Polytope of Type {12,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,43022)
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 : {6,12,4}*576b, {12,12,2}*576b, {12,6,4}*576c
3-fold quotients : {4,12,4}*384a
4-fold quotients : {6,12,2}*288b, {6,6,4}*288b, {12,6,2}*288c
6-fold quotients : {2,12,4}*192a, {4,12,2}*192a, {4,6,4}*192a
8-fold quotients : {6,6,2}*144b
9-fold quotients : {4,4,4}*128
12-fold quotients : {2,12,2}*96, {2,6,4}*96a, {4,6,2}*96a
16-fold quotients : {6,3,2}*72
18-fold quotients : {2,4,4}*64, {4,4,2}*64, {4,2,4}*64
24-fold quotients : {2,6,2}*48
36-fold quotients : {2,2,4}*32, {2,4,2}*32, {4,2,2}*32
48-fold quotients : {2,3,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,361)( 2,366)( 3,368)( 4,364)( 5,369)( 6,362)( 7,367)( 8,363)
( 9,365)( 10,370)( 11,375)( 12,377)( 13,373)( 14,378)( 15,371)( 16,376)
( 17,372)( 18,374)( 19,379)( 20,384)( 21,386)( 22,382)( 23,387)( 24,380)
( 25,385)( 26,381)( 27,383)( 28,388)( 29,393)( 30,395)( 31,391)( 32,396)
( 33,389)( 34,394)( 35,390)( 36,392)( 37,397)( 38,402)( 39,404)( 40,400)
( 41,405)( 42,398)( 43,403)( 44,399)( 45,401)( 46,406)( 47,411)( 48,413)
( 49,409)( 50,414)( 51,407)( 52,412)( 53,408)( 54,410)( 55,415)( 56,420)
( 57,422)( 58,418)( 59,423)( 60,416)( 61,421)( 62,417)( 63,419)( 64,424)
( 65,429)( 66,431)( 67,427)( 68,432)( 69,425)( 70,430)( 71,426)( 72,428)
( 73,289)( 74,294)( 75,296)( 76,292)( 77,297)( 78,290)( 79,295)( 80,291)
( 81,293)( 82,298)( 83,303)( 84,305)( 85,301)( 86,306)( 87,299)( 88,304)
( 89,300)( 90,302)( 91,307)( 92,312)( 93,314)( 94,310)( 95,315)( 96,308)
( 97,313)( 98,309)( 99,311)(100,316)(101,321)(102,323)(103,319)(104,324)
(105,317)(106,322)(107,318)(108,320)(109,325)(110,330)(111,332)(112,328)
(113,333)(114,326)(115,331)(116,327)(117,329)(118,334)(119,339)(120,341)
(121,337)(122,342)(123,335)(124,340)(125,336)(126,338)(127,343)(128,348)
(129,350)(130,346)(131,351)(132,344)(133,349)(134,345)(135,347)(136,352)
(137,357)(138,359)(139,355)(140,360)(141,353)(142,358)(143,354)(144,356)
(145,514)(146,519)(147,521)(148,517)(149,522)(150,515)(151,520)(152,516)
(153,518)(154,505)(155,510)(156,512)(157,508)(158,513)(159,506)(160,511)
(161,507)(162,509)(163,532)(164,537)(165,539)(166,535)(167,540)(168,533)
(169,538)(170,534)(171,536)(172,523)(173,528)(174,530)(175,526)(176,531)
(177,524)(178,529)(179,525)(180,527)(181,550)(182,555)(183,557)(184,553)
(185,558)(186,551)(187,556)(188,552)(189,554)(190,541)(191,546)(192,548)
(193,544)(194,549)(195,542)(196,547)(197,543)(198,545)(199,568)(200,573)
(201,575)(202,571)(203,576)(204,569)(205,574)(206,570)(207,572)(208,559)
(209,564)(210,566)(211,562)(212,567)(213,560)(214,565)(215,561)(216,563)
(217,442)(218,447)(219,449)(220,445)(221,450)(222,443)(223,448)(224,444)
(225,446)(226,433)(227,438)(228,440)(229,436)(230,441)(231,434)(232,439)
(233,435)(234,437)(235,460)(236,465)(237,467)(238,463)(239,468)(240,461)
(241,466)(242,462)(243,464)(244,451)(245,456)(246,458)(247,454)(248,459)
(249,452)(250,457)(251,453)(252,455)(253,478)(254,483)(255,485)(256,481)
(257,486)(258,479)(259,484)(260,480)(261,482)(262,469)(263,474)(264,476)
(265,472)(266,477)(267,470)(268,475)(269,471)(270,473)(271,496)(272,501)
(273,503)(274,499)(275,504)(276,497)(277,502)(278,498)(279,500)(280,487)
(281,492)(282,494)(283,490)(284,495)(285,488)(286,493)(287,489)(288,491);;
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, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)
( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)
( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)( 51, 53)
( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 65, 66)( 67, 70)( 68, 72)( 69, 71)
( 73,109)( 74,111)( 75,110)( 76,115)( 77,117)( 78,116)( 79,112)( 80,114)
( 81,113)( 82,118)( 83,120)( 84,119)( 85,124)( 86,126)( 87,125)( 88,121)
( 89,123)( 90,122)( 91,127)( 92,129)( 93,128)( 94,133)( 95,135)( 96,134)
( 97,130)( 98,132)( 99,131)(100,136)(101,138)(102,137)(103,142)(104,144)
(105,143)(106,139)(107,141)(108,140)(145,163)(146,165)(147,164)(148,169)
(149,171)(150,170)(151,166)(152,168)(153,167)(154,172)(155,174)(156,173)
(157,178)(158,180)(159,179)(160,175)(161,177)(162,176)(181,199)(182,201)
(183,200)(184,205)(185,207)(186,206)(187,202)(188,204)(189,203)(190,208)
(191,210)(192,209)(193,214)(194,216)(195,215)(196,211)(197,213)(198,212)
(217,271)(218,273)(219,272)(220,277)(221,279)(222,278)(223,274)(224,276)
(225,275)(226,280)(227,282)(228,281)(229,286)(230,288)(231,287)(232,283)
(233,285)(234,284)(235,253)(236,255)(237,254)(238,259)(239,261)(240,260)
(241,256)(242,258)(243,257)(244,262)(245,264)(246,263)(247,268)(248,270)
(249,269)(250,265)(251,267)(252,266)(289,325)(290,327)(291,326)(292,331)
(293,333)(294,332)(295,328)(296,330)(297,329)(298,334)(299,336)(300,335)
(301,340)(302,342)(303,341)(304,337)(305,339)(306,338)(307,343)(308,345)
(309,344)(310,349)(311,351)(312,350)(313,346)(314,348)(315,347)(316,352)
(317,354)(318,353)(319,358)(320,360)(321,359)(322,355)(323,357)(324,356)
(362,363)(364,367)(365,369)(366,368)(371,372)(373,376)(374,378)(375,377)
(380,381)(382,385)(383,387)(384,386)(389,390)(391,394)(392,396)(393,395)
(398,399)(400,403)(401,405)(402,404)(407,408)(409,412)(410,414)(411,413)
(416,417)(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)(429,431)
(433,487)(434,489)(435,488)(436,493)(437,495)(438,494)(439,490)(440,492)
(441,491)(442,496)(443,498)(444,497)(445,502)(446,504)(447,503)(448,499)
(449,501)(450,500)(451,469)(452,471)(453,470)(454,475)(455,477)(456,476)
(457,472)(458,474)(459,473)(460,478)(461,480)(462,479)(463,484)(464,486)
(465,485)(466,481)(467,483)(468,482)(505,523)(506,525)(507,524)(508,529)
(509,531)(510,530)(511,526)(512,528)(513,527)(514,532)(515,534)(516,533)
(517,538)(518,540)(519,539)(520,535)(521,537)(522,536)(541,559)(542,561)
(543,560)(544,565)(545,567)(546,566)(547,562)(548,564)(549,563)(550,568)
(551,570)(552,569)(553,574)(554,576)(555,575)(556,571)(557,573)(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*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,361)( 2,366)( 3,368)( 4,364)( 5,369)( 6,362)( 7,367)
( 8,363)( 9,365)( 10,370)( 11,375)( 12,377)( 13,373)( 14,378)( 15,371)
( 16,376)( 17,372)( 18,374)( 19,379)( 20,384)( 21,386)( 22,382)( 23,387)
( 24,380)( 25,385)( 26,381)( 27,383)( 28,388)( 29,393)( 30,395)( 31,391)
( 32,396)( 33,389)( 34,394)( 35,390)( 36,392)( 37,397)( 38,402)( 39,404)
( 40,400)( 41,405)( 42,398)( 43,403)( 44,399)( 45,401)( 46,406)( 47,411)
( 48,413)( 49,409)( 50,414)( 51,407)( 52,412)( 53,408)( 54,410)( 55,415)
( 56,420)( 57,422)( 58,418)( 59,423)( 60,416)( 61,421)( 62,417)( 63,419)
( 64,424)( 65,429)( 66,431)( 67,427)( 68,432)( 69,425)( 70,430)( 71,426)
( 72,428)( 73,289)( 74,294)( 75,296)( 76,292)( 77,297)( 78,290)( 79,295)
( 80,291)( 81,293)( 82,298)( 83,303)( 84,305)( 85,301)( 86,306)( 87,299)
( 88,304)( 89,300)( 90,302)( 91,307)( 92,312)( 93,314)( 94,310)( 95,315)
( 96,308)( 97,313)( 98,309)( 99,311)(100,316)(101,321)(102,323)(103,319)
(104,324)(105,317)(106,322)(107,318)(108,320)(109,325)(110,330)(111,332)
(112,328)(113,333)(114,326)(115,331)(116,327)(117,329)(118,334)(119,339)
(120,341)(121,337)(122,342)(123,335)(124,340)(125,336)(126,338)(127,343)
(128,348)(129,350)(130,346)(131,351)(132,344)(133,349)(134,345)(135,347)
(136,352)(137,357)(138,359)(139,355)(140,360)(141,353)(142,358)(143,354)
(144,356)(145,514)(146,519)(147,521)(148,517)(149,522)(150,515)(151,520)
(152,516)(153,518)(154,505)(155,510)(156,512)(157,508)(158,513)(159,506)
(160,511)(161,507)(162,509)(163,532)(164,537)(165,539)(166,535)(167,540)
(168,533)(169,538)(170,534)(171,536)(172,523)(173,528)(174,530)(175,526)
(176,531)(177,524)(178,529)(179,525)(180,527)(181,550)(182,555)(183,557)
(184,553)(185,558)(186,551)(187,556)(188,552)(189,554)(190,541)(191,546)
(192,548)(193,544)(194,549)(195,542)(196,547)(197,543)(198,545)(199,568)
(200,573)(201,575)(202,571)(203,576)(204,569)(205,574)(206,570)(207,572)
(208,559)(209,564)(210,566)(211,562)(212,567)(213,560)(214,565)(215,561)
(216,563)(217,442)(218,447)(219,449)(220,445)(221,450)(222,443)(223,448)
(224,444)(225,446)(226,433)(227,438)(228,440)(229,436)(230,441)(231,434)
(232,439)(233,435)(234,437)(235,460)(236,465)(237,467)(238,463)(239,468)
(240,461)(241,466)(242,462)(243,464)(244,451)(245,456)(246,458)(247,454)
(248,459)(249,452)(250,457)(251,453)(252,455)(253,478)(254,483)(255,485)
(256,481)(257,486)(258,479)(259,484)(260,480)(261,482)(262,469)(263,474)
(264,476)(265,472)(266,477)(267,470)(268,475)(269,471)(270,473)(271,496)
(272,501)(273,503)(274,499)(275,504)(276,497)(277,502)(278,498)(279,500)
(280,487)(281,492)(282,494)(283,490)(284,495)(285,488)(286,493)(287,489)
(288,491);
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, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)
( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)
( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)
( 51, 53)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 65, 66)( 67, 70)( 68, 72)
( 69, 71)( 73,109)( 74,111)( 75,110)( 76,115)( 77,117)( 78,116)( 79,112)
( 80,114)( 81,113)( 82,118)( 83,120)( 84,119)( 85,124)( 86,126)( 87,125)
( 88,121)( 89,123)( 90,122)( 91,127)( 92,129)( 93,128)( 94,133)( 95,135)
( 96,134)( 97,130)( 98,132)( 99,131)(100,136)(101,138)(102,137)(103,142)
(104,144)(105,143)(106,139)(107,141)(108,140)(145,163)(146,165)(147,164)
(148,169)(149,171)(150,170)(151,166)(152,168)(153,167)(154,172)(155,174)
(156,173)(157,178)(158,180)(159,179)(160,175)(161,177)(162,176)(181,199)
(182,201)(183,200)(184,205)(185,207)(186,206)(187,202)(188,204)(189,203)
(190,208)(191,210)(192,209)(193,214)(194,216)(195,215)(196,211)(197,213)
(198,212)(217,271)(218,273)(219,272)(220,277)(221,279)(222,278)(223,274)
(224,276)(225,275)(226,280)(227,282)(228,281)(229,286)(230,288)(231,287)
(232,283)(233,285)(234,284)(235,253)(236,255)(237,254)(238,259)(239,261)
(240,260)(241,256)(242,258)(243,257)(244,262)(245,264)(246,263)(247,268)
(248,270)(249,269)(250,265)(251,267)(252,266)(289,325)(290,327)(291,326)
(292,331)(293,333)(294,332)(295,328)(296,330)(297,329)(298,334)(299,336)
(300,335)(301,340)(302,342)(303,341)(304,337)(305,339)(306,338)(307,343)
(308,345)(309,344)(310,349)(311,351)(312,350)(313,346)(314,348)(315,347)
(316,352)(317,354)(318,353)(319,358)(320,360)(321,359)(322,355)(323,357)
(324,356)(362,363)(364,367)(365,369)(366,368)(371,372)(373,376)(374,378)
(375,377)(380,381)(382,385)(383,387)(384,386)(389,390)(391,394)(392,396)
(393,395)(398,399)(400,403)(401,405)(402,404)(407,408)(409,412)(410,414)
(411,413)(416,417)(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)
(429,431)(433,487)(434,489)(435,488)(436,493)(437,495)(438,494)(439,490)
(440,492)(441,491)(442,496)(443,498)(444,497)(445,502)(446,504)(447,503)
(448,499)(449,501)(450,500)(451,469)(452,471)(453,470)(454,475)(455,477)
(456,476)(457,472)(458,474)(459,473)(460,478)(461,480)(462,479)(463,484)
(464,486)(465,485)(466,481)(467,483)(468,482)(505,523)(506,525)(507,524)
(508,529)(509,531)(510,530)(511,526)(512,528)(513,527)(514,532)(515,534)
(516,533)(517,538)(518,540)(519,539)(520,535)(521,537)(522,536)(541,559)
(542,561)(543,560)(544,565)(545,567)(546,566)(547,562)(548,564)(549,563)
(550,568)(551,570)(552,569)(553,574)(554,576)(555,575)(556,571)(557,573)
(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*s0*s1*s2*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope