Polytope of Type {6,6,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,16}*1152b
Also Known As : {{6,6|2},{6,16|2}}. if this polytope has another name.
Group : SmallGroup(1152,133448)
Rank : 4
Schlafli Type : {6,6,16}
Number of vertices, edges, etc : 6, 18, 48, 16
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 : {6,6,8}*576a
3-fold quotients : {2,6,16}*384, {6,2,16}*384
4-fold quotients : {6,6,4}*288a
6-fold quotients : {3,2,16}*192, {2,6,8}*192, {6,2,8}*192
8-fold quotients : {6,6,2}*144a
9-fold quotients : {2,2,16}*128
12-fold quotients : {3,2,8}*96, {2,6,4}*96a, {6,2,4}*96
18-fold quotients : {2,2,8}*64
24-fold quotients : {3,2,4}*48, {2,6,2}*48, {6,2,2}*48
36-fold quotients : {2,2,4}*32
48-fold quotients : {2,3,2}*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 := ( 1,146)( 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 := ( 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)( 19,244)( 20,251)( 21,249)( 22,250)( 23,248)( 24,246)
( 25,247)( 26,245)( 27,252)( 28,235)( 29,242)( 30,240)( 31,241)( 32,239)
( 33,237)( 34,238)( 35,236)( 36,243)( 37,271)( 38,278)( 39,276)( 40,277)
( 41,275)( 42,273)( 43,274)( 44,272)( 45,279)( 46,280)( 47,287)( 48,285)
( 49,286)( 50,284)( 51,282)( 52,283)( 53,281)( 54,288)( 55,253)( 56,260)
( 57,258)( 58,259)( 59,257)( 60,255)( 61,256)( 62,254)( 63,261)( 64,262)
( 65,269)( 66,267)( 67,268)( 68,266)( 69,264)( 70,265)( 71,263)( 72,270)
( 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)( 91,172)( 92,179)( 93,177)( 94,178)( 95,176)( 96,174)
( 97,175)( 98,173)( 99,180)(100,163)(101,170)(102,168)(103,169)(104,167)
(105,165)(106,166)(107,164)(108,171)(109,199)(110,206)(111,204)(112,205)
(113,203)(114,201)(115,202)(116,200)(117,207)(118,208)(119,215)(120,213)
(121,214)(122,212)(123,210)(124,211)(125,209)(126,216)(127,181)(128,188)
(129,186)(130,187)(131,185)(132,183)(133,184)(134,182)(135,189)(136,190)
(137,197)(138,195)(139,196)(140,194)(141,192)(142,193)(143,191)(144,198)
(289,541)(290,548)(291,546)(292,547)(293,545)(294,543)(295,544)(296,542)
(297,549)(298,550)(299,557)(300,555)(301,556)(302,554)(303,552)(304,553)
(305,551)(306,558)(307,568)(308,575)(309,573)(310,574)(311,572)(312,570)
(313,571)(314,569)(315,576)(316,559)(317,566)(318,564)(319,565)(320,563)
(321,561)(322,562)(323,560)(324,567)(325,505)(326,512)(327,510)(328,511)
(329,509)(330,507)(331,508)(332,506)(333,513)(334,514)(335,521)(336,519)
(337,520)(338,518)(339,516)(340,517)(341,515)(342,522)(343,532)(344,539)
(345,537)(346,538)(347,536)(348,534)(349,535)(350,533)(351,540)(352,523)
(353,530)(354,528)(355,529)(356,527)(357,525)(358,526)(359,524)(360,531)
(361,469)(362,476)(363,474)(364,475)(365,473)(366,471)(367,472)(368,470)
(369,477)(370,478)(371,485)(372,483)(373,484)(374,482)(375,480)(376,481)
(377,479)(378,486)(379,496)(380,503)(381,501)(382,502)(383,500)(384,498)
(385,499)(386,497)(387,504)(388,487)(389,494)(390,492)(391,493)(392,491)
(393,489)(394,490)(395,488)(396,495)(397,433)(398,440)(399,438)(400,439)
(401,437)(402,435)(403,436)(404,434)(405,441)(406,442)(407,449)(408,447)
(409,448)(410,446)(411,444)(412,445)(413,443)(414,450)(415,460)(416,467)
(417,465)(418,466)(419,464)(420,462)(421,463)(422,461)(423,468)(424,451)
(425,458)(426,456)(427,457)(428,455)(429,453)(430,454)(431,452)(432,459);;
s3 := ( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)( 8,296)
( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)
( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)( 24,321)
( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)( 32,311)
( 33,312)( 34,313)( 35,314)( 36,315)( 37,343)( 38,344)( 39,345)( 40,346)
( 41,347)( 42,348)( 43,349)( 44,350)( 45,351)( 46,352)( 47,353)( 48,354)
