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