Polytope of Type {12,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,4}*1152c
if this polytope has a name.
Group : SmallGroup(1152,43025)
Rank : 4
Schlafli Type : {12,12,4}
Number of vertices, edges, etc : 12, 72, 24, 4
Order of s0s1s2s3 : 12
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 : {12,12,2}*576c, {12,6,4}*576b, {6,12,4}*576c
3-fold quotients : {12,4,4}*384
4-fold quotients : {12,6,2}*288b, {6,6,4}*288c, {6,12,2}*288c
6-fold quotients : {12,4,2}*192a, {12,2,4}*192, {6,4,4}*192
8-fold quotients : {3,6,4}*144, {6,6,2}*144c
9-fold quotients : {4,4,4}*128
12-fold quotients : {12,2,2}*96, {6,2,4}*96, {6,4,2}*96a
16-fold quotients : {3,6,2}*72
18-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
24-fold quotients : {3,2,4}*48, {6,2,2}*48
36-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
48-fold quotients : {3,2,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,361)( 2,363)( 3,362)( 4,367)( 5,369)( 6,368)( 7,364)( 8,366)
( 9,365)( 10,370)( 11,372)( 12,371)( 13,376)( 14,378)( 15,377)( 16,373)
( 17,375)( 18,374)( 19,379)( 20,381)( 21,380)( 22,385)( 23,387)( 24,386)
( 25,382)( 26,384)( 27,383)( 28,388)( 29,390)( 30,389)( 31,394)( 32,396)
( 33,395)( 34,391)( 35,393)( 36,392)( 37,397)( 38,399)( 39,398)( 40,403)
( 41,405)( 42,404)( 43,400)( 44,402)( 45,401)( 46,406)( 47,408)( 48,407)
( 49,412)( 50,414)( 51,413)( 52,409)( 53,411)( 54,410)( 55,415)( 56,417)
( 57,416)( 58,421)( 59,423)( 60,422)( 61,418)( 62,420)( 63,419)( 64,424)
( 65,426)( 66,425)( 67,430)( 68,432)( 69,431)( 70,427)( 71,429)( 72,428)
( 73,289)( 74,291)( 75,290)( 76,295)( 77,297)( 78,296)( 79,292)( 80,294)
( 81,293)( 82,298)( 83,300)( 84,299)( 85,304)( 86,306)( 87,305)( 88,301)
( 89,303)( 90,302)( 91,307)( 92,309)( 93,308)( 94,313)( 95,315)( 96,314)
( 97,310)( 98,312)( 99,311)(100,316)(101,318)(102,317)(103,322)(104,324)
(105,323)(106,319)(107,321)(108,320)(109,325)(110,327)(111,326)(112,331)
(113,333)(114,332)(115,328)(116,330)(117,329)(118,334)(119,336)(120,335)
(121,340)(122,342)(123,341)(124,337)(125,339)(126,338)(127,343)(128,345)
(129,344)(130,349)(131,351)(132,350)(133,346)(134,348)(135,347)(136,352)
(137,354)(138,353)(139,358)(140,360)(141,359)(142,355)(143,357)(144,356)
(145,514)(146,516)(147,515)(148,520)(149,522)(150,521)(151,517)(152,519)
(153,518)(154,505)(155,507)(156,506)(157,511)(158,513)(159,512)(160,508)
(161,510)(162,509)(163,532)(164,534)(165,533)(166,538)(167,540)(168,539)
(169,535)(170,537)(171,536)(172,523)(173,525)(174,524)(175,529)(176,531)
(177,530)(178,526)(179,528)(180,527)(181,550)(182,552)(183,551)(184,556)
(185,558)(186,557)(187,553)(188,555)(189,554)(190,541)(191,543)(192,542)
(193,547)(194,549)(195,548)(196,544)(197,546)(198,545)(199,568)(200,570)
(201,569)(202,574)(203,576)(204,575)(205,571)(206,573)(207,572)(208,559)
(209,561)(210,560)(211,565)(212,567)(213,566)(214,562)(215,564)(216,563)
(217,442)(218,444)(219,443)(220,448)(221,450)(222,449)(223,445)(224,447)
(225,446)(226,433)(227,435)(228,434)(229,439)(230,441)(231,440)(232,436)
(233,438)(234,437)(235,460)(236,462)(237,461)(238,466)(239,468)(240,467)
(241,463)(242,465)(243,464)(244,451)(245,453)(246,452)(247,457)(248,459)
(249,458)(250,454)(251,456)(252,455)(253,478)(254,480)(255,479)(256,484)
(257,486)(258,485)(259,481)(260,483)(261,482)(262,469)(263,471)(264,470)
(265,475)(266,477)(267,476)(268,472)(269,474)(270,473)(271,496)(272,498)
(273,497)(274,502)(275,504)(276,503)(277,499)(278,501)(279,500)(280,487)
(281,489)(282,488)(283,493)(284,495)(285,494)(286,490)(287,492)(288,491);;
s1 := ( 1,146)( 2,145)( 3,147)( 4,152)( 5,151)( 6,153)( 7,149)( 8,148)
( 9,150)( 10,155)( 11,154)( 12,156)( 13,161)( 14,160)( 15,162)( 16,158)
( 17,157)( 18,159)( 19,164)( 20,163)( 21,165)( 22,170)( 23,169)( 24,171)
( 25,167)( 26,166)( 27,168)( 28,173)( 29,172)( 30,174)( 31,179)( 32,178)
( 33,180)( 34,176)( 35,175)( 36,177)( 37,182)( 38,181)( 39,183)( 40,188)
( 41,187)( 42,189)( 43,185)( 44,184)( 45,186)( 46,191)( 47,190)( 48,192)
( 49,197)( 50,196)( 51,198)( 52,194)( 53,193)( 54,195)( 55,200)( 56,199)
( 57,201)( 58,206)( 59,205)( 60,207)( 61,203)( 62,202)( 63,204)( 64,209)
( 65,208)( 66,210)( 67,215)( 68,214)( 69,216)( 70,212)( 71,211)( 72,213)
( 73,218)( 74,217)( 75,219)( 76,224)( 77,223)( 78,225)( 79,221)( 80,220)
( 81,222)( 82,227)( 83,226)( 84,228)( 85,233)( 86,232)( 87,234)( 88,230)
( 89,229)( 90,231)( 91,236)( 92,235)( 93,237)( 94,242)( 95,241)( 96,243)
( 97,239)( 98,238)( 99,240)(100,245)(101,244)(102,246)(103,251)(104,250)
(105,252)(106,248)(107,247)(108,249)(109,254)(110,253)(111,255)(112,260)
(113,259)(114,261)(115,257)(116,256)(117,258)(118,263)(119,262)(120,264)
(121,269)(122,268)(123,270)(124,266)(125,265)(126,267)(127,272)(128,271)
(129,273)(130,278)(131,277)(132,279)(133,275)(134,274)(135,276)(136,281)
(137,280)(138,282)(139,287)(140,286)(141,288)(142,284)(143,283)(144,285)
(289,434)(290,433)(291,435)(292,440)(293,439)(294,441)(295,437)(296,436)
(297,438)(298,443)(299,442)(300,444)(301,449)(302,448)(303,450)(304,446)
(305,445)(306,447)(307,452)(308,451)(309,453)(310,458)(311,457)(312,459)
(313,455)(314,454)(315,456)(316,461)(317,460)(318,462)(319,467)(320,466)
(321,468)(322,464)(323,463)(324,465)(325,470)(326,469)(327,471)(328,476)
(329,475)(330,477)(331,473)(332,472)(333,474)(334,479)(335,478)(336,480)
(337,485)(338,484)(339,486)(340,482)(341,481)(342,483)(343,488)(344,487)
(345,489)(346,494)(347,493)(348,495)(349,491)(350,490)(351,492)(352,497)
(353,496)(354,498)(355,503)(356,502)(357,504)(358,500)(359,499)(360,501)
(361,506)(362,505)(363,507)(364,512)(365,511)(366,513)(367,509)(368,508)
(369,510)(370,515)(371,514)(372,516)(373,521)(374,520)(375,522)(376,518)
(377,517)(378,519)(379,524)(380,523)(381,525)(382,530)(383,529)(384,531)
(385,527)(386,526)(387,528)(388,533)(389,532)(390,534)(391,539)(392,538)
(393,540)(394,536)(395,535)(396,537)(397,542)(398,541)(399,543)(400,548)
(401,547)(402,549)(403,545)(404,544)(405,546)(406,551)(407,550)(408,552)
(409,557)(410,556)(411,558)(412,554)(413,553)(414,555)(415,560)(416,559)
(417,561)(418,566)(419,565)(420,567)(421,563)(422,562)(423,564)(424,569)
(425,568)(426,570)(427,575)(428,574)(429,576)(430,572)(431,571)(432,573);;
s2 := ( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)( 21, 26)
( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 38, 42)( 39, 44)( 41, 45)( 47, 51)
( 48, 53)( 50, 54)( 56, 60)( 57, 62)( 59, 63)( 65, 69)( 66, 71)( 68, 72)
( 73,109)( 74,114)( 75,116)( 76,112)( 77,117)( 78,110)( 79,115)( 80,111)
( 81,113)( 82,118)( 83,123)( 84,125)( 85,121)( 86,126)( 87,119)( 88,124)
( 89,120)( 90,122)( 91,127)( 92,132)( 93,134)( 94,130)( 95,135)( 96,128)
( 97,133)( 98,129)( 99,131)(100,136)(101,141)(102,143)(103,139)(104,144)
(105,137)(106,142)(107,138)(108,140)(145,163)(146,168)(147,170)(148,166)
(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)(156,179)
(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,199)(182,204)
(183,206)(184,202)(185,207)(186,200)(187,205)(188,201)(189,203)(190,208)
(191,213)(192,215)(193,211)(194,216)(195,209)(196,214)(197,210)(198,212)
(217,271)(218,276)(219,278)(220,274)(221,279)(222,272)(223,277)(224,273)
(225,275)(226,280)(227,285)(228,287)(229,283)(230,288)(231,281)(232,286)
(233,282)(234,284)(235,253)(236,258)(237,260)(238,256)(239,261)(240,254)
(241,259)(242,255)(243,257)(244,262)(245,267)(246,269)(247,265)(248,270)
(249,263)(250,268)(251,264)(252,266)(289,325)(290,330)(291,332)(292,328)
(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)(300,341)
(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)(308,348)
(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)(316,352)
(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)(324,356)
(362,366)(363,368)(365,369)(371,375)(372,377)(374,378)(380,384)(381,386)
(383,387)(389,393)(390,395)(392,396)(398,402)(399,404)(401,405)(407,411)
(408,413)(410,414)(416,420)(417,422)(419,423)(425,429)(426,431)(428,432)
(433,487)(434,492)(435,494)(436,490)(437,495)(438,488)(439,493)(440,489)
(441,491)(442,496)(443,501)(444,503)(445,499)(446,504)(447,497)(448,502)
(449,498)(450,500)(451,469)(452,474)(453,476)(454,472)(455,477)(456,470)
(457,475)(458,471)(459,473)(460,478)(461,483)(462,485)(463,481)(464,486)
(465,479)(466,484)(467,480)(468,482)(505,523)(506,528)(507,530)(508,526)
(509,531)(510,524)(511,529)(512,525)(513,527)(514,532)(515,537)(516,539)
(517,535)(518,540)(519,533)(520,538)(521,534)(522,536)(541,559)(542,564)
(543,566)(544,562)(545,567)(546,560)(547,565)(548,561)(549,563)(550,568)
(551,573)(552,575)(553,571)(554,576)(555,569)(556,574)(557,570)(558,572);;
s3 := ( 1, 73)( 2, 74)( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)
( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)
( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)
( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)
( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)
( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)
( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)
( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)
( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)
(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)
(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)
(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)
(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)
(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)
(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)
(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)
(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)
(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288)
(289,361)(290,362)(291,363)(292,364)(293,365)(294,366)(295,367)(296,368)
(297,369)(298,370)(299,371)(300,372)(301,373)(302,374)(303,375)(304,376)
(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)(312,384)
(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)(320,392)
(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)(328,400)
(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)(336,408)
(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)(344,416)
(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)(352,424)
(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)(360,432)
(433,505)(434,506)(435,507)(436,508)(437,509)(438,510)(439,511)(440,512)
(441,513)(442,514)(443,515)(444,516)(445,517)(446,518)(447,519)(448,520)
(449,521)(450,522)(451,523)(452,524)(453,525)(454,526)(455,527)(456,528)
(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)(464,536)
(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)(472,544)
(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)(480,552)
(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)(488,560)
(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)(496,568)
(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)(504,576);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,361)( 2,363)( 3,362)( 4,367)( 5,369)( 6,368)( 7,364)
( 8,366)( 9,365)( 10,370)( 11,372)( 12,371)( 13,376)( 14,378)( 15,377)
( 16,373)( 17,375)( 18,374)( 19,379)( 20,381)( 21,380)( 22,385)( 23,387)
( 24,386)( 25,382)( 26,384)( 27,383)( 28,388)( 29,390)( 30,389)( 31,394)
( 32,396)( 33,395)( 34,391)( 35,393)( 36,392)( 37,397)( 38,399)( 39,398)
( 40,403)( 41,405)( 42,404)( 43,400)( 44,402)( 45,401)( 46,406)( 47,408)
( 48,407)( 49,412)( 50,414)( 51,413)( 52,409)( 53,411)( 54,410)( 55,415)
( 56,417)( 57,416)( 58,421)( 59,423)( 60,422)( 61,418)( 62,420)( 63,419)
( 64,424)( 65,426)( 66,425)( 67,430)( 68,432)( 69,431)( 70,427)( 71,429)
( 72,428)( 73,289)( 74,291)( 75,290)( 76,295)( 77,297)( 78,296)( 79,292)
( 80,294)( 81,293)( 82,298)( 83,300)( 84,299)( 85,304)( 86,306)( 87,305)
( 88,301)( 89,303)( 90,302)( 91,307)( 92,309)( 93,308)( 94,313)( 95,315)
( 96,314)( 97,310)( 98,312)( 99,311)(100,316)(101,318)(102,317)(103,322)
(104,324)(105,323)(106,319)(107,321)(108,320)(109,325)(110,327)(111,326)
(112,331)(113,333)(114,332)(115,328)(116,330)(117,329)(118,334)(119,336)
(120,335)(121,340)(122,342)(123,341)(124,337)(125,339)(126,338)(127,343)
(128,345)(129,344)(130,349)(131,351)(132,350)(133,346)(134,348)(135,347)
(136,352)(137,354)(138,353)(139,358)(140,360)(141,359)(142,355)(143,357)
(144,356)(145,514)(146,516)(147,515)(148,520)(149,522)(150,521)(151,517)
(152,519)(153,518)(154,505)(155,507)(156,506)(157,511)(158,513)(159,512)
(160,508)(161,510)(162,509)(163,532)(164,534)(165,533)(166,538)(167,540)
(168,539)(169,535)(170,537)(171,536)(172,523)(173,525)(174,524)(175,529)
(176,531)(177,530)(178,526)(179,528)(180,527)(181,550)(182,552)(183,551)
(184,556)(185,558)(186,557)(187,553)(188,555)(189,554)(190,541)(191,543)
(192,542)(193,547)(194,549)(195,548)(196,544)(197,546)(198,545)(199,568)
(200,570)(201,569)(202,574)(203,576)(204,575)(205,571)(206,573)(207,572)
(208,559)(209,561)(210,560)(211,565)(212,567)(213,566)(214,562)(215,564)
(216,563)(217,442)(218,444)(219,443)(220,448)(221,450)(222,449)(223,445)
(224,447)(225,446)(226,433)(227,435)(228,434)(229,439)(230,441)(231,440)
(232,436)(233,438)(234,437)(235,460)(236,462)(237,461)(238,466)(239,468)
(240,467)(241,463)(242,465)(243,464)(244,451)(245,453)(246,452)(247,457)
(248,459)(249,458)(250,454)(251,456)(252,455)(253,478)(254,480)(255,479)
(256,484)(257,486)(258,485)(259,481)(260,483)(261,482)(262,469)(263,471)
(264,470)(265,475)(266,477)(267,476)(268,472)(269,474)(270,473)(271,496)
(272,498)(273,497)(274,502)(275,504)(276,503)(277,499)(278,501)(279,500)
(280,487)(281,489)(282,488)(283,493)(284,495)(285,494)(286,490)(287,492)
(288,491);
s1 := Sym(576)!( 1,146)( 2,145)( 3,147)( 4,152)( 5,151)( 6,153)( 7,149)
( 8,148)( 9,150)( 10,155)( 11,154)( 12,156)( 13,161)( 14,160)( 15,162)
( 16,158)( 17,157)( 18,159)( 19,164)( 20,163)( 21,165)( 22,170)( 23,169)
( 24,171)( 25,167)( 26,166)( 27,168)( 28,173)( 29,172)( 30,174)( 31,179)
( 32,178)( 33,180)( 34,176)( 35,175)( 36,177)( 37,182)( 38,181)( 39,183)
( 40,188)( 41,187)( 42,189)( 43,185)( 44,184)( 45,186)( 46,191)( 47,190)
( 48,192)( 49,197)( 50,196)( 51,198)( 52,194)( 53,193)( 54,195)( 55,200)
( 56,199)( 57,201)( 58,206)( 59,205)( 60,207)( 61,203)( 62,202)( 63,204)
( 64,209)( 65,208)( 66,210)( 67,215)( 68,214)( 69,216)( 70,212)( 71,211)
( 72,213)( 73,218)( 74,217)( 75,219)( 76,224)( 77,223)( 78,225)( 79,221)
( 80,220)( 81,222)( 82,227)( 83,226)( 84,228)( 85,233)( 86,232)( 87,234)
( 88,230)( 89,229)( 90,231)( 91,236)( 92,235)( 93,237)( 94,242)( 95,241)
( 96,243)( 97,239)( 98,238)( 99,240)(100,245)(101,244)(102,246)(103,251)
(104,250)(105,252)(106,248)(107,247)(108,249)(109,254)(110,253)(111,255)
(112,260)(113,259)(114,261)(115,257)(116,256)(117,258)(118,263)(119,262)
(120,264)(121,269)(122,268)(123,270)(124,266)(125,265)(126,267)(127,272)
(128,271)(129,273)(130,278)(131,277)(132,279)(133,275)(134,274)(135,276)
(136,281)(137,280)(138,282)(139,287)(140,286)(141,288)(142,284)(143,283)
(144,285)(289,434)(290,433)(291,435)(292,440)(293,439)(294,441)(295,437)
(296,436)(297,438)(298,443)(299,442)(300,444)(301,449)(302,448)(303,450)
(304,446)(305,445)(306,447)(307,452)(308,451)(309,453)(310,458)(311,457)
(312,459)(313,455)(314,454)(315,456)(316,461)(317,460)(318,462)(319,467)
(320,466)(321,468)(322,464)(323,463)(324,465)(325,470)(326,469)(327,471)
(328,476)(329,475)(330,477)(331,473)(332,472)(333,474)(334,479)(335,478)
(336,480)(337,485)(338,484)(339,486)(340,482)(341,481)(342,483)(343,488)
(344,487)(345,489)(346,494)(347,493)(348,495)(349,491)(350,490)(351,492)
(352,497)(353,496)(354,498)(355,503)(356,502)(357,504)(358,500)(359,499)
(360,501)(361,506)(362,505)(363,507)(364,512)(365,511)(366,513)(367,509)
(368,508)(369,510)(370,515)(371,514)(372,516)(373,521)(374,520)(375,522)
(376,518)(377,517)(378,519)(379,524)(380,523)(381,525)(382,530)(383,529)
(384,531)(385,527)(386,526)(387,528)(388,533)(389,532)(390,534)(391,539)
(392,538)(393,540)(394,536)(395,535)(396,537)(397,542)(398,541)(399,543)
(400,548)(401,547)(402,549)(403,545)(404,544)(405,546)(406,551)(407,550)
(408,552)(409,557)(410,556)(411,558)(412,554)(413,553)(414,555)(415,560)
(416,559)(417,561)(418,566)(419,565)(420,567)(421,563)(422,562)(423,564)
(424,569)(425,568)(426,570)(427,575)(428,574)(429,576)(430,572)(431,571)
(432,573);
s2 := Sym(576)!( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 20, 24)
( 21, 26)( 23, 27)( 29, 33)( 30, 35)( 32, 36)( 38, 42)( 39, 44)( 41, 45)
( 47, 51)( 48, 53)( 50, 54)( 56, 60)( 57, 62)( 59, 63)( 65, 69)( 66, 71)
( 68, 72)( 73,109)( 74,114)( 75,116)( 76,112)( 77,117)( 78,110)( 79,115)
( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)( 85,121)( 86,126)( 87,119)
( 88,124)( 89,120)( 90,122)( 91,127)( 92,132)( 93,134)( 94,130)( 95,135)
( 96,128)( 97,133)( 98,129)( 99,131)(100,136)(101,141)(102,143)(103,139)
(104,144)(105,137)(106,142)(107,138)(108,140)(145,163)(146,168)(147,170)
(148,166)(149,171)(150,164)(151,169)(152,165)(153,167)(154,172)(155,177)
(156,179)(157,175)(158,180)(159,173)(160,178)(161,174)(162,176)(181,199)
(182,204)(183,206)(184,202)(185,207)(186,200)(187,205)(188,201)(189,203)
(190,208)(191,213)(192,215)(193,211)(194,216)(195,209)(196,214)(197,210)
(198,212)(217,271)(218,276)(219,278)(220,274)(221,279)(222,272)(223,277)
(224,273)(225,275)(226,280)(227,285)(228,287)(229,283)(230,288)(231,281)
(232,286)(233,282)(234,284)(235,253)(236,258)(237,260)(238,256)(239,261)
(240,254)(241,259)(242,255)(243,257)(244,262)(245,267)(246,269)(247,265)
(248,270)(249,263)(250,268)(251,264)(252,266)(289,325)(290,330)(291,332)
(292,328)(293,333)(294,326)(295,331)(296,327)(297,329)(298,334)(299,339)
(300,341)(301,337)(302,342)(303,335)(304,340)(305,336)(306,338)(307,343)
