Polytope of Type {16,6,6}

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