Polytope of Type {16,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,6,6}*1152a
Also Known As : {{16,6|2},{6,6|2}}. if this polytope has another name.
Group : SmallGroup(1152,133448)
Rank : 4
Schlafli Type : {16,6,6}
Number of vertices, edges, etc : 16, 48, 18, 6
Order of s0s1s2s3 : 48
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 : {8,6,6}*576a
3-fold quotients : {16,2,6}*384, {16,6,2}*384
4-fold quotients : {4,6,6}*288a
6-fold quotients : {16,2,3}*192, {8,2,6}*192, {8,6,2}*192
8-fold quotients : {2,6,6}*144a
9-fold quotients : {16,2,2}*128
12-fold quotients : {8,2,3}*96, {4,2,6}*96, {4,6,2}*96a
18-fold quotients : {8,2,2}*64
24-fold quotients : {4,2,3}*48, {2,2,6}*48, {2,6,2}*48
36-fold quotients : {4,2,2}*32
48-fold quotients : {2,2,3}*24, {2,3,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 19, 28)( 20, 29)( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)( 26, 35)
( 27, 36)( 37, 55)( 38, 56)( 39, 57)( 40, 58)( 41, 59)( 42, 60)( 43, 61)
( 44, 62)( 45, 63)( 46, 64)( 47, 65)( 48, 66)( 49, 67)( 50, 68)( 51, 69)
( 52, 70)( 53, 71)( 54, 72)( 91,100)( 92,101)( 93,102)( 94,103)( 95,104)
( 96,105)( 97,106)( 98,107)( 99,108)(109,127)(110,128)(111,129)(112,130)
(113,131)(114,132)(115,133)(116,134)(117,135)(118,136)(119,137)(120,138)
(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(163,172)(164,173)
(165,174)(166,175)(167,176)(168,177)(169,178)(170,179)(171,180)(181,199)
(182,200)(183,201)(184,202)(185,203)(186,204)(187,205)(188,206)(189,207)
(190,208)(191,209)(192,210)(193,211)(194,212)(195,213)(196,214)(197,215)
(198,216)(235,244)(236,245)(237,246)(238,247)(239,248)(240,249)(241,250)
(242,251)(243,252)(253,271)(254,272)(255,273)(256,274)(257,275)(258,276)
(259,277)(260,278)(261,279)(262,280)(263,281)(264,282)(265,283)(266,284)
(267,285)(268,286)(269,287)(270,288)(289,325)(290,326)(291,327)(292,328)
(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)(300,336)
(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,352)(308,353)
(309,354)(310,355)(311,356)(312,357)(313,358)(314,359)(315,360)(316,343)
(317,344)(318,345)(319,346)(320,347)(321,348)(322,349)(323,350)(324,351)
(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)(368,404)
(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)(376,412)
(377,413)(378,414)(379,424)(380,425)(381,426)(382,427)(383,428)(384,429)
(385,430)(386,431)(387,432)(388,415)(389,416)(390,417)(391,418)(392,419)
(393,420)(394,421)(395,422)(396,423)(433,469)(434,470)(435,471)(436,472)
(437,473)(438,474)(439,475)(440,476)(441,477)(442,478)(443,479)(444,480)
(445,481)(446,482)(447,483)(448,484)(449,485)(450,486)(451,496)(452,497)
(453,498)(454,499)(455,500)(456,501)(457,502)(458,503)(459,504)(460,487)
(461,488)(462,489)(463,490)(464,491)(465,492)(466,493)(467,494)(468,495)
(505,541)(506,542)(507,543)(508,544)(509,545)(510,546)(511,547)(512,548)
(513,549)(514,550)(515,551)(516,552)(517,553)(518,554)(519,555)(520,556)
(521,557)(522,558)(523,568)(524,569)(525,570)(526,571)(527,572)(528,573)
(529,574)(530,575)(531,576)(532,559)(533,560)(534,561)(535,562)(536,563)
(537,564)(538,565)(539,566)(540,567);;
s1 := ( 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)( 19,388)( 20,393)( 21,395)( 22,391)( 23,396)( 24,389)
( 25,394)( 26,390)( 27,392)( 28,379)( 29,384)( 30,386)( 31,382)( 32,387)
( 33,380)( 34,385)( 35,381)( 36,383)( 37,415)( 38,420)( 39,422)( 40,418)
( 41,423)( 42,416)( 43,421)( 44,417)( 45,419)( 46,424)( 47,429)( 48,431)
( 49,427)( 50,432)( 51,425)( 52,430)( 53,426)( 54,428)( 55,397)( 56,402)
( 57,404)( 58,400)( 59,405)( 60,398)( 61,403)( 62,399)( 63,401)( 64,406)
( 65,411)( 66,413)( 67,409)( 68,414)( 69,407)( 70,412)( 71,408)( 72,410)
( 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)( 91,316)( 92,321)( 93,323)( 94,319)( 95,324)( 96,317)
( 97,322)( 98,318)( 99,320)(100,307)(101,312)(102,314)(103,310)(104,315)
(105,308)(106,313)(107,309)(108,311)(109,343)(110,348)(111,350)(112,346)
(113,351)(114,344)(115,349)(116,345)(117,347)(118,352)(119,357)(120,359)
(121,355)(122,360)(123,353)(124,358)(125,354)(126,356)(127,325)(128,330)
(129,332)(130,328)(131,333)(132,326)(133,331)(134,327)(135,329)(136,334)
(137,339)(138,341)(139,337)(140,342)(141,335)(142,340)(143,336)(144,338)
(145,505)(146,510)(147,512)(148,508)(149,513)(150,506)(151,511)(152,507)
(153,509)(154,514)(155,519)(156,521)(157,517)(158,522)(159,515)(160,520)
(161,516)(162,518)(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)(181,559)(182,564)(183,566)(184,562)
(185,567)(186,560)(187,565)(188,561)(189,563)(190,568)(191,573)(192,575)
(193,571)(194,576)(195,569)(196,574)(197,570)(198,572)(199,541)(200,546)
(201,548)(202,544)(203,549)(204,542)(205,547)(206,543)(207,545)(208,550)
(209,555)(210,557)(211,553)(212,558)(213,551)(214,556)(215,552)(216,554)
(217,433)(218,438)(219,440)(220,436)(221,441)(222,434)(223,439)(224,435)
(225,437)(226,442)(227,447)(228,449)(229,445)(230,450)(231,443)(232,448)
(233,444)(234,446)(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)(253,487)(254,492)(255,494)(256,490)
(257,495)(258,488)(259,493)(260,489)(261,491)(262,496)(263,501)(264,503)
(265,499)(266,504)(267,497)(268,502)(269,498)(270,500)(271,469)(272,474)
(273,476)(274,472)(275,477)(276,470)(277,475)(278,471)(279,473)(280,478)
(281,483)(282,485)(283,481)(284,486)(285,479)(286,484)(287,480)(288,482);;
s2 := ( 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);;
s3 := ( 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);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 19, 28)( 20, 29)( 21, 30)( 22, 31)( 23, 32)( 24, 33)( 25, 34)
( 26, 35)( 27, 36)( 37, 55)( 38, 56)( 39, 57)( 40, 58)( 41, 59)( 42, 60)
( 43, 61)( 44, 62)( 45, 63)( 46, 64)( 47, 65)( 48, 66)( 49, 67)( 50, 68)
( 51, 69)( 52, 70)( 53, 71)( 54, 72)( 91,100)( 92,101)( 93,102)( 94,103)
( 95,104)( 96,105)( 97,106)( 98,107)( 99,108)(109,127)(110,128)(111,129)
(112,130)(113,131)(114,132)(115,133)(116,134)(117,135)(118,136)(119,137)
(120,138)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(163,172)
(164,173)(165,174)(166,175)(167,176)(168,177)(169,178)(170,179)(171,180)
(181,199)(182,200)(183,201)(184,202)(185,203)(186,204)(187,205)(188,206)
(189,207)(190,208)(191,209)(192,210)(193,211)(194,212)(195,213)(196,214)
(197,215)(198,216)(235,244)(236,245)(237,246)(238,247)(239,248)(240,249)
(241,250)(242,251)(243,252)(253,271)(254,272)(255,273)(256,274)(257,275)
(258,276)(259,277)(260,278)(261,279)(262,280)(263,281)(264,282)(265,283)
(266,284)(267,285)(268,286)(269,287)(270,288)(289,325)(290,326)(291,327)
(292,328)(293,329)(294,330)(295,331)(296,332)(297,333)(298,334)(299,335)
(300,336)(301,337)(302,338)(303,339)(304,340)(305,341)(306,342)(307,352)
(308,353)(309,354)(310,355)(311,356)(312,357)(313,358)(314,359)(315,360)
(316,343)(317,344)(318,345)(319,346)(320,347)(321,348)(322,349)(323,350)
(324,351)(361,397)(362,398)(363,399)(364,400)(365,401)(366,402)(367,403)
(368,404)(369,405)(370,406)(371,407)(372,408)(373,409)(374,410)(375,411)
(376,412)(377,413)(378,414)(379,424)(380,425)(381,426)(382,427)(383,428)
(384,429)(385,430)(386,431)(387,432)(388,415)(389,416)(390,417)(391,418)
(392,419)(393,420)(394,421)(395,422)(396,423)(433,469)(434,470)(435,471)
(436,472)(437,473)(438,474)(439,475)(440,476)(441,477)(442,478)(443,479)
(444,480)(445,481)(446,482)(447,483)(448,484)(449,485)(450,486)(451,496)
(452,497)(453,498)(454,499)(455,500)(456,501)(457,502)(458,503)(459,504)
(460,487)(461,488)(462,489)(463,490)(464,491)(465,492)(466,493)(467,494)
(468,495)(505,541)(506,542)(507,543)(508,544)(509,545)(510,546)(511,547)
(512,548)(513,549)(514,550)(515,551)(516,552)(517,553)(518,554)(519,555)
(520,556)(521,557)(522,558)(523,568)(524,569)(525,570)(526,571)(527,572)
(528,573)(529,574)(530,575)(531,576)(532,559)(533,560)(534,561)(535,562)
(536,563)(537,564)(538,565)(539,566)(540,567);
s1 := 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)( 19,388)( 20,393)( 21,395)( 22,391)( 23,396)
( 24,389)( 25,394)( 26,390)( 27,392)( 28,379)( 29,384)( 30,386)( 31,382)
( 32,387)( 33,380)( 34,385)( 35,381)( 36,383)( 37,415)( 38,420)( 39,422)
( 40,418)( 41,423)( 42,416)( 43,421)( 44,417)( 45,419)( 46,424)( 47,429)
( 48,431)( 49,427)( 50,432)( 51,425)( 52,430)( 53,426)( 54,428)( 55,397)
( 56,402)( 57,404)( 58,400)( 59,405)( 60,398)( 61,403)( 62,399)( 63,401)
( 64,406)( 65,411)( 66,413)( 67,409)( 68,414)( 69,407)( 70,412)( 71,408)
( 72,410)( 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)( 91,316)( 92,321)( 93,323)( 94,319)( 95,324)
( 96,317)( 97,322)( 98,318)( 99,320)(100,307)(101,312)(102,314)(103,310)
(104,315)(105,308)(106,313)(107,309)(108,311)(109,343)(110,348)(111,350)
(112,346)(113,351)(114,344)(115,349)(116,345)(117,347)(118,352)(119,357)
(120,359)(121,355)(122,360)(123,353)(124,358)(125,354)(126,356)(127,325)
(128,330)(129,332)(130,328)(131,333)(132,326)(133,331)(134,327)(135,329)
(136,334)(137,339)(138,341)(139,337)(140,342)(141,335)(142,340)(143,336)
(144,338)(145,505)(146,510)(147,512)(148,508)(149,513)(150,506)(151,511)
(152,507)(153,509)(154,514)(155,519)(156,521)(157,517)(158,522)(159,515)
(160,520)(161,516)(162,518)(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)(181,559)(182,564)(183,566)
(184,562)(185,567)(186,560)(187,565)(188,561)(189,563)(190,568)(191,573)
(192,575)(193,571)(194,576)(195,569)(196,574)(197,570)(198,572)(199,541)
(200,546)(201,548)(202,544)(203,549)(204,542)(205,547)(206,543)(207,545)
(208,550)(209,555)(210,557)(211,553)(212,558)(213,551)(214,556)(215,552)
(216,554)(217,433)(218,438)(219,440)(220,436)(221,441)(222,434)(223,439)
(224,435)(225,437)(226,442)(227,447)(228,449)(229,445)(230,450)(231,443)
(232,448)(233,444)(234,446)(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)(253,487)(254,492)(255,494)
(256,490)(257,495)(258,488)(259,493)(260,489)(261,491)(262,496)(263,501)
(264,503)(265,499)(266,504)(267,497)(268,502)(269,498)(270,500)(271,469)
(272,474)(273,476)(274,472)(275,477)(276,470)(277,475)(278,471)(279,473)
(280,478)(281,483)(282,485)(283,481)(284,486)(285,479)(286,484)(287,480)
(288,482);
s2 := 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);
s3 := 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);
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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*s0*s1*s0*s1 >;
References : None.
to this polytope