(308,348)(309,350)(310,346)(311,351)(312,344)(313,349)(314,345)(315,347)
(316,352)(317,357)(318,359)(319,355)(320,360)(321,353)(322,358)(323,354)
(324,356)(362,366)(363,368)(365,369)(371,375)(372,377)(374,378)(380,384)
(381,386)(383,387)(389,393)(390,395)(392,396)(398,402)(399,404)(401,405)
(407,411)(408,413)(410,414)(416,420)(417,422)(419,423)(425,429)(426,431)
(428,432)(433,487)(434,492)(435,494)(436,490)(437,495)(438,488)(439,493)
(440,489)(441,491)(442,496)(443,501)(444,503)(445,499)(446,504)(447,497)
(448,502)(449,498)(450,500)(451,469)(452,474)(453,476)(454,472)(455,477)
(456,470)(457,475)(458,471)(459,473)(460,478)(461,483)(462,485)(463,481)
(464,486)(465,479)(466,484)(467,480)(468,482)(505,523)(506,528)(507,530)
(508,526)(509,531)(510,524)(511,529)(512,525)(513,527)(514,532)(515,537)
(516,539)(517,535)(518,540)(519,533)(520,538)(521,534)(522,536)(541,559)
(542,564)(543,566)(544,562)(545,567)(546,560)(547,565)(548,561)(549,563)
(550,568)(551,573)(552,575)(553,571)(554,576)(555,569)(556,574)(557,570)
(558,572);
s3 := Sym(576)!( 1, 73)( 2, 74)( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)
( 8, 80)( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)
( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)
( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)
( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)
( 40,112)( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)
( 48,120)( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)
( 56,128)( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)
( 64,136)( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)
( 72,144)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)
(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)
(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)
(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)
(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)
(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)
(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)
(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)
(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)
(216,288)(289,361)(290,362)(291,363)(292,364)(293,365)(294,366)(295,367)
(296,368)(297,369)(298,370)(299,371)(300,372)(301,373)(302,374)(303,375)
(304,376)(305,377)(306,378)(307,379)(308,380)(309,381)(310,382)(311,383)
(312,384)(313,385)(314,386)(315,387)(316,388)(317,389)(318,390)(319,391)
(320,392)(321,393)(322,394)(323,395)(324,396)(325,397)(326,398)(327,399)
(328,400)(329,401)(330,402)(331,403)(332,404)(333,405)(334,406)(335,407)
(336,408)(337,409)(338,410)(339,411)(340,412)(341,413)(342,414)(343,415)
(344,416)(345,417)(346,418)(347,419)(348,420)(349,421)(350,422)(351,423)
(352,424)(353,425)(354,426)(355,427)(356,428)(357,429)(358,430)(359,431)
(360,432)(433,505)(434,506)(435,507)(436,508)(437,509)(438,510)(439,511)
(440,512)(441,513)(442,514)(443,515)(444,516)(445,517)(446,518)(447,519)
(448,520)(449,521)(450,522)(451,523)(452,524)(453,525)(454,526)(455,527)
(456,528)(457,529)(458,530)(459,531)(460,532)(461,533)(462,534)(463,535)
(464,536)(465,537)(466,538)(467,539)(468,540)(469,541)(470,542)(471,543)
(472,544)(473,545)(474,546)(475,547)(476,548)(477,549)(478,550)(479,551)
(480,552)(481,553)(482,554)(483,555)(484,556)(485,557)(486,558)(487,559)
(488,560)(489,561)(490,562)(491,563)(492,564)(493,565)(494,566)(495,567)
(496,568)(497,569)(498,570)(499,571)(500,572)(501,573)(502,574)(503,575)
(504,576);
poly := sub<Sym(576)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope