Group : SmallGroup(1152,119752)
Rank : 4
Schlafli Type : {12,6,8}
Number of vertices, edges, etc : 12, 36, 24, 8
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 : {12,6,4}*576a, {6,6,8}*576a
3-fold quotients : {12,2,8}*384, {4,6,8}*384a
4-fold quotients : {12,6,2}*288a, {6,6,4}*288a
6-fold quotients : {12,2,4}*192, {4,6,4}*192a, {2,6,8}*192, {6,2,8}*192
8-fold quotients : {6,6,2}*144a
9-fold quotients : {4,2,8}*128
12-fold quotients : {3,2,8}*96, {12,2,2}*96, {2,6,4}*96a, {4,6,2}*96a, {6,2,4}*96
18-fold quotients : {4,2,4}*64, {2,2,8}*64
24-fold quotients : {3,2,4}*48, {2,6,2}*48, {6,2,2}*48
36-fold quotients : {2,2,4}*32, {4,2,2}*32
48-fold quotients : {2,3,2}*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 := ( 1,109)( 2,116)( 3,114)( 4,115)( 5,113)( 6,111)( 7,112)( 8,110)
( 9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)( 16,121)
( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)( 24,129)
( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)( 32,140)
( 33,138)( 34,139)( 35,137)( 36,144)( 37, 82)( 38, 89)( 39, 87)( 40, 88)
( 41, 86)( 42, 84)( 43, 85)( 44, 83)( 45, 90)( 46, 73)( 47, 80)( 48, 78)
( 49, 79)( 50, 77)( 51, 75)( 52, 76)( 53, 74)( 54, 81)( 55,100)( 56,107)
( 57,105)( 58,106)( 59,104)( 60,102)( 61,103)( 62,101)( 63,108)( 64, 91)
( 65, 98)( 66, 96)( 67, 97)( 68, 95)( 69, 93)( 70, 94)( 71, 92)( 72, 99)
(145,271)(146,278)(147,276)(148,277)(149,275)(150,273)(151,274)(152,272)
(153,279)(154,280)(155,287)(156,285)(157,286)(158,284)(159,282)(160,283)
(161,281)(162,288)(163,253)(164,260)(165,258)(166,259)(167,257)(168,255)
(169,256)(170,254)(171,261)(172,262)(173,269)(174,267)(175,268)(176,266)
(177,264)(178,265)(179,263)(180,270)(181,244)(182,251)(183,249)(184,250)
(185,248)(186,246)(187,247)(188,245)(189,252)(190,235)(191,242)(192,240)
(193,241)(194,239)(195,237)(196,238)(197,236)(198,243)(199,226)(200,233)
(201,231)(202,232)(203,230)(204,228)(205,229)(206,227)(207,234)(208,217)
(209,224)(210,222)(211,223)(212,221)(213,219)(214,220)(215,218)(216,225)
(289,361)(290,368)(291,366)(292,367)(293,365)(294,363)(295,364)(296,362)
(297,369)(298,370)(299,377)(300,375)(301,376)(302,374)(303,372)(304,373)
(305,371)(306,378)(307,379)(308,386)(309,384)(310,385)(311,383)(312,381)
(313,382)(314,380)(315,387)(316,388)(317,395)(318,393)(319,394)(320,392)
(321,390)(322,391)(323,389)(324,396)(325,397)(326,404)(327,402)(328,403)
(329,401)(330,399)(331,400)(332,398)(333,405)(334,406)(335,413)(336,411)
(337,412)(338,410)(339,408)(340,409)(341,407)(342,414)(343,415)(344,422)
(345,420)(346,421)(347,419)(348,417)(349,418)(350,416)(351,423)(352,424)
(353,431)(354,429)(355,430)(356,428)(357,426)(358,427)(359,425)(360,432)
(433,523)(434,530)(435,528)(436,529)(437,527)(438,525)(439,526)(440,524)
(441,531)(442,532)(443,539)(444,537)(445,538)(446,536)(447,534)(448,535)
(449,533)(450,540)(451,505)(452,512)(453,510)(454,511)(455,509)(456,507)
(457,508)(458,506)(459,513)(460,514)(461,521)(462,519)(463,520)(464,518)
(465,516)(466,517)(467,515)(468,522)(469,559)(470,566)(471,564)(472,565)
(473,563)(474,561)(475,562)(476,560)(477,567)(478,568)(479,575)(480,573)
(481,574)(482,572)(483,570)(484,571)(485,569)(486,576)(487,541)(488,548)
(489,546)(490,547)(491,545)(492,543)(493,544)(494,542)(495,549)(496,550)
