Polytope of Type {6,8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,12}*1152a
Also Known As : {{6,8|2},{8,12|2}}. if this polytope has another name.
Group : SmallGroup(1152,97531)
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, {6,8,6}*576
3-fold quotients : {2,8,12}*384a, {6,8,4}*384a
4-fold quotients : {6,2,12}*288, {6,4,6}*288
6-fold quotients : {2,4,12}*192a, {6,4,4}*192, {2,8,6}*192, {6,8,2}*192
8-fold quotients : {3,2,12}*144, {6,2,6}*144
9-fold quotients : {2,8,4}*128a
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, {2,8,2}*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)( 19,383)( 20,385)( 21,381)( 22,386)( 23,379)( 24,384)
( 25,380)( 26,382)( 27,387)( 28,392)( 29,394)( 30,390)( 31,395)( 32,388)
( 33,393)( 34,389)( 35,391)( 36,396)( 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)( 55,428)( 56,430)
( 57,426)( 58,431)( 59,424)( 60,429)( 61,425)( 62,427)( 63,432)( 64,419)
( 65,421)( 66,417)( 67,422)( 68,415)( 69,420)( 70,416)( 71,418)( 72,423)
( 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)( 91,311)( 92,313)( 93,309)( 94,314)( 95,307)( 96,312)
( 97,308)( 98,310)( 99,315)(100,320)(101,322)(102,318)(103,323)(104,316)
(105,321)(106,317)(107,319)(108,324)(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)(127,356)(128,358)
(129,354)(130,359)(131,352)(132,357)(133,353)(134,355)(135,360)(136,347)
(137,349)(138,345)(139,350)(140,343)(141,348)(142,344)(143,346)(144,351)
(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)(163,527)(164,529)(165,525)(166,530)(167,523)(168,528)
(169,524)(170,526)(171,531)(172,536)(173,538)(174,534)(175,539)(176,532)
(177,537)(178,533)(179,535)(180,540)(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)(199,572)(200,574)
(201,570)(202,575)(203,568)(204,573)(205,569)(206,571)(207,576)(208,563)
(209,565)(210,561)(211,566)(212,559)(213,564)(214,560)(215,562)(216,567)
(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)(235,455)(236,457)(237,453)(238,458)(239,451)(240,456)
(241,452)(242,454)(243,459)(244,464)(245,466)(246,462)(247,467)(248,460)
(249,465)(250,461)(251,463)(252,468)(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)(271,500)(272,502)
(273,498)(274,503)(275,496)(276,501)(277,497)(278,499)(279,504)(280,491)
(281,493)(282,489)(283,494)(284,487)(285,492)(286,488)(287,490)(288,495);;
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)
(433,559)(434,566)(435,564)(436,565)(437,563)(438,561)(439,562)(440,560)
(441,567)(442,568)(443,575)(444,573)(445,574)(446,572)(447,570)(448,571)
(449,569)(450,576)(451,541)(452,548)(453,546)(454,547)(455,545)(456,543)
(457,544)(458,542)(459,549)(460,550)(461,557)(462,555)(463,556)(464,554)
(465,552)(466,553)(467,551)(468,558)(469,523)(470,530)(471,528)(472,529)
(473,527)(474,525)(475,526)(476,524)(477,531)(478,532)(479,539)(480,537)
(481,538)(482,536)(483,534)(484,535)(485,533)(486,540)(487,505)(488,512)
(489,510)(490,511)(491,509)(492,507)(493,508)(494,506)(495,513)(496,514)
(497,521)(498,519)(499,520)(500,518)(501,516)(502,517)(503,515)(504,522);;
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)( 37,256)( 38,254)( 39,261)( 40,253)
( 41,260)( 42,258)( 43,259)( 44,257)( 45,255)( 46,265)( 47,263)( 48,270)
( 49,262)( 50,269)( 51,267)( 52,268)( 53,266)( 54,264)( 55,274)( 56,272)
( 57,279)( 58,271)( 59,278)( 60,276)( 61,277)( 62,275)( 63,273)( 64,283)
( 65,281)( 66,288)( 67,280)( 68,287)( 69,285)( 70,286)( 71,284)( 72,282)
( 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)(109,184)(110,182)(111,189)(112,181)
(113,188)(114,186)(115,187)(116,185)(117,183)(118,193)(119,191)(120,198)
(121,190)(122,197)(123,195)(124,196)(125,194)(126,192)(127,202)(128,200)
(129,207)(130,199)(131,206)(132,204)(133,205)(134,203)(135,201)(136,211)
(137,209)(138,216)(139,208)(140,215)(141,213)(142,214)(143,212)(144,210)
(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)(325,544)(326,542)(327,549)(328,541)
(329,548)(330,546)(331,547)(332,545)(333,543)(334,553)(335,551)(336,558)
(337,550)(338,557)(339,555)(340,556)(341,554)(342,552)(343,562)(344,560)
(345,567)(346,559)(347,566)(348,564)(349,565)(350,563)(351,561)(352,571)
(353,569)(354,576)(355,568)(356,575)(357,573)(358,574)(359,572)(360,570)
(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)(397,472)(398,470)(399,477)(400,469)
(401,476)(402,474)(403,475)(404,473)(405,471)(406,481)(407,479)(408,486)
(409,478)(410,485)(411,483)(412,484)(413,482)(414,480)(415,490)(416,488)
(417,495)(418,487)(419,494)(420,492)(421,493)(422,491)(423,489)(424,499)
(425,497)(426,504)(427,496)(428,503)(429,501)(430,502)(431,500)(432,498);;
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, 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)( 19,383)( 20,385)( 21,381)( 22,386)( 23,379)
( 24,384)( 25,380)( 26,382)( 27,387)( 28,392)( 29,394)( 30,390)( 31,395)
( 32,388)( 33,393)( 34,389)( 35,391)( 36,396)( 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)( 55,428)
( 56,430)( 57,426)( 58,431)( 59,424)( 60,429)( 61,425)( 62,427)( 63,432)
( 64,419)( 65,421)( 66,417)( 67,422)( 68,415)( 69,420)( 70,416)( 71,418)
( 72,423)( 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)( 91,311)( 92,313)( 93,309)( 94,314)( 95,307)
( 96,312)( 97,308)( 98,310)( 99,315)(100,320)(101,322)(102,318)(103,323)
(104,316)(105,321)(106,317)(107,319)(108,324)(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)(127,356)
(128,358)(129,354)(130,359)(131,352)(132,357)(133,353)(134,355)(135,360)
(136,347)(137,349)(138,345)(139,350)(140,343)(141,348)(142,344)(143,346)
(144,351)(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)(163,527)(164,529)(165,525)(166,530)(167,523)
(168,528)(169,524)(170,526)(171,531)(172,536)(173,538)(174,534)(175,539)
(176,532)(177,537)(178,533)(179,535)(180,540)(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)(199,572)
(200,574)(201,570)(202,575)(203,568)(204,573)(205,569)(206,571)(207,576)
(208,563)(209,565)(210,561)(211,566)(212,559)(213,564)(214,560)(215,562)
(216,567)(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)(235,455)(236,457)(237,453)(238,458)(239,451)
(240,456)(241,452)(242,454)(243,459)(244,464)(245,466)(246,462)(247,467)
(248,460)(249,465)(250,461)(251,463)(252,468)(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)(271,500)
(272,502)(273,498)(274,503)(275,496)(276,501)(277,497)(278,499)(279,504)
(280,491)(281,493)(282,489)(283,494)(284,487)(285,492)(286,488)(287,490)
(288,495);
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)(433,559)(434,566)(435,564)(436,565)(437,563)(438,561)(439,562)
(440,560)(441,567)(442,568)(443,575)(444,573)(445,574)(446,572)(447,570)
(448,571)(449,569)(450,576)(451,541)(452,548)(453,546)(454,547)(455,545)
(456,543)(457,544)(458,542)(459,549)(460,550)(461,557)(462,555)(463,556)
(464,554)(465,552)(466,553)(467,551)(468,558)(469,523)(470,530)(471,528)
(472,529)(473,527)(474,525)(475,526)(476,524)(477,531)(478,532)(479,539)
(480,537)(481,538)(482,536)(483,534)(484,535)(485,533)(486,540)(487,505)
(488,512)(489,510)(490,511)(491,509)(492,507)(493,508)(494,506)(495,513)
(496,514)(497,521)(498,519)(499,520)(500,518)(501,516)(502,517)(503,515)
(504,522);
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)( 37,256)( 38,254)( 39,261)
( 40,253)( 41,260)( 42,258)( 43,259)( 44,257)( 45,255)( 46,265)( 47,263)
( 48,270)( 49,262)( 50,269)( 51,267)( 52,268)( 53,266)( 54,264)( 55,274)
( 56,272)( 57,279)( 58,271)( 59,278)( 60,276)( 61,277)( 62,275)( 63,273)
( 64,283)( 65,281)( 66,288)( 67,280)( 68,287)( 69,285)( 70,286)( 71,284)
( 72,282)( 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)(109,184)(110,182)(111,189)
(112,181)(113,188)(114,186)(115,187)(116,185)(117,183)(118,193)(119,191)
(120,198)(121,190)(122,197)(123,195)(124,196)(125,194)(126,192)(127,202)
(128,200)(129,207)(130,199)(131,206)(132,204)(133,205)(134,203)(135,201)
(136,211)(137,209)(138,216)(139,208)(140,215)(141,213)(142,214)(143,212)
(144,210)(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)(325,544)(326,542)(327,549)
(328,541)(329,548)(330,546)(331,547)(332,545)(333,543)(334,553)(335,551)
(336,558)(337,550)(338,557)(339,555)(340,556)(341,554)(342,552)(343,562)
(344,560)(345,567)(346,559)(347,566)(348,564)(349,565)(350,563)(351,561)
(352,571)(353,569)(354,576)(355,568)(356,575)(357,573)(358,574)(359,572)
(360,570)(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)(397,472)(398,470)(399,477)
(400,469)(401,476)(402,474)(403,475)(404,473)(405,471)(406,481)(407,479)
(408,486)(409,478)(410,485)(411,483)(412,484)(413,482)(414,480)(415,490)
(416,488)(417,495)(418,487)(419,494)(420,492)(421,493)(422,491)(423,489)
(424,499)(425,497)(426,504)(427,496)(428,503)(429,501)(430,502)(431,500)
(432,498);
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,
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