( 49,355)( 50,356)( 51,357)( 52,358)( 53,359)( 54,360)( 55,325)( 56,326)
( 57,327)( 58,328)( 59,329)( 60,330)( 61,331)( 62,332)( 63,333)( 64,334)
( 65,335)( 66,336)( 67,337)( 68,338)( 69,339)( 70,340)( 71,341)( 72,342)
( 73,361)( 74,362)( 75,363)( 76,364)( 77,365)( 78,366)( 79,367)( 80,368)
( 81,369)( 82,370)( 83,371)( 84,372)( 85,373)( 86,374)( 87,375)( 88,376)
( 89,377)( 90,378)( 91,388)( 92,389)( 93,390)( 94,391)( 95,392)( 96,393)
( 97,394)( 98,395)( 99,396)(100,379)(101,380)(102,381)(103,382)(104,383)
(105,384)(106,385)(107,386)(108,387)(109,415)(110,416)(111,417)(112,418)
(113,419)(114,420)(115,421)(116,422)(117,423)(118,424)(119,425)(120,426)
(121,427)(122,428)(123,429)(124,430)(125,431)(126,432)(127,397)(128,398)
(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)(136,406)
(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)(144,414)
(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)
(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)
(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)(168,465)
(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)(176,455)
(177,456)(178,457)(179,458)(180,459)(181,487)(182,488)(183,489)(184,490)
(185,491)(186,492)(187,493)(188,494)(189,495)(190,496)(191,497)(192,498)
(193,499)(194,500)(195,501)(196,502)(197,503)(198,504)(199,469)(200,470)
(201,471)(202,472)(203,473)(204,474)(205,475)(206,476)(207,477)(208,478)
(209,479)(210,480)(211,481)(212,482)(213,483)(214,484)(215,485)(216,486)
(217,505)(218,506)(219,507)(220,508)(221,509)(222,510)(223,511)(224,512)
(225,513)(226,514)(227,515)(228,516)(229,517)(230,518)(231,519)(232,520)
(233,521)(234,522)(235,532)(236,533)(237,534)(238,535)(239,536)(240,537)
(241,538)(242,539)(243,540)(244,523)(245,524)(246,525)(247,526)(248,527)
(249,528)(250,529)(251,530)(252,531)(253,559)(254,560)(255,561)(256,562)
(257,563)(258,564)(259,565)(260,566)(261,567)(262,568)(263,569)(264,570)
(265,571)(266,572)(267,573)(268,574)(269,575)(270,576)(271,541)(272,542)
(273,543)(274,544)(275,545)(276,546)(277,547)(278,548)(279,549)(280,550)
(281,551)(282,552)(283,553)(284,554)(285,555)(286,556)(287,557)(288,558);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*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)!( 1,146)( 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)!( 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)( 19,244)( 20,251)( 21,249)( 22,250)( 23,248)
( 24,246)( 25,247)( 26,245)( 27,252)( 28,235)( 29,242)( 30,240)( 31,241)
( 32,239)( 33,237)( 34,238)( 35,236)( 36,243)( 37,271)( 38,278)( 39,276)
( 40,277)( 41,275)( 42,273)( 43,274)( 44,272)( 45,279)( 46,280)( 47,287)
( 48,285)( 49,286)( 50,284)( 51,282)( 52,283)( 53,281)( 54,288)( 55,253)
( 56,260)( 57,258)( 58,259)( 59,257)( 60,255)( 61,256)( 62,254)( 63,261)
( 64,262)( 65,269)( 66,267)( 67,268)( 68,266)( 69,264)( 70,265)( 71,263)
( 72,270)( 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)( 91,172)( 92,179)( 93,177)( 94,178)( 95,176)
( 96,174)( 97,175)( 98,173)( 99,180)(100,163)(101,170)(102,168)(103,169)
(104,167)(105,165)(106,166)(107,164)(108,171)(109,199)(110,206)(111,204)
(112,205)(113,203)(114,201)(115,202)(116,200)(117,207)(118,208)(119,215)
(120,213)(121,214)(122,212)(123,210)(124,211)(125,209)(126,216)(127,181)
(128,188)(129,186)(130,187)(131,185)(132,183)(133,184)(134,182)(135,189)
(136,190)(137,197)(138,195)(139,196)(140,194)(141,192)(142,193)(143,191)
(144,198)(289,541)(290,548)(291,546)(292,547)(293,545)(294,543)(295,544)
(296,542)(297,549)(298,550)(299,557)(300,555)(301,556)(302,554)(303,552)
(304,553)(305,551)(306,558)(307,568)(308,575)(309,573)(310,574)(311,572)
(312,570)(313,571)(314,569)(315,576)(316,559)(317,566)(318,564)(319,565)
(320,563)(321,561)(322,562)(323,560)(324,567)(325,505)(326,512)(327,510)
(328,511)(329,509)(330,507)(331,508)(332,506)(333,513)(334,514)(335,521)
(336,519)(337,520)(338,518)(339,516)(340,517)(341,515)(342,522)(343,532)
(344,539)(345,537)(346,538)(347,536)(348,534)(349,535)(350,533)(351,540)
(352,523)(353,530)(354,528)(355,529)(356,527)(357,525)(358,526)(359,524)
(360,531)(361,469)(362,476)(363,474)(364,475)(365,473)(366,471)(367,472)
(368,470)(369,477)(370,478)(371,485)(372,483)(373,484)(374,482)(375,480)
(376,481)(377,479)(378,486)(379,496)(380,503)(381,501)(382,502)(383,500)
(384,498)(385,499)(386,497)(387,504)(388,487)(389,494)(390,492)(391,493)
(392,491)(393,489)(394,490)(395,488)(396,495)(397,433)(398,440)(399,438)
(400,439)(401,437)(402,435)(403,436)(404,434)(405,441)(406,442)(407,449)
(408,447)(409,448)(410,446)(411,444)(412,445)(413,443)(414,450)(415,460)
(416,467)(417,465)(418,466)(419,464)(420,462)(421,463)(422,461)(423,468)
(424,451)(425,458)(426,456)(427,457)(428,455)(429,453)(430,454)(431,452)
(432,459);
s3 := Sym(576)!( 1,289)( 2,290)( 3,291)( 4,292)( 5,293)( 6,294)( 7,295)
( 8,296)( 9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)
( 16,304)( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)
( 24,321)( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)
( 32,311)( 33,312)( 34,313)( 35,314)( 36,315)( 37,343)( 38,344)( 39,345)
( 40,346)( 41,347)( 42,348)( 43,349)( 44,350)( 45,351)( 46,352)( 47,353)
( 48,354)( 49,355)( 50,356)( 51,357)( 52,358)( 53,359)( 54,360)( 55,325)
( 56,326)( 57,327)( 58,328)( 59,329)( 60,330)( 61,331)( 62,332)( 63,333)
( 64,334)( 65,335)( 66,336)( 67,337)( 68,338)( 69,339)( 70,340)( 71,341)
( 72,342)( 73,361)( 74,362)( 75,363)( 76,364)( 77,365)( 78,366)( 79,367)
( 80,368)( 81,369)( 82,370)( 83,371)( 84,372)( 85,373)( 86,374)( 87,375)
( 88,376)( 89,377)( 90,378)( 91,388)( 92,389)( 93,390)( 94,391)( 95,392)
( 96,393)( 97,394)( 98,395)( 99,396)(100,379)(101,380)(102,381)(103,382)
(104,383)(105,384)(106,385)(107,386)(108,387)(109,415)(110,416)(111,417)
(112,418)(113,419)(114,420)(115,421)(116,422)(117,423)(118,424)(119,425)
(120,426)(121,427)(122,428)(123,429)(124,430)(125,431)(126,432)(127,397)
(128,398)(129,399)(130,400)(131,401)(132,402)(133,403)(134,404)(135,405)
(136,406)(137,407)(138,408)(139,409)(140,410)(141,411)(142,412)(143,413)
(144,414)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)
(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)
(160,448)(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)
(168,465)(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)
(176,455)(177,456)(178,457)(179,458)(180,459)(181,487)(182,488)(183,489)
(184,490)(185,491)(186,492)(187,493)(188,494)(189,495)(190,496)(191,497)
(192,498)(193,499)(194,500)(195,501)(196,502)(197,503)(198,504)(199,469)
(200,470)(201,471)(202,472)(203,473)(204,474)(205,475)(206,476)(207,477)
(208,478)(209,479)(210,480)(211,481)(212,482)(213,483)(214,484)(215,485)
(216,486)(217,505)(218,506)(219,507)(220,508)(221,509)(222,510)(223,511)
(224,512)(225,513)(226,514)(227,515)(228,516)(229,517)(230,518)(231,519)
(232,520)(233,521)(234,522)(235,532)(236,533)(237,534)(238,535)(239,536)
(240,537)(241,538)(242,539)(243,540)(244,523)(245,524)(246,525)(247,526)
(248,527)(249,528)(250,529)(251,530)(252,531)(253,559)(254,560)(255,561)
(256,562)(257,563)(258,564)(259,565)(260,566)(261,567)(262,568)(263,569)
(264,570)(265,571)(266,572)(267,573)(268,574)(269,575)(270,576)(271,541)
(272,542)(273,543)(274,544)(275,545)(276,546)(277,547)(278,548)(279,549)
(280,550)(281,551)(282,552)(283,553)(284,554)(285,555)(286,556)(287,557)
(288,558);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*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