(497,557)(498,555)(499,556)(500,554)(501,552)(502,553)(503,551)(504,558);;
s1 := ( 1,148)( 2,150)( 3,149)( 4,145)( 5,147)( 6,146)( 7,151)( 8,153)
( 9,152)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)( 16,160)
( 17,162)( 18,161)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)( 24,164)
( 25,169)( 26,171)( 27,170)( 28,175)( 29,177)( 30,176)( 31,172)( 32,174)
( 33,173)( 34,178)( 35,180)( 36,179)( 37,184)( 38,186)( 39,185)( 40,181)
( 41,183)( 42,182)( 43,187)( 44,189)( 45,188)( 46,193)( 47,195)( 48,194)
( 49,190)( 50,192)( 51,191)( 52,196)( 53,198)( 54,197)( 55,202)( 56,204)
( 57,203)( 58,199)( 59,201)( 60,200)( 61,205)( 62,207)( 63,206)( 64,211)
( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,214)( 71,216)( 72,215)
( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,223)( 80,225)
( 81,224)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)( 88,232)
( 89,234)( 90,233)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)( 96,236)
( 97,241)( 98,243)( 99,242)(100,247)(101,249)(102,248)(103,244)(104,246)
(105,245)(106,250)(107,252)(108,251)(109,256)(110,258)(111,257)(112,253)
(113,255)(114,254)(115,259)(116,261)(117,260)(118,265)(119,267)(120,266)
(121,262)(122,264)(123,263)(124,268)(125,270)(126,269)(127,274)(128,276)
(129,275)(130,271)(131,273)(132,272)(133,277)(134,279)(135,278)(136,283)
(137,285)(138,284)(139,280)(140,282)(141,281)(142,286)(143,288)(144,287)
(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,439)(296,441)
(297,440)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)(304,448)
(305,450)(306,449)(307,454)(308,456)(309,455)(310,451)(311,453)(312,452)
(313,457)(314,459)(315,458)(316,463)(317,465)(318,464)(319,460)(320,462)
(321,461)(322,466)(323,468)(324,467)(325,472)(326,474)(327,473)(328,469)
(329,471)(330,470)(331,475)(332,477)(333,476)(334,481)(335,483)(336,482)
(337,478)(338,480)(339,479)(340,484)(341,486)(342,485)(343,490)(344,492)
(345,491)(346,487)(347,489)(348,488)(349,493)(350,495)(351,494)(352,499)
(353,501)(354,500)(355,496)(356,498)(357,497)(358,502)(359,504)(360,503)
(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,511)(368,513)
(369,512)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)(376,520)
(377,522)(378,521)(379,526)(380,528)(381,527)(382,523)(383,525)(384,524)
(385,529)(386,531)(387,530)(388,535)(389,537)(390,536)(391,532)(392,534)
(393,533)(394,538)(395,540)(396,539)(397,544)(398,546)(399,545)(400,541)
(401,543)(402,542)(403,547)(404,549)(405,548)(406,553)(407,555)(408,554)
(409,550)(410,552)(411,551)(412,556)(413,558)(414,557)(415,562)(416,564)
(417,563)(418,559)(419,561)(420,560)(421,565)(422,567)(423,566)(424,571)
(425,573)(426,572)(427,568)(428,570)(429,569)(430,574)(431,576)(432,575);;
s2 := ( 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)( 37,122)( 38,124)( 39,120)( 40,125)
( 41,118)( 42,123)( 43,119)( 44,121)( 45,126)( 46,113)( 47,115)( 48,111)
( 49,116)( 50,109)( 51,114)( 52,110)( 53,112)( 54,117)( 55,140)( 56,142)
( 57,138)( 58,143)( 59,136)( 60,141)( 61,137)( 62,139)( 63,144)( 64,131)
( 65,133)( 66,129)( 67,134)( 68,127)( 69,132)( 70,128)( 71,130)( 72,135)
(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)(181,266)(182,268)(183,264)(184,269)
(185,262)(186,267)(187,263)(188,265)(189,270)(190,257)(191,259)(192,255)
(193,260)(194,253)(195,258)(196,254)(197,256)(198,261)(199,284)(200,286)
(201,282)(202,287)(203,280)(204,285)(205,281)(206,283)(207,288)(208,275)
(209,277)(210,273)(211,278)(212,271)(213,276)(214,272)(215,274)(216,279)
(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)(325,410)(326,412)(327,408)(328,413)
(329,406)(330,411)(331,407)(332,409)(333,414)(334,401)(335,403)(336,399)
(337,404)(338,397)(339,402)(340,398)(341,400)(342,405)(343,428)(344,430)
(345,426)(346,431)(347,424)(348,429)(349,425)(350,427)(351,432)(352,419)
(353,421)(354,417)(355,422)(356,415)(357,420)(358,416)(359,418)(360,423)
(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)(469,554)(470,556)(471,552)(472,557)
(473,550)(474,555)(475,551)(476,553)(477,558)(478,545)(479,547)(480,543)
(481,548)(482,541)(483,546)(484,542)(485,544)(486,549)(487,572)(488,574)
(489,570)(490,575)(491,568)(492,573)(493,569)(494,571)(495,576)(496,563)
(497,565)(498,561)(499,566)(500,559)(501,564)(502,560)(503,562)(504,567);;
s3 := ( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)( 8,296)
( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)
( 17,305)( 18,306)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)( 24,312)
( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)
( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)( 40,337)
( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)
( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,352)( 56,353)
( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)( 64,343)
( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)( 72,351)
( 73,397)( 74,398)( 75,399)( 76,400)( 77,401)( 78,402)( 79,403)( 80,404)
( 81,405)( 82,406)( 83,407)( 84,408)( 85,409)( 86,410)( 87,411)( 88,412)
( 89,413)( 90,414)( 91,415)( 92,416)( 93,417)( 94,418)( 95,419)( 96,420)
( 97,421)( 98,422)( 99,423)(100,424)(101,425)(102,426)(103,427)(104,428)
(105,429)(106,430)(107,431)(108,432)(109,361)(110,362)(111,363)(112,364)
(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)(120,372)
(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,379)(128,380)
(129,381)(130,382)(131,383)(132,384)(133,385)(134,386)(135,387)(136,388)
(137,389)(138,390)(139,391)(140,392)(141,393)(142,394)(143,395)(144,396)
(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)
(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)
(161,449)(162,450)(163,451)(164,452)(165,453)(166,454)(167,455)(168,456)
(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)(176,464)
(177,465)(178,466)(179,467)(180,468)(181,478)(182,479)(183,480)(184,481)
(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)(192,471)
(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,496)(200,497)
(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)(208,487)
(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)
(217,541)(218,542)(219,543)(220,544)(221,545)(222,546)(223,547)(224,548)
(225,549)(226,550)(227,551)(228,552)(229,553)(230,554)(231,555)(232,556)
(233,557)(234,558)(235,559)(236,560)(237,561)(238,562)(239,563)(240,564)
(241,565)(242,566)(243,567)(244,568)(245,569)(246,570)(247,571)(248,572)
(249,573)(250,574)(251,575)(252,576)(253,505)(254,506)(255,507)(256,508)
(257,509)(258,510)(259,511)(260,512)(261,513)(262,514)(263,515)(264,516)
(265,517)(266,518)(267,519)(268,520)(269,521)(270,522)(271,523)(272,524)
(273,525)(274,526)(275,527)(276,528)(277,529)(278,530)(279,531)(280,532)
(281,533)(282,534)(283,535)(284,536)(285,537)(286,538)(287,539)(288,540);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)!( 1,109)( 2,116)( 3,114)( 4,115)( 5,113)( 6,111)( 7,112)
( 8,110)( 9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)
( 16,121)( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)
( 24,129)( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)
( 32,140)( 33,138)( 34,139)( 35,137)( 36,144)( 37, 82)( 38, 89)( 39, 87)
( 40, 88)( 41, 86)( 42, 84)( 43, 85)( 44, 83)( 45, 90)( 46, 73)( 47, 80)
( 48, 78)( 49, 79)( 50, 77)( 51, 75)( 52, 76)( 53, 74)( 54, 81)( 55,100)
( 56,107)( 57,105)( 58,106)( 59,104)( 60,102)( 61,103)( 62,101)( 63,108)
( 64, 91)( 65, 98)( 66, 96)( 67, 97)( 68, 95)( 69, 93)( 70, 94)( 71, 92)
( 72, 99)(145,271)(146,278)(147,276)(148,277)(149,275)(150,273)(151,274)
(152,272)(153,279)(154,280)(155,287)(156,285)(157,286)(158,284)(159,282)
(160,283)(161,281)(162,288)(163,253)(164,260)(165,258)(166,259)(167,257)
(168,255)(169,256)(170,254)(171,261)(172,262)(173,269)(174,267)(175,268)
(176,266)(177,264)(178,265)(179,263)(180,270)(181,244)(182,251)(183,249)
(184,250)(185,248)(186,246)(187,247)(188,245)(189,252)(190,235)(191,242)
(192,240)(193,241)(194,239)(195,237)(196,238)(197,236)(198,243)(199,226)
(200,233)(201,231)(202,232)(203,230)(204,228)(205,229)(206,227)(207,234)
(208,217)(209,224)(210,222)(211,223)(212,221)(213,219)(214,220)(215,218)
(216,225)(289,361)(290,368)(291,366)(292,367)(293,365)(294,363)(295,364)
(296,362)(297,369)(298,370)(299,377)(300,375)(301,376)(302,374)(303,372)
(304,373)(305,371)(306,378)(307,379)(308,386)(309,384)(310,385)(311,383)
(312,381)(313,382)(314,380)(315,387)(316,388)(317,395)(318,393)(319,394)
(320,392)(321,390)(322,391)(323,389)(324,396)(325,397)(326,404)(327,402)
(328,403)(329,401)(330,399)(331,400)(332,398)(333,405)(334,406)(335,413)
(336,411)(337,412)(338,410)(339,408)(340,409)(341,407)(342,414)(343,415)
(344,422)(345,420)(346,421)(347,419)(348,417)(349,418)(350,416)(351,423)
(352,424)(353,431)(354,429)(355,430)(356,428)(357,426)(358,427)(359,425)
(360,432)(433,523)(434,530)(435,528)(436,529)(437,527)(438,525)(439,526)
(440,524)(441,531)(442,532)(443,539)(444,537)(445,538)(446,536)(447,534)
(448,535)(449,533)(450,540)(451,505)(452,512)(453,510)(454,511)(455,509)
(456,507)(457,508)(458,506)(459,513)(460,514)(461,521)(462,519)(463,520)
(464,518)(465,516)(466,517)(467,515)(468,522)(469,559)(470,566)(471,564)
(472,565)(473,563)(474,561)(475,562)(476,560)(477,567)(478,568)(479,575)
(480,573)(481,574)(482,572)(483,570)(484,571)(485,569)(486,576)(487,541)
(488,548)(489,546)(490,547)(491,545)(492,543)(493,544)(494,542)(495,549)
(496,550)(497,557)(498,555)(499,556)(500,554)(501,552)(502,553)(503,551)
(504,558);
s1 := Sym(576)!( 1,148)( 2,150)( 3,149)( 4,145)( 5,147)( 6,146)( 7,151)
( 8,153)( 9,152)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)
( 16,160)( 17,162)( 18,161)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)
( 24,164)( 25,169)( 26,171)( 27,170)( 28,175)( 29,177)( 30,176)( 31,172)
( 32,174)( 33,173)( 34,178)( 35,180)( 36,179)( 37,184)( 38,186)( 39,185)
( 40,181)( 41,183)( 42,182)( 43,187)( 44,189)( 45,188)( 46,193)( 47,195)
( 48,194)( 49,190)( 50,192)( 51,191)( 52,196)( 53,198)( 54,197)( 55,202)
( 56,204)( 57,203)( 58,199)( 59,201)( 60,200)( 61,205)( 62,207)( 63,206)
( 64,211)( 65,213)( 66,212)( 67,208)( 68,210)( 69,209)( 70,214)( 71,216)
( 72,215)( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,223)
( 80,225)( 81,224)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)
( 88,232)( 89,234)( 90,233)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)
( 96,236)( 97,241)( 98,243)( 99,242)(100,247)(101,249)(102,248)(103,244)
(104,246)(105,245)(106,250)(107,252)(108,251)(109,256)(110,258)(111,257)
(112,253)(113,255)(114,254)(115,259)(116,261)(117,260)(118,265)(119,267)
(120,266)(121,262)(122,264)(123,263)(124,268)(125,270)(126,269)(127,274)
(128,276)(129,275)(130,271)(131,273)(132,272)(133,277)(134,279)(135,278)
(136,283)(137,285)(138,284)(139,280)(140,282)(141,281)(142,286)(143,288)
(144,287)(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,439)
(296,441)(297,440)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)
(304,448)(305,450)(306,449)(307,454)(308,456)(309,455)(310,451)(311,453)
(312,452)(313,457)(314,459)(315,458)(316,463)(317,465)(318,464)(319,460)
(320,462)(321,461)(322,466)(323,468)(324,467)(325,472)(326,474)(327,473)
(328,469)(329,471)(330,470)(331,475)(332,477)(333,476)(334,481)(335,483)
(336,482)(337,478)(338,480)(339,479)(340,484)(341,486)(342,485)(343,490)
(344,492)(345,491)(346,487)(347,489)(348,488)(349,493)(350,495)(351,494)
(352,499)(353,501)(354,500)(355,496)(356,498)(357,497)(358,502)(359,504)
(360,503)(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,511)
(368,513)(369,512)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)
(376,520)(377,522)(378,521)(379,526)(380,528)(381,527)(382,523)(383,525)
(384,524)(385,529)(386,531)(387,530)(388,535)(389,537)(390,536)(391,532)
(392,534)(393,533)(394,538)(395,540)(396,539)(397,544)(398,546)(399,545)
(400,541)(401,543)(402,542)(403,547)(404,549)(405,548)(406,553)(407,555)
(408,554)(409,550)(410,552)(411,551)(412,556)(413,558)(414,557)(415,562)
(416,564)(417,563)(418,559)(419,561)(420,560)(421,565)(422,567)(423,566)
(424,571)(425,573)(426,572)(427,568)(428,570)(429,569)(430,574)(431,576)
(432,575);
s2 := 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)( 37,122)( 38,124)( 39,120)
( 40,125)( 41,118)( 42,123)( 43,119)( 44,121)( 45,126)( 46,113)( 47,115)
( 48,111)( 49,116)( 50,109)( 51,114)( 52,110)( 53,112)( 54,117)( 55,140)
( 56,142)( 57,138)( 58,143)( 59,136)( 60,141)( 61,137)( 62,139)( 63,144)
( 64,131)( 65,133)( 66,129)( 67,134)( 68,127)( 69,132)( 70,128)( 71,130)
( 72,135)(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)(181,266)(182,268)(183,264)
(184,269)(185,262)(186,267)(187,263)(188,265)(189,270)(190,257)(191,259)
(192,255)(193,260)(194,253)(195,258)(196,254)(197,256)(198,261)(199,284)
(200,286)(201,282)(202,287)(203,280)(204,285)(205,281)(206,283)(207,288)
(208,275)(209,277)(210,273)(211,278)(212,271)(213,276)(214,272)(215,274)
(216,279)(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)(325,410)(326,412)(327,408)
(328,413)(329,406)(330,411)(331,407)(332,409)(333,414)(334,401)(335,403)
(336,399)(337,404)(338,397)(339,402)(340,398)(341,400)(342,405)(343,428)
(344,430)(345,426)(346,431)(347,424)(348,429)(349,425)(350,427)(351,432)
(352,419)(353,421)(354,417)(355,422)(356,415)(357,420)(358,416)(359,418)
(360,423)(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)(469,554)(470,556)(471,552)
(472,557)(473,550)(474,555)(475,551)(476,553)(477,558)(478,545)(479,547)
(480,543)(481,548)(482,541)(483,546)(484,542)(485,544)(486,549)(487,572)
(488,574)(489,570)(490,575)(491,568)(492,573)(493,569)(494,571)(495,576)
(496,563)(497,565)(498,561)(499,566)(500,559)(501,564)(502,560)(503,562)
(504,567);
s3 := Sym(576)!( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)
( 8,296)( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)
( 16,304)( 17,305)( 18,306)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)
( 24,312)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)
( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)
( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)
( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,352)
( 56,353)( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)
( 64,343)( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)
( 72,351)( 73,397)( 74,398)( 75,399)( 76,400)( 77,401)( 78,402)( 79,403)
( 80,404)( 81,405)( 82,406)( 83,407)( 84,408)( 85,409)( 86,410)( 87,411)
( 88,412)( 89,413)( 90,414)( 91,415)( 92,416)( 93,417)( 94,418)( 95,419)
( 96,420)( 97,421)( 98,422)( 99,423)(100,424)(101,425)(102,426)(103,427)
(104,428)(105,429)(106,430)(107,431)(108,432)(109,361)(110,362)(111,363)
(112,364)(113,365)(114,366)(115,367)(116,368)(117,369)(118,370)(119,371)
(120,372)(121,373)(122,374)(123,375)(124,376)(125,377)(126,378)(127,379)
(128,380)(129,381)(130,382)(131,383)(132,384)(133,385)(134,386)(135,387)
(136,388)(137,389)(138,390)(139,391)(140,392)(141,393)(142,394)(143,395)
(144,396)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)
(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)
(160,448)(161,449)(162,450)(163,451)(164,452)(165,453)(166,454)(167,455)
(168,456)(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)
(176,464)(177,465)(178,466)(179,467)(180,468)(181,478)(182,479)(183,480)
(184,481)(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)
(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,496)
(200,497)(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)
(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)
(216,495)(217,541)(218,542)(219,543)(220,544)(221,545)(222,546)(223,547)
(224,548)(225,549)(226,550)(227,551)(228,552)(229,553)(230,554)(231,555)
(232,556)(233,557)(234,558)(235,559)(236,560)(237,561)(238,562)(239,563)
(240,564)(241,565)(242,566)(243,567)(244,568)(245,569)(246,570)(247,571)
(248,572)(249,573)(250,574)(251,575)(252,576)(253,505)(254,506)(255,507)
(256,508)(257,509)(258,510)(259,511)(260,512)(261,513)(262,514)(263,515)
(264,516)(265,517)(266,518)(267,519)(268,520)(269,521)(270,522)(271,523)
(272,524)(273,525)(274,526)(275,527)(276,528)(277,529)(278,530)(279,531)
(280,532)(281,533)(282,534)(283,535)(284,536)(285,537)(286,538)(287,539)
(288,540);
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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