Polytope of Type {16,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,6,6}*1152c
if this polytope has a name.
Group : SmallGroup(1152,133450)
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 : {16,6,3}*576, {8,6,6}*576c
3-fold quotients : {16,2,6}*384
4-fold quotients : {8,6,3}*288, {4,6,6}*288c
6-fold quotients : {16,2,3}*192, {8,2,6}*192
8-fold quotients : {4,6,3}*144, {2,6,6}*144b
9-fold quotients : {16,2,2}*128
12-fold quotients : {8,2,3}*96, {4,2,6}*96
16-fold quotients : {2,6,3}*72
18-fold quotients : {8,2,2}*64
24-fold quotients : {4,2,3}*48, {2,2,6}*48
36-fold quotients : {4,2,2}*32
48-fold quotients : {2,2,3}*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 := ( 1,289)( 2,294)( 3,296)( 4,292)( 5,297)( 6,290)( 7,295)( 8,291)
( 9,293)( 10,298)( 11,303)( 12,305)( 13,301)( 14,306)( 15,299)( 16,304)
( 17,300)( 18,302)( 19,316)( 20,321)( 21,323)( 22,319)( 23,324)( 24,317)
( 25,322)( 26,318)( 27,320)( 28,307)( 29,312)( 30,314)( 31,310)( 32,315)
( 33,308)( 34,313)( 35,309)( 36,311)( 37,343)( 38,348)( 39,350)( 40,346)
( 41,351)( 42,344)( 43,349)( 44,345)( 45,347)( 46,352)( 47,357)( 48,359)
( 49,355)( 50,360)( 51,353)( 52,358)( 53,354)( 54,356)( 55,325)( 56,330)
( 57,332)( 58,328)( 59,333)( 60,326)( 61,331)( 62,327)( 63,329)( 64,334)
( 65,339)( 66,341)( 67,337)( 68,342)( 69,335)( 70,340)( 71,336)( 72,338)
( 73,361)( 74,366)( 75,368)( 76,364)( 77,369)( 78,362)( 79,367)( 80,363)
( 81,365)( 82,370)( 83,375)( 84,377)( 85,373)( 86,378)( 87,371)( 88,376)
( 89,372)( 90,374)( 91,388)( 92,393)( 93,395)( 94,391)( 95,396)( 96,389)
( 97,394)( 98,390)( 99,392)(100,379)(101,384)(102,386)(103,382)(104,387)
(105,380)(106,385)(107,381)(108,383)(109,415)(110,420)(111,422)(112,418)
(113,423)(114,416)(115,421)(116,417)(117,419)(118,424)(119,429)(120,431)
(121,427)(122,432)(123,425)(124,430)(125,426)(126,428)(127,397)(128,402)
(129,404)(130,400)(131,405)(132,398)(133,403)(134,399)(135,401)(136,406)
(137,411)(138,413)(139,409)(140,414)(141,407)(142,412)(143,408)(144,410)
(145,433)(146,438)(147,440)(148,436)(149,441)(150,434)(151,439)(152,435)
(153,437)(154,442)(155,447)(156,449)(157,445)(158,450)(159,443)(160,448)
(161,444)(162,446)(163,460)(164,465)(165,467)(166,463)(167,468)(168,461)
(169,466)(170,462)(171,464)(172,451)(173,456)(174,458)(175,454)(176,459)
(177,452)(178,457)(179,453)(180,455)(181,487)(182,492)(183,494)(184,490)
(185,495)(186,488)(187,493)(188,489)(189,491)(190,496)(191,501)(192,503)
(193,499)(194,504)(195,497)(196,502)(197,498)(198,500)(199,469)(200,474)
(201,476)(202,472)(203,477)(204,470)(205,475)(206,471)(207,473)(208,478)
(209,483)(210,485)(211,481)(212,486)(213,479)(214,484)(215,480)(216,482)
(217,505)(218,510)(219,512)(220,508)(221,513)(222,506)(223,511)(224,507)
(225,509)(226,514)(227,519)(228,521)(229,517)(230,522)(231,515)(232,520)
(233,516)(234,518)(235,532)(236,537)(237,539)(238,535)(239,540)(240,533)
(241,538)(242,534)(243,536)(244,523)(245,528)(246,530)(247,526)(248,531)
(249,524)(250,529)(251,525)(252,527)(253,559)(254,564)(255,566)(256,562)
(257,567)(258,560)(259,565)(260,561)(261,563)(262,568)(263,573)(264,575)
(265,571)(266,576)(267,569)(268,574)(269,570)(270,572)(271,541)(272,546)
(273,548)(274,544)(275,549)(276,542)(277,547)(278,543)(279,545)(280,550)
(281,555)(282,557)(283,553)(284,558)(285,551)(286,556)(287,552)(288,554);;
s2 := ( 1, 74)( 2, 73)( 3, 75)( 4, 80)( 5, 79)( 6, 81)( 7, 77)( 8, 76)
( 9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)( 16, 86)
( 17, 85)( 18, 87)( 19, 92)( 20, 91)( 21, 93)( 22, 98)( 23, 97)( 24, 99)
( 25, 95)( 26, 94)( 27, 96)( 28,101)( 29,100)( 30,102)( 31,107)( 32,106)
( 33,108)( 34,104)( 35,103)( 36,105)( 37,110)( 38,109)( 39,111)( 40,116)
( 41,115)( 42,117)( 43,113)( 44,112)( 45,114)( 46,119)( 47,118)( 48,120)
( 49,125)( 50,124)( 51,126)( 52,122)( 53,121)( 54,123)( 55,128)( 56,127)
( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,137)
( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141)
(145,218)(146,217)(147,219)(148,224)(149,223)(150,225)(151,221)(152,220)
(153,222)(154,227)(155,226)(156,228)(157,233)(158,232)(159,234)(160,230)
(161,229)(162,231)(163,236)(164,235)(165,237)(166,242)(167,241)(168,243)
(169,239)(170,238)(171,240)(172,245)(173,244)(174,246)(175,251)(176,250)
(177,252)(178,248)(179,247)(180,249)(181,254)(182,253)(183,255)(184,260)
(185,259)(186,261)(187,257)(188,256)(189,258)(190,263)(191,262)(192,264)
(193,269)(194,268)(195,270)(196,266)(197,265)(198,267)(199,272)(200,271)
(201,273)(202,278)(203,277)(204,279)(205,275)(206,274)(207,276)(208,281)
(209,280)(210,282)(211,287)(212,286)(213,288)(214,284)(215,283)(216,285)
(289,362)(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)(296,364)
(297,366)(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)(304,374)
(305,373)(306,375)(307,380)(308,379)(309,381)(310,386)(311,385)(312,387)
(313,383)(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)(320,394)
(321,396)(322,392)(323,391)(324,393)(325,398)(326,397)(327,399)(328,404)
(329,403)(330,405)(331,401)(332,400)(333,402)(334,407)(335,406)(336,408)
(337,413)(338,412)(339,414)(340,410)(341,409)(342,411)(343,416)(344,415)
(345,417)(346,422)(347,421)(348,423)(349,419)(350,418)(351,420)(352,425)
(353,424)(354,426)(355,431)(356,430)(357,432)(358,428)(359,427)(360,429)
(433,506)(434,505)(435,507)(436,512)(437,511)(438,513)(439,509)(440,508)
(441,510)(442,515)(443,514)(444,516)(445,521)(446,520)(447,522)(448,518)
(449,517)(450,519)(451,524)(452,523)(453,525)(454,530)(455,529)(456,531)
(457,527)(458,526)(459,528)(460,533)(461,532)(462,534)(463,539)(464,538)
(465,540)(466,536)(467,535)(468,537)(469,542)(470,541)(471,543)(472,548)
(473,547)(474,549)(475,545)(476,544)(477,546)(478,551)(479,550)(480,552)
(481,557)(482,556)(483,558)(484,554)(485,553)(486,555)(487,560)(488,559)
(489,561)(490,566)(491,565)(492,567)(493,563)(494,562)(495,564)(496,569)
(497,568)(498,570)(499,575)(500,574)(501,576)(502,572)(503,571)(504,573);;
s3 := ( 1,217)( 2,219)( 3,218)( 4,223)( 5,225)( 6,224)( 7,220)( 8,222)
( 9,221)( 10,226)( 11,228)( 12,227)( 13,232)( 14,234)( 15,233)( 16,229)
( 17,231)( 18,230)( 19,235)( 20,237)( 21,236)( 22,241)( 23,243)( 24,242)
( 25,238)( 26,240)( 27,239)( 28,244)( 29,246)( 30,245)( 31,250)( 32,252)
( 33,251)( 34,247)( 35,249)( 36,248)( 37,253)( 38,255)( 39,254)( 40,259)
( 41,261)( 42,260)( 43,256)( 44,258)( 45,257)( 46,262)( 47,264)( 48,263)
( 49,268)( 50,270)( 51,269)( 52,265)( 53,267)( 54,266)( 55,271)( 56,273)
( 57,272)( 58,277)( 59,279)( 60,278)( 61,274)( 62,276)( 63,275)( 64,280)
( 65,282)( 66,281)( 67,286)( 68,288)( 69,287)( 70,283)( 71,285)( 72,284)
( 73,145)( 74,147)( 75,146)( 76,151)( 77,153)( 78,152)( 79,148)( 80,150)
( 81,149)( 82,154)( 83,156)( 84,155)( 85,160)( 86,162)( 87,161)( 88,157)
( 89,159)( 90,158)( 91,163)( 92,165)( 93,164)( 94,169)( 95,171)( 96,170)
( 97,166)( 98,168)( 99,167)(100,172)(101,174)(102,173)(103,178)(104,180)
(105,179)(106,175)(107,177)(108,176)(109,181)(110,183)(111,182)(112,187)
(113,189)(114,188)(115,184)(116,186)(117,185)(118,190)(119,192)(120,191)
(121,196)(122,198)(123,197)(124,193)(125,195)(126,194)(127,199)(128,201)
(129,200)(130,205)(131,207)(132,206)(133,202)(134,204)(135,203)(136,208)
(137,210)(138,209)(139,214)(140,216)(141,215)(142,211)(143,213)(144,212)
(289,505)(290,507)(291,506)(292,511)(293,513)(294,512)(295,508)(296,510)
(297,509)(298,514)(299,516)(300,515)(301,520)(302,522)(303,521)(304,517)
(305,519)(306,518)(307,523)(308,525)(309,524)(310,529)(311,531)(312,530)
(313,526)(314,528)(315,527)(316,532)(317,534)(318,533)(319,538)(320,540)
(321,539)(322,535)(323,537)(324,536)(325,541)(326,543)(327,542)(328,547)
(329,549)(330,548)(331,544)(332,546)(333,545)(334,550)(335,552)(336,551)
(337,556)(338,558)(339,557)(340,553)(341,555)(342,554)(343,559)(344,561)
(345,560)(346,565)(347,567)(348,566)(349,562)(350,564)(351,563)(352,568)
(353,570)(354,569)(355,574)(356,576)(357,575)(358,571)(359,573)(360,572)
(361,433)(362,435)(363,434)(364,439)(365,441)(366,440)(367,436)(368,438)
(369,437)(370,442)(371,444)(372,443)(373,448)(374,450)(375,449)(376,445)
(377,447)(378,446)(379,451)(380,453)(381,452)(382,457)(383,459)(384,458)
(385,454)(386,456)(387,455)(388,460)(389,462)(390,461)(391,466)(392,468)
(393,467)(394,463)(395,465)(396,464)(397,469)(398,471)(399,470)(400,475)
(401,477)(402,476)(403,472)(404,474)(405,473)(406,478)(407,480)(408,479)
(409,484)(410,486)(411,485)(412,481)(413,483)(414,482)(415,487)(416,489)
(417,488)(418,493)(419,495)(420,494)(421,490)(422,492)(423,491)(424,496)
(425,498)(426,497)(427,502)(428,504)(429,503)(430,499)(431,501)(432,500);;
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*s1*s2*s3*s1*s2*s1*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)!( 1,289)( 2,294)( 3,296)( 4,292)( 5,297)( 6,290)( 7,295)
( 8,291)( 9,293)( 10,298)( 11,303)( 12,305)( 13,301)( 14,306)( 15,299)
( 16,304)( 17,300)( 18,302)( 19,316)( 20,321)( 21,323)( 22,319)( 23,324)
( 24,317)( 25,322)( 26,318)( 27,320)( 28,307)( 29,312)( 30,314)( 31,310)
( 32,315)( 33,308)( 34,313)( 35,309)( 36,311)( 37,343)( 38,348)( 39,350)
( 40,346)( 41,351)( 42,344)( 43,349)( 44,345)( 45,347)( 46,352)( 47,357)
( 48,359)( 49,355)( 50,360)( 51,353)( 52,358)( 53,354)( 54,356)( 55,325)
( 56,330)( 57,332)( 58,328)( 59,333)( 60,326)( 61,331)( 62,327)( 63,329)
( 64,334)( 65,339)( 66,341)( 67,337)( 68,342)( 69,335)( 70,340)( 71,336)
( 72,338)( 73,361)( 74,366)( 75,368)( 76,364)( 77,369)( 78,362)( 79,367)
( 80,363)( 81,365)( 82,370)( 83,375)( 84,377)( 85,373)( 86,378)( 87,371)
( 88,376)( 89,372)( 90,374)( 91,388)( 92,393)( 93,395)( 94,391)( 95,396)
( 96,389)( 97,394)( 98,390)( 99,392)(100,379)(101,384)(102,386)(103,382)
(104,387)(105,380)(106,385)(107,381)(108,383)(109,415)(110,420)(111,422)
(112,418)(113,423)(114,416)(115,421)(116,417)(117,419)(118,424)(119,429)
(120,431)(121,427)(122,432)(123,425)(124,430)(125,426)(126,428)(127,397)
(128,402)(129,404)(130,400)(131,405)(132,398)(133,403)(134,399)(135,401)
(136,406)(137,411)(138,413)(139,409)(140,414)(141,407)(142,412)(143,408)
(144,410)(145,433)(146,438)(147,440)(148,436)(149,441)(150,434)(151,439)
(152,435)(153,437)(154,442)(155,447)(156,449)(157,445)(158,450)(159,443)
(160,448)(161,444)(162,446)(163,460)(164,465)(165,467)(166,463)(167,468)
(168,461)(169,466)(170,462)(171,464)(172,451)(173,456)(174,458)(175,454)
(176,459)(177,452)(178,457)(179,453)(180,455)(181,487)(182,492)(183,494)
(184,490)(185,495)(186,488)(187,493)(188,489)(189,491)(190,496)(191,501)
(192,503)(193,499)(194,504)(195,497)(196,502)(197,498)(198,500)(199,469)
(200,474)(201,476)(202,472)(203,477)(204,470)(205,475)(206,471)(207,473)
(208,478)(209,483)(210,485)(211,481)(212,486)(213,479)(214,484)(215,480)
(216,482)(217,505)(218,510)(219,512)(220,508)(221,513)(222,506)(223,511)
(224,507)(225,509)(226,514)(227,519)(228,521)(229,517)(230,522)(231,515)
(232,520)(233,516)(234,518)(235,532)(236,537)(237,539)(238,535)(239,540)
(240,533)(241,538)(242,534)(243,536)(244,523)(245,528)(246,530)(247,526)
(248,531)(249,524)(250,529)(251,525)(252,527)(253,559)(254,564)(255,566)
(256,562)(257,567)(258,560)(259,565)(260,561)(261,563)(262,568)(263,573)
(264,575)(265,571)(266,576)(267,569)(268,574)(269,570)(270,572)(271,541)
(272,546)(273,548)(274,544)(275,549)(276,542)(277,547)(278,543)(279,545)
(280,550)(281,555)(282,557)(283,553)(284,558)(285,551)(286,556)(287,552)
(288,554);
s2 := Sym(576)!( 1, 74)( 2, 73)( 3, 75)( 4, 80)( 5, 79)( 6, 81)( 7, 77)
( 8, 76)( 9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)
( 16, 86)( 17, 85)( 18, 87)( 19, 92)( 20, 91)( 21, 93)( 22, 98)( 23, 97)
( 24, 99)( 25, 95)( 26, 94)( 27, 96)( 28,101)( 29,100)( 30,102)( 31,107)
( 32,106)( 33,108)( 34,104)( 35,103)( 36,105)( 37,110)( 38,109)( 39,111)
( 40,116)( 41,115)( 42,117)( 43,113)( 44,112)( 45,114)( 46,119)( 47,118)
( 48,120)( 49,125)( 50,124)( 51,126)( 52,122)( 53,121)( 54,123)( 55,128)
( 56,127)( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)
( 64,137)( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)
( 72,141)(145,218)(146,217)(147,219)(148,224)(149,223)(150,225)(151,221)
(152,220)(153,222)(154,227)(155,226)(156,228)(157,233)(158,232)(159,234)
(160,230)(161,229)(162,231)(163,236)(164,235)(165,237)(166,242)(167,241)
(168,243)(169,239)(170,238)(171,240)(172,245)(173,244)(174,246)(175,251)
(176,250)(177,252)(178,248)(179,247)(180,249)(181,254)(182,253)(183,255)
(184,260)(185,259)(186,261)(187,257)(188,256)(189,258)(190,263)(191,262)
(192,264)(193,269)(194,268)(195,270)(196,266)(197,265)(198,267)(199,272)
(200,271)(201,273)(202,278)(203,277)(204,279)(205,275)(206,274)(207,276)
(208,281)(209,280)(210,282)(211,287)(212,286)(213,288)(214,284)(215,283)
(216,285)(289,362)(290,361)(291,363)(292,368)(293,367)(294,369)(295,365)
(296,364)(297,366)(298,371)(299,370)(300,372)(301,377)(302,376)(303,378)
(304,374)(305,373)(306,375)(307,380)(308,379)(309,381)(310,386)(311,385)
(312,387)(313,383)(314,382)(315,384)(316,389)(317,388)(318,390)(319,395)
(320,394)(321,396)(322,392)(323,391)(324,393)(325,398)(326,397)(327,399)
(328,404)(329,403)(330,405)(331,401)(332,400)(333,402)(334,407)(335,406)
(336,408)(337,413)(338,412)(339,414)(340,410)(341,409)(342,411)(343,416)
(344,415)(345,417)(346,422)(347,421)(348,423)(349,419)(350,418)(351,420)
(352,425)(353,424)(354,426)(355,431)(356,430)(357,432)(358,428)(359,427)
(360,429)(433,506)(434,505)(435,507)(436,512)(437,511)(438,513)(439,509)
(440,508)(441,510)(442,515)(443,514)(444,516)(445,521)(446,520)(447,522)
(448,518)(449,517)(450,519)(451,524)(452,523)(453,525)(454,530)(455,529)
(456,531)(457,527)(458,526)(459,528)(460,533)(461,532)(462,534)(463,539)
(464,538)(465,540)(466,536)(467,535)(468,537)(469,542)(470,541)(471,543)
(472,548)(473,547)(474,549)(475,545)(476,544)(477,546)(478,551)(479,550)
(480,552)(481,557)(482,556)(483,558)(484,554)(485,553)(486,555)(487,560)
(488,559)(489,561)(490,566)(491,565)(492,567)(493,563)(494,562)(495,564)
(496,569)(497,568)(498,570)(499,575)(500,574)(501,576)(502,572)(503,571)
(504,573);
s3 := Sym(576)!( 1,217)( 2,219)( 3,218)( 4,223)( 5,225)( 6,224)( 7,220)
( 8,222)( 9,221)( 10,226)( 11,228)( 12,227)( 13,232)( 14,234)( 15,233)
( 16,229)( 17,231)( 18,230)( 19,235)( 20,237)( 21,236)( 22,241)( 23,243)
( 24,242)( 25,238)( 26,240)( 27,239)( 28,244)( 29,246)( 30,245)( 31,250)
( 32,252)( 33,251)( 34,247)( 35,249)( 36,248)( 37,253)( 38,255)( 39,254)
( 40,259)( 41,261)( 42,260)( 43,256)( 44,258)( 45,257)( 46,262)( 47,264)
( 48,263)( 49,268)( 50,270)( 51,269)( 52,265)( 53,267)( 54,266)( 55,271)
( 56,273)( 57,272)( 58,277)( 59,279)( 60,278)( 61,274)( 62,276)( 63,275)
( 64,280)( 65,282)( 66,281)( 67,286)( 68,288)( 69,287)( 70,283)( 71,285)
( 72,284)( 73,145)( 74,147)( 75,146)( 76,151)( 77,153)( 78,152)( 79,148)
( 80,150)( 81,149)( 82,154)( 83,156)( 84,155)( 85,160)( 86,162)( 87,161)
( 88,157)( 89,159)( 90,158)( 91,163)( 92,165)( 93,164)( 94,169)( 95,171)
( 96,170)( 97,166)( 98,168)( 99,167)(100,172)(101,174)(102,173)(103,178)
(104,180)(105,179)(106,175)(107,177)(108,176)(109,181)(110,183)(111,182)
(112,187)(113,189)(114,188)(115,184)(116,186)(117,185)(118,190)(119,192)
(120,191)(121,196)(122,198)(123,197)(124,193)(125,195)(126,194)(127,199)
(128,201)(129,200)(130,205)(131,207)(132,206)(133,202)(134,204)(135,203)
(136,208)(137,210)(138,209)(139,214)(140,216)(141,215)(142,211)(143,213)
(144,212)(289,505)(290,507)(291,506)(292,511)(293,513)(294,512)(295,508)
(296,510)(297,509)(298,514)(299,516)(300,515)(301,520)(302,522)(303,521)
(304,517)(305,519)(306,518)(307,523)(308,525)(309,524)(310,529)(311,531)
(312,530)(313,526)(314,528)(315,527)(316,532)(317,534)(318,533)(319,538)
(320,540)(321,539)(322,535)(323,537)(324,536)(325,541)(326,543)(327,542)
(328,547)(329,549)(330,548)(331,544)(332,546)(333,545)(334,550)(335,552)
(336,551)(337,556)(338,558)(339,557)(340,553)(341,555)(342,554)(343,559)
(344,561)(345,560)(346,565)(347,567)(348,566)(349,562)(350,564)(351,563)
(352,568)(353,570)(354,569)(355,574)(356,576)(357,575)(358,571)(359,573)
(360,572)(361,433)(362,435)(363,434)(364,439)(365,441)(366,440)(367,436)
(368,438)(369,437)(370,442)(371,444)(372,443)(373,448)(374,450)(375,449)
(376,445)(377,447)(378,446)(379,451)(380,453)(381,452)(382,457)(383,459)
(384,458)(385,454)(386,456)(387,455)(388,460)(389,462)(390,461)(391,466)
(392,468)(393,467)(394,463)(395,465)(396,464)(397,469)(398,471)(399,470)
(400,475)(401,477)(402,476)(403,472)(404,474)(405,473)(406,478)(407,480)
(408,479)(409,484)(410,486)(411,485)(412,481)(413,483)(414,482)(415,487)
(416,489)(417,488)(418,493)(419,495)(420,494)(421,490)(422,492)(423,491)
(424,496)(425,498)(426,497)(427,502)(428,504)(429,503)(430,499)(431,501)
(432,500);
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*s1*s2*s3*s1*s2*s1*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