Polytope of Type {12,4,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,12}*1152
Also Known As : {{12,4|2},{4,12|2}}. if this polytope has another name.
Group : SmallGroup(1152,43026)
Rank : 4
Schlafli Type : {12,4,12}
Number of vertices, edges, etc : 12, 24, 24, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Self-Dual
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 : {12,2,12}*576, {6,4,12}*576, {12,4,6}*576
3-fold quotients : {4,4,12}*384, {12,4,4}*384
4-fold quotients : {6,2,12}*288, {12,2,6}*288, {6,4,6}*288
6-fold quotients : {2,4,12}*192a, {12,4,2}*192a, {4,2,12}*192, {12,2,4}*192, {4,4,6}*192, {6,4,4}*192
8-fold quotients : {3,2,12}*144, {12,2,3}*144, {6,2,6}*144
9-fold quotients : {4,4,4}*128
12-fold quotients : {2,2,12}*96, {12,2,2}*96, {2,4,6}*96a, {4,2,6}*96, {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, {4,4,2}*64, {4,2,4}*64
24-fold quotients : {3,2,4}*48, {4,2,3}*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, {4,2,2}*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)( 37,401)( 38,403)( 39,399)( 40,404)
( 41,397)( 42,402)( 43,398)( 44,400)( 45,405)( 46,410)( 47,412)( 48,408)
( 49,413)( 50,406)( 51,411)( 52,407)( 53,409)( 54,414)( 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)
( 73,329)( 74,331)( 75,327)( 76,332)( 77,325)( 78,330)( 79,326)( 80,328)
( 81,333)( 82,338)( 83,340)( 84,336)( 85,341)( 86,334)( 87,339)( 88,335)
( 89,337)( 90,342)( 91,347)( 92,349)( 93,345)( 94,350)( 95,343)( 96,348)
( 97,344)( 98,346)( 99,351)(100,356)(101,358)(102,354)(103,359)(104,352)
(105,357)(106,353)(107,355)(108,360)(109,293)(110,295)(111,291)(112,296)
(113,289)(114,294)(115,290)(116,292)(117,297)(118,302)(119,304)(120,300)
(121,305)(122,298)(123,303)(124,299)(125,301)(126,306)(127,311)(128,313)
(129,309)(130,314)(131,307)(132,312)(133,308)(134,310)(135,315)(136,320)
(137,322)(138,318)(139,323)(140,316)(141,321)(142,317)(143,319)(144,324)
(145,536)(146,538)(147,534)(148,539)(149,532)(150,537)(151,533)(152,535)
(153,540)(154,527)(155,529)(156,525)(157,530)(158,523)(159,528)(160,524)
(161,526)(162,531)(163,518)(164,520)(165,516)(166,521)(167,514)(168,519)
(169,515)(170,517)(171,522)(172,509)(173,511)(174,507)(175,512)(176,505)
(177,510)(178,506)(179,508)(180,513)(181,572)(182,574)(183,570)(184,575)
(185,568)(186,573)(187,569)(188,571)(189,576)(190,563)(191,565)(192,561)
(193,566)(194,559)(195,564)(196,560)(197,562)(198,567)(199,554)(200,556)
(201,552)(202,557)(203,550)(204,555)(205,551)(206,553)(207,558)(208,545)
(209,547)(210,543)(211,548)(212,541)(213,546)(214,542)(215,544)(216,549)
(217,500)(218,502)(219,498)(220,503)(221,496)(222,501)(223,497)(224,499)
(225,504)(226,491)(227,493)(228,489)(229,494)(230,487)(231,492)(232,488)
(233,490)(234,495)(235,482)(236,484)(237,480)(238,485)(239,478)(240,483)
(241,479)(242,481)(243,486)(244,473)(245,475)(246,471)(247,476)(248,469)
(249,474)(250,470)(251,472)(252,477)(253,464)(254,466)(255,462)(256,467)
(257,460)(258,465)(259,461)(260,463)(261,468)(262,455)(263,457)(264,453)
(265,458)(266,451)(267,456)(268,452)(269,454)(270,459)(271,446)(272,448)
(273,444)(274,449)(275,442)(276,447)(277,443)(278,445)(279,450)(280,437)
(281,439)(282,435)(283,440)(284,433)(285,438)(286,434)(287,436)(288,441);;
s2 := ( 1,217)( 2,224)( 3,222)( 4,223)( 5,221)( 6,219)( 7,220)( 8,218)
( 9,225)( 10,226)( 11,233)( 12,231)( 13,232)( 14,230)( 15,228)( 16,229)
( 17,227)( 18,234)( 19,235)( 20,242)( 21,240)( 22,241)( 23,239)( 24,237)
( 25,238)( 26,236)( 27,243)( 28,244)( 29,251)( 30,249)( 31,250)( 32,248)
( 33,246)( 34,247)( 35,245)( 36,252)( 37,253)( 38,260)( 39,258)( 40,259)
( 41,257)( 42,255)( 43,256)( 44,254)( 45,261)( 46,262)( 47,269)( 48,267)
( 49,268)( 50,266)( 51,264)( 52,265)( 53,263)( 54,270)( 55,271)( 56,278)
( 57,276)( 58,277)( 59,275)( 60,273)( 61,274)( 62,272)( 63,279)( 64,280)
( 65,287)( 66,285)( 67,286)( 68,284)( 69,282)( 70,283)( 71,281)( 72,288)
( 73,145)( 74,152)( 75,150)( 76,151)( 77,149)( 78,147)( 79,148)( 80,146)
( 81,153)( 82,154)( 83,161)( 84,159)( 85,160)( 86,158)( 87,156)( 88,157)
( 89,155)( 90,162)( 91,163)( 92,170)( 93,168)( 94,169)( 95,167)( 96,165)
( 97,166)( 98,164)( 99,171)(100,172)(101,179)(102,177)(103,178)(104,176)
(105,174)(106,175)(107,173)(108,180)(109,181)(110,188)(111,186)(112,187)
(113,185)(114,183)(115,184)(116,182)(117,189)(118,190)(119,197)(120,195)
(121,196)(122,194)(123,192)(124,193)(125,191)(126,198)(127,199)(128,206)
(129,204)(130,205)(131,203)(132,201)(133,202)(134,200)(135,207)(136,208)
(137,215)(138,213)(139,214)(140,212)(141,210)(142,211)(143,209)(144,216)
(289,505)(290,512)(291,510)(292,511)(293,509)(294,507)(295,508)(296,506)
(297,513)(298,514)(299,521)(300,519)(301,520)(302,518)(303,516)(304,517)
(305,515)(306,522)(307,523)(308,530)(309,528)(310,529)(311,527)(312,525)
(313,526)(314,524)(315,531)(316,532)(317,539)(318,537)(319,538)(320,536)
(321,534)(322,535)(323,533)(324,540)(325,541)(326,548)(327,546)(328,547)
(329,545)(330,543)(331,544)(332,542)(333,549)(334,550)(335,557)(336,555)
(337,556)(338,554)(339,552)(340,553)(341,551)(342,558)(343,559)(344,566)
(345,564)(346,565)(347,563)(348,561)(349,562)(350,560)(351,567)(352,568)
(353,575)(354,573)(355,574)(356,572)(357,570)(358,571)(359,569)(360,576)
(361,433)(362,440)(363,438)(364,439)(365,437)(366,435)(367,436)(368,434)
(369,441)(370,442)(371,449)(372,447)(373,448)(374,446)(375,444)(376,445)
(377,443)(378,450)(379,451)(380,458)(381,456)(382,457)(383,455)(384,453)
(385,454)(386,452)(387,459)(388,460)(389,467)(390,465)(391,466)(392,464)
(393,462)(394,463)(395,461)(396,468)(397,469)(398,476)(399,474)(400,475)
(401,473)(402,471)(403,472)(404,470)(405,477)(406,478)(407,485)(408,483)
(409,484)(410,482)(411,480)(412,481)(413,479)(414,486)(415,487)(416,494)
(417,492)(418,493)(419,491)(420,489)(421,490)(422,488)(423,495)(424,496)
(425,503)(426,501)(427,502)(428,500)(429,498)(430,499)(431,497)(432,504);;
s3 := ( 1,364)( 2,362)( 3,369)( 4,361)( 5,368)( 6,366)( 7,367)( 8,365)
( 9,363)( 10,373)( 11,371)( 12,378)( 13,370)( 14,377)( 15,375)( 16,376)
( 17,374)( 18,372)( 19,382)( 20,380)( 21,387)( 22,379)( 23,386)( 24,384)
( 25,385)( 26,383)( 27,381)( 28,391)( 29,389)( 30,396)( 31,388)( 32,395)
( 33,393)( 34,394)( 35,392)( 36,390)( 37,400)( 38,398)( 39,405)( 40,397)
( 41,404)( 42,402)( 43,403)( 44,401)( 45,399)( 46,409)( 47,407)( 48,414)
( 49,406)( 50,413)( 51,411)( 52,412)( 53,410)( 54,408)( 55,418)( 56,416)
( 57,423)( 58,415)( 59,422)( 60,420)( 61,421)( 62,419)( 63,417)( 64,427)
( 65,425)( 66,432)( 67,424)( 68,431)( 69,429)( 70,430)( 71,428)( 72,426)
( 73,292)( 74,290)( 75,297)( 76,289)( 77,296)( 78,294)( 79,295)( 80,293)
( 81,291)( 82,301)( 83,299)( 84,306)( 85,298)( 86,305)( 87,303)( 88,304)
( 89,302)( 90,300)( 91,310)( 92,308)( 93,315)( 94,307)( 95,314)( 96,312)
( 97,313)( 98,311)( 99,309)(100,319)(101,317)(102,324)(103,316)(104,323)
(105,321)(106,322)(107,320)(108,318)(109,328)(110,326)(111,333)(112,325)
(113,332)(114,330)(115,331)(116,329)(117,327)(118,337)(119,335)(120,342)
(121,334)(122,341)(123,339)(124,340)(125,338)(126,336)(127,346)(128,344)
(129,351)(130,343)(131,350)(132,348)(133,349)(134,347)(135,345)(136,355)
(137,353)(138,360)(139,352)(140,359)(141,357)(142,358)(143,356)(144,354)
(145,517)(146,515)(147,522)(148,514)(149,521)(150,519)(151,520)(152,518)
(153,516)(154,508)(155,506)(156,513)(157,505)(158,512)(159,510)(160,511)
(161,509)(162,507)(163,535)(164,533)(165,540)(166,532)(167,539)(168,537)
(169,538)(170,536)(171,534)(172,526)(173,524)(174,531)(175,523)(176,530)
(177,528)(178,529)(179,527)(180,525)(181,553)(182,551)(183,558)(184,550)
(185,557)(186,555)(187,556)(188,554)(189,552)(190,544)(191,542)(192,549)
(193,541)(194,548)(195,546)(196,547)(197,545)(198,543)(199,571)(200,569)
(201,576)(202,568)(203,575)(204,573)(205,574)(206,572)(207,570)(208,562)
(209,560)(210,567)(211,559)(212,566)(213,564)(214,565)(215,563)(216,561)
(217,445)(218,443)(219,450)(220,442)(221,449)(222,447)(223,448)(224,446)
(225,444)(226,436)(227,434)(228,441)(229,433)(230,440)(231,438)(232,439)
(233,437)(234,435)(235,463)(236,461)(237,468)(238,460)(239,467)(240,465)
(241,466)(242,464)(243,462)(244,454)(245,452)(246,459)(247,451)(248,458)
(249,456)(250,457)(251,455)(252,453)(253,481)(254,479)(255,486)(256,478)
(257,485)(258,483)(259,484)(260,482)(261,480)(262,472)(263,470)(264,477)
(265,469)(266,476)(267,474)(268,475)(269,473)(270,471)(271,499)(272,497)
(273,504)(274,496)(275,503)(276,501)(277,502)(278,500)(279,498)(280,490)
(281,488)(282,495)(283,487)(284,494)(285,492)(286,493)(287,491)(288,489);;
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*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,
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)( 37,401)( 38,403)( 39,399)
( 40,404)( 41,397)( 42,402)( 43,398)( 44,400)( 45,405)( 46,410)( 47,412)
( 48,408)( 49,413)( 50,406)( 51,411)( 52,407)( 53,409)( 54,414)( 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)( 73,329)( 74,331)( 75,327)( 76,332)( 77,325)( 78,330)( 79,326)
( 80,328)( 81,333)( 82,338)( 83,340)( 84,336)( 85,341)( 86,334)( 87,339)
( 88,335)( 89,337)( 90,342)( 91,347)( 92,349)( 93,345)( 94,350)( 95,343)
( 96,348)( 97,344)( 98,346)( 99,351)(100,356)(101,358)(102,354)(103,359)
(104,352)(105,357)(106,353)(107,355)(108,360)(109,293)(110,295)(111,291)
(112,296)(113,289)(114,294)(115,290)(116,292)(117,297)(118,302)(119,304)
(120,300)(121,305)(122,298)(123,303)(124,299)(125,301)(126,306)(127,311)
(128,313)(129,309)(130,314)(131,307)(132,312)(133,308)(134,310)(135,315)
(136,320)(137,322)(138,318)(139,323)(140,316)(141,321)(142,317)(143,319)
(144,324)(145,536)(146,538)(147,534)(148,539)(149,532)(150,537)(151,533)
(152,535)(153,540)(154,527)(155,529)(156,525)(157,530)(158,523)(159,528)
(160,524)(161,526)(162,531)(163,518)(164,520)(165,516)(166,521)(167,514)
(168,519)(169,515)(170,517)(171,522)(172,509)(173,511)(174,507)(175,512)
(176,505)(177,510)(178,506)(179,508)(180,513)(181,572)(182,574)(183,570)
(184,575)(185,568)(186,573)(187,569)(188,571)(189,576)(190,563)(191,565)
(192,561)(193,566)(194,559)(195,564)(196,560)(197,562)(198,567)(199,554)
(200,556)(201,552)(202,557)(203,550)(204,555)(205,551)(206,553)(207,558)
(208,545)(209,547)(210,543)(211,548)(212,541)(213,546)(214,542)(215,544)
(216,549)(217,500)(218,502)(219,498)(220,503)(221,496)(222,501)(223,497)
(224,499)(225,504)(226,491)(227,493)(228,489)(229,494)(230,487)(231,492)
(232,488)(233,490)(234,495)(235,482)(236,484)(237,480)(238,485)(239,478)
(240,483)(241,479)(242,481)(243,486)(244,473)(245,475)(246,471)(247,476)
(248,469)(249,474)(250,470)(251,472)(252,477)(253,464)(254,466)(255,462)
(256,467)(257,460)(258,465)(259,461)(260,463)(261,468)(262,455)(263,457)
(264,453)(265,458)(266,451)(267,456)(268,452)(269,454)(270,459)(271,446)
(272,448)(273,444)(274,449)(275,442)(276,447)(277,443)(278,445)(279,450)
(280,437)(281,439)(282,435)(283,440)(284,433)(285,438)(286,434)(287,436)
(288,441);
s2 := Sym(576)!( 1,217)( 2,224)( 3,222)( 4,223)( 5,221)( 6,219)( 7,220)
( 8,218)( 9,225)( 10,226)( 11,233)( 12,231)( 13,232)( 14,230)( 15,228)
( 16,229)( 17,227)( 18,234)( 19,235)( 20,242)( 21,240)( 22,241)( 23,239)
( 24,237)( 25,238)( 26,236)( 27,243)( 28,244)( 29,251)( 30,249)( 31,250)
( 32,248)( 33,246)( 34,247)( 35,245)( 36,252)( 37,253)( 38,260)( 39,258)
( 40,259)( 41,257)( 42,255)( 43,256)( 44,254)( 45,261)( 46,262)( 47,269)
( 48,267)( 49,268)( 50,266)( 51,264)( 52,265)( 53,263)( 54,270)( 55,271)
( 56,278)( 57,276)( 58,277)( 59,275)( 60,273)( 61,274)( 62,272)( 63,279)
( 64,280)( 65,287)( 66,285)( 67,286)( 68,284)( 69,282)( 70,283)( 71,281)
( 72,288)( 73,145)( 74,152)( 75,150)( 76,151)( 77,149)( 78,147)( 79,148)
( 80,146)( 81,153)( 82,154)( 83,161)( 84,159)( 85,160)( 86,158)( 87,156)
( 88,157)( 89,155)( 90,162)( 91,163)( 92,170)( 93,168)( 94,169)( 95,167)
( 96,165)( 97,166)( 98,164)( 99,171)(100,172)(101,179)(102,177)(103,178)
(104,176)(105,174)(106,175)(107,173)(108,180)(109,181)(110,188)(111,186)
(112,187)(113,185)(114,183)(115,184)(116,182)(117,189)(118,190)(119,197)
(120,195)(121,196)(122,194)(123,192)(124,193)(125,191)(126,198)(127,199)
(128,206)(129,204)(130,205)(131,203)(132,201)(133,202)(134,200)(135,207)
(136,208)(137,215)(138,213)(139,214)(140,212)(141,210)(142,211)(143,209)
(144,216)(289,505)(290,512)(291,510)(292,511)(293,509)(294,507)(295,508)
(296,506)(297,513)(298,514)(299,521)(300,519)(301,520)(302,518)(303,516)
(304,517)(305,515)(306,522)(307,523)(308,530)(309,528)(310,529)(311,527)
(312,525)(313,526)(314,524)(315,531)(316,532)(317,539)(318,537)(319,538)
(320,536)(321,534)(322,535)(323,533)(324,540)(325,541)(326,548)(327,546)
(328,547)(329,545)(330,543)(331,544)(332,542)(333,549)(334,550)(335,557)
(336,555)(337,556)(338,554)(339,552)(340,553)(341,551)(342,558)(343,559)
(344,566)(345,564)(346,565)(347,563)(348,561)(349,562)(350,560)(351,567)
(352,568)(353,575)(354,573)(355,574)(356,572)(357,570)(358,571)(359,569)
(360,576)(361,433)(362,440)(363,438)(364,439)(365,437)(366,435)(367,436)
(368,434)(369,441)(370,442)(371,449)(372,447)(373,448)(374,446)(375,444)
(376,445)(377,443)(378,450)(379,451)(380,458)(381,456)(382,457)(383,455)
(384,453)(385,454)(386,452)(387,459)(388,460)(389,467)(390,465)(391,466)
(392,464)(393,462)(394,463)(395,461)(396,468)(397,469)(398,476)(399,474)
(400,475)(401,473)(402,471)(403,472)(404,470)(405,477)(406,478)(407,485)
(408,483)(409,484)(410,482)(411,480)(412,481)(413,479)(414,486)(415,487)
(416,494)(417,492)(418,493)(419,491)(420,489)(421,490)(422,488)(423,495)
(424,496)(425,503)(426,501)(427,502)(428,500)(429,498)(430,499)(431,497)
(432,504);
s3 := Sym(576)!( 1,364)( 2,362)( 3,369)( 4,361)( 5,368)( 6,366)( 7,367)
( 8,365)( 9,363)( 10,373)( 11,371)( 12,378)( 13,370)( 14,377)( 15,375)
( 16,376)( 17,374)( 18,372)( 19,382)( 20,380)( 21,387)( 22,379)( 23,386)
( 24,384)( 25,385)( 26,383)( 27,381)( 28,391)( 29,389)( 30,396)( 31,388)
( 32,395)( 33,393)( 34,394)( 35,392)( 36,390)( 37,400)( 38,398)( 39,405)
( 40,397)( 41,404)( 42,402)( 43,403)( 44,401)( 45,399)( 46,409)( 47,407)
( 48,414)( 49,406)( 50,413)( 51,411)( 52,412)( 53,410)( 54,408)( 55,418)
( 56,416)( 57,423)( 58,415)( 59,422)( 60,420)( 61,421)( 62,419)( 63,417)
( 64,427)( 65,425)( 66,432)( 67,424)( 68,431)( 69,429)( 70,430)( 71,428)
( 72,426)( 73,292)( 74,290)( 75,297)( 76,289)( 77,296)( 78,294)( 79,295)
( 80,293)( 81,291)( 82,301)( 83,299)( 84,306)( 85,298)( 86,305)( 87,303)
( 88,304)( 89,302)( 90,300)( 91,310)( 92,308)( 93,315)( 94,307)( 95,314)
( 96,312)( 97,313)( 98,311)( 99,309)(100,319)(101,317)(102,324)(103,316)
(104,323)(105,321)(106,322)(107,320)(108,318)(109,328)(110,326)(111,333)
(112,325)(113,332)(114,330)(115,331)(116,329)(117,327)(118,337)(119,335)
(120,342)(121,334)(122,341)(123,339)(124,340)(125,338)(126,336)(127,346)
(128,344)(129,351)(130,343)(131,350)(132,348)(133,349)(134,347)(135,345)
(136,355)(137,353)(138,360)(139,352)(140,359)(141,357)(142,358)(143,356)
(144,354)(145,517)(146,515)(147,522)(148,514)(149,521)(150,519)(151,520)
(152,518)(153,516)(154,508)(155,506)(156,513)(157,505)(158,512)(159,510)
(160,511)(161,509)(162,507)(163,535)(164,533)(165,540)(166,532)(167,539)
(168,537)(169,538)(170,536)(171,534)(172,526)(173,524)(174,531)(175,523)
(176,530)(177,528)(178,529)(179,527)(180,525)(181,553)(182,551)(183,558)
(184,550)(185,557)(186,555)(187,556)(188,554)(189,552)(190,544)(191,542)
(192,549)(193,541)(194,548)(195,546)(196,547)(197,545)(198,543)(199,571)
(200,569)(201,576)(202,568)(203,575)(204,573)(205,574)(206,572)(207,570)
(208,562)(209,560)(210,567)(211,559)(212,566)(213,564)(214,565)(215,563)
(216,561)(217,445)(218,443)(219,450)(220,442)(221,449)(222,447)(223,448)
(224,446)(225,444)(226,436)(227,434)(228,441)(229,433)(230,440)(231,438)
(232,439)(233,437)(234,435)(235,463)(236,461)(237,468)(238,460)(239,467)
(240,465)(241,466)(242,464)(243,462)(244,454)(245,452)(246,459)(247,451)
(248,458)(249,456)(250,457)(251,455)(252,453)(253,481)(254,479)(255,486)
(256,478)(257,485)(258,483)(259,484)(260,482)(261,480)(262,472)(263,470)
(264,477)(265,469)(266,476)(267,474)(268,475)(269,473)(270,471)(271,499)
(272,497)(273,504)(274,496)(275,503)(276,501)(277,502)(278,500)(279,498)
(280,490)(281,488)(282,495)(283,487)(284,494)(285,492)(286,493)(287,491)
(288,489);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*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,
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