Polytope of Type {6,16,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,16,6}*1152
Also Known As : {{6,16|2},{16,6|2}}. if this polytope has another name.
Group : SmallGroup(1152,133448)
Rank : 4
Schlafli Type : {6,16,6}
Number of vertices, edges, etc : 6, 48, 48, 6
Order of s0s1s2s3 : 48
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 : {6,8,6}*576
3-fold quotients : {2,16,6}*384, {6,16,2}*384
4-fold quotients : {6,4,6}*288
6-fold quotients : {2,8,6}*192, {6,8,2}*192
8-fold quotients : {6,2,6}*144
9-fold quotients : {2,16,2}*128
12-fold quotients : {2,4,6}*96a, {6,4,2}*96a
16-fold quotients : {3,2,6}*72, {6,2,3}*72
18-fold quotients : {2,8,2}*64
24-fold quotients : {2,2,6}*48, {6,2,2}*48
32-fold quotients : {3,2,3}*36
36-fold quotients : {2,4,2}*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, 77)( 2, 79)( 3, 75)( 4, 80)( 5, 73)( 6, 78)( 7, 74)( 8, 76)
( 9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)( 16, 83)
( 17, 85)( 18, 90)( 19,104)( 20,106)( 21,102)( 22,107)( 23,100)( 24,105)
( 25,101)( 26,103)( 27,108)( 28, 95)( 29, 97)( 30, 93)( 31, 98)( 32, 91)
( 33, 96)( 34, 92)( 35, 94)( 36, 99)( 37,131)( 38,133)( 39,129)( 40,134)
( 41,127)( 42,132)( 43,128)( 44,130)( 45,135)( 46,140)( 47,142)( 48,138)
( 49,143)( 50,136)( 51,141)( 52,137)( 53,139)( 54,144)( 55,113)( 56,115)
( 57,111)( 58,116)( 59,109)( 60,114)( 61,110)( 62,112)( 63,117)( 64,122)
( 65,124)( 66,120)( 67,125)( 68,118)( 69,123)( 70,119)( 71,121)( 72,126)
(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)(152,220)
(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)(160,227)
(161,229)(162,234)(163,248)(164,250)(165,246)(166,251)(167,244)(168,249)
(169,245)(170,247)(171,252)(172,239)(173,241)(174,237)(175,242)(176,235)
(177,240)(178,236)(179,238)(180,243)(181,275)(182,277)(183,273)(184,278)
(185,271)(186,276)(187,272)(188,274)(189,279)(190,284)(191,286)(192,282)
(193,287)(194,280)(195,285)(196,281)(197,283)(198,288)(199,257)(200,259)
(201,255)(202,260)(203,253)(204,258)(205,254)(206,256)(207,261)(208,266)
(209,268)(210,264)(211,269)(212,262)(213,267)(214,263)(215,265)(216,270)
(289,401)(290,403)(291,399)(292,404)(293,397)(294,402)(295,398)(296,400)
(297,405)(298,410)(299,412)(300,408)(301,413)(302,406)(303,411)(304,407)
(305,409)(306,414)(307,428)(308,430)(309,426)(310,431)(311,424)(312,429)
(313,425)(314,427)(315,432)(316,419)(317,421)(318,417)(319,422)(320,415)
(321,420)(322,416)(323,418)(324,423)(325,365)(326,367)(327,363)(328,368)
(329,361)(330,366)(331,362)(332,364)(333,369)(334,374)(335,376)(336,372)
(337,377)(338,370)(339,375)(340,371)(341,373)(342,378)(343,392)(344,394)
(345,390)(346,395)(347,388)(348,393)(349,389)(350,391)(351,396)(352,383)
(353,385)(354,381)(355,386)(356,379)(357,384)(358,380)(359,382)(360,387)
(433,545)(434,547)(435,543)(436,548)(437,541)(438,546)(439,542)(440,544)
(441,549)(442,554)(443,556)(444,552)(445,557)(446,550)(447,555)(448,551)
(449,553)(450,558)(451,572)(452,574)(453,570)(454,575)(455,568)(456,573)
(457,569)(458,571)(459,576)(460,563)(461,565)(462,561)(463,566)(464,559)
(465,564)(466,560)(467,562)(468,567)(469,509)(470,511)(471,507)(472,512)
(473,505)(474,510)(475,506)(476,508)(477,513)(478,518)(479,520)(480,516)
(481,521)(482,514)(483,519)(484,515)(485,517)(486,522)(487,536)(488,538)
(489,534)(490,539)(491,532)(492,537)(493,533)(494,535)(495,540)(496,527)
(497,529)(498,525)(499,530)(500,523)(501,528)(502,524)(503,526)(504,531);;
s2 := ( 1,505)( 2,512)( 3,510)( 4,511)( 5,509)( 6,507)( 7,508)( 8,506)
( 9,513)( 10,514)( 11,521)( 12,519)( 13,520)( 14,518)( 15,516)( 16,517)
( 17,515)( 18,522)( 19,532)( 20,539)( 21,537)( 22,538)( 23,536)( 24,534)
( 25,535)( 26,533)( 27,540)( 28,523)( 29,530)( 30,528)( 31,529)( 32,527)
( 33,525)( 34,526)( 35,524)( 36,531)( 37,559)( 38,566)( 39,564)( 40,565)
( 41,563)( 42,561)( 43,562)( 44,560)( 45,567)( 46,568)( 47,575)( 48,573)
( 49,574)( 50,572)( 51,570)( 52,571)( 53,569)( 54,576)( 55,541)( 56,548)
( 57,546)( 58,547)( 59,545)( 60,543)( 61,544)( 62,542)( 63,549)( 64,550)
( 65,557)( 66,555)( 67,556)( 68,554)( 69,552)( 70,553)( 71,551)( 72,558)
( 73,433)( 74,440)( 75,438)( 76,439)( 77,437)( 78,435)( 79,436)( 80,434)
( 81,441)( 82,442)( 83,449)( 84,447)( 85,448)( 86,446)( 87,444)( 88,445)
( 89,443)( 90,450)( 91,460)( 92,467)( 93,465)( 94,466)( 95,464)( 96,462)
( 97,463)( 98,461)( 99,468)(100,451)(101,458)(102,456)(103,457)(104,455)
(105,453)(106,454)(107,452)(108,459)(109,487)(110,494)(111,492)(112,493)
(113,491)(114,489)(115,490)(116,488)(117,495)(118,496)(119,503)(120,501)
(121,502)(122,500)(123,498)(124,499)(125,497)(126,504)(127,469)(128,476)
(129,474)(130,475)(131,473)(132,471)(133,472)(134,470)(135,477)(136,478)
(137,485)(138,483)(139,484)(140,482)(141,480)(142,481)(143,479)(144,486)
(145,361)(146,368)(147,366)(148,367)(149,365)(150,363)(151,364)(152,362)
(153,369)(154,370)(155,377)(156,375)(157,376)(158,374)(159,372)(160,373)
(161,371)(162,378)(163,388)(164,395)(165,393)(166,394)(167,392)(168,390)
(169,391)(170,389)(171,396)(172,379)(173,386)(174,384)(175,385)(176,383)
(177,381)(178,382)(179,380)(180,387)(181,415)(182,422)(183,420)(184,421)
(185,419)(186,417)(187,418)(188,416)(189,423)(190,424)(191,431)(192,429)
(193,430)(194,428)(195,426)(196,427)(197,425)(198,432)(199,397)(200,404)
(201,402)(202,403)(203,401)(204,399)(205,400)(206,398)(207,405)(208,406)
(209,413)(210,411)(211,412)(212,410)(213,408)(214,409)(215,407)(216,414)
(217,289)(218,296)(219,294)(220,295)(221,293)(222,291)(223,292)(224,290)
(225,297)(226,298)(227,305)(228,303)(229,304)(230,302)(231,300)(232,301)
(233,299)(234,306)(235,316)(236,323)(237,321)(238,322)(239,320)(240,318)
(241,319)(242,317)(243,324)(244,307)(245,314)(246,312)(247,313)(248,311)
(249,309)(250,310)(251,308)(252,315)(253,343)(254,350)(255,348)(256,349)
(257,347)(258,345)(259,346)(260,344)(261,351)(262,352)(263,359)(264,357)
(265,358)(266,356)(267,354)(268,355)(269,353)(270,360)(271,325)(272,332)
(273,330)(274,331)(275,329)(276,327)(277,328)(278,326)(279,333)(280,334)
(281,341)(282,339)(283,340)(284,338)(285,336)(286,337)(287,335)(288,342);;
s3 := ( 1,220)( 2,218)( 3,225)( 4,217)( 5,224)( 6,222)( 7,223)( 8,221)
( 9,219)( 10,229)( 11,227)( 12,234)( 13,226)( 14,233)( 15,231)( 16,232)
( 17,230)( 18,228)( 19,238)( 20,236)( 21,243)( 22,235)( 23,242)( 24,240)
( 25,241)( 26,239)( 27,237)( 28,247)( 29,245)( 30,252)( 31,244)( 32,251)
( 33,249)( 34,250)( 35,248)( 36,246)( 37,256)( 38,254)( 39,261)( 40,253)
( 41,260)( 42,258)( 43,259)( 44,257)( 45,255)( 46,265)( 47,263)( 48,270)
( 49,262)( 50,269)( 51,267)( 52,268)( 53,266)( 54,264)( 55,274)( 56,272)
( 57,279)( 58,271)( 59,278)( 60,276)( 61,277)( 62,275)( 63,273)( 64,283)
( 65,281)( 66,288)( 67,280)( 68,287)( 69,285)( 70,286)( 71,284)( 72,282)
( 73,148)( 74,146)( 75,153)( 76,145)( 77,152)( 78,150)( 79,151)( 80,149)
( 81,147)( 82,157)( 83,155)( 84,162)( 85,154)( 86,161)( 87,159)( 88,160)
( 89,158)( 90,156)( 91,166)( 92,164)( 93,171)( 94,163)( 95,170)( 96,168)
( 97,169)( 98,167)( 99,165)(100,175)(101,173)(102,180)(103,172)(104,179)
(105,177)(106,178)(107,176)(108,174)(109,184)(110,182)(111,189)(112,181)
(113,188)(114,186)(115,187)(116,185)(117,183)(118,193)(119,191)(120,198)
(121,190)(122,197)(123,195)(124,196)(125,194)(126,192)(127,202)(128,200)
(129,207)(130,199)(131,206)(132,204)(133,205)(134,203)(135,201)(136,211)
(137,209)(138,216)(139,208)(140,215)(141,213)(142,214)(143,212)(144,210)
(289,508)(290,506)(291,513)(292,505)(293,512)(294,510)(295,511)(296,509)
(297,507)(298,517)(299,515)(300,522)(301,514)(302,521)(303,519)(304,520)
(305,518)(306,516)(307,526)(308,524)(309,531)(310,523)(311,530)(312,528)
(313,529)(314,527)(315,525)(316,535)(317,533)(318,540)(319,532)(320,539)
(321,537)(322,538)(323,536)(324,534)(325,544)(326,542)(327,549)(328,541)
(329,548)(330,546)(331,547)(332,545)(333,543)(334,553)(335,551)(336,558)
(337,550)(338,557)(339,555)(340,556)(341,554)(342,552)(343,562)(344,560)
(345,567)(346,559)(347,566)(348,564)(349,565)(350,563)(351,561)(352,571)
(353,569)(354,576)(355,568)(356,575)(357,573)(358,574)(359,572)(360,570)
(361,436)(362,434)(363,441)(364,433)(365,440)(366,438)(367,439)(368,437)
(369,435)(370,445)(371,443)(372,450)(373,442)(374,449)(375,447)(376,448)
(377,446)(378,444)(379,454)(380,452)(381,459)(382,451)(383,458)(384,456)
(385,457)(386,455)(387,453)(388,463)(389,461)(390,468)(391,460)(392,467)
(393,465)(394,466)(395,464)(396,462)(397,472)(398,470)(399,477)(400,469)
(401,476)(402,474)(403,475)(404,473)(405,471)(406,481)(407,479)(408,486)
(409,478)(410,485)(411,483)(412,484)(413,482)(414,480)(415,490)(416,488)
(417,495)(418,487)(419,494)(420,492)(421,493)(422,491)(423,489)(424,499)
(425,497)(426,504)(427,496)(428,503)(429,501)(430,502)(431,500)(432,498);;
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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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, 77)( 2, 79)( 3, 75)( 4, 80)( 5, 73)( 6, 78)( 7, 74)
( 8, 76)( 9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)
( 16, 83)( 17, 85)( 18, 90)( 19,104)( 20,106)( 21,102)( 22,107)( 23,100)
( 24,105)( 25,101)( 26,103)( 27,108)( 28, 95)( 29, 97)( 30, 93)( 31, 98)
( 32, 91)( 33, 96)( 34, 92)( 35, 94)( 36, 99)( 37,131)( 38,133)( 39,129)
( 40,134)( 41,127)( 42,132)( 43,128)( 44,130)( 45,135)( 46,140)( 47,142)
( 48,138)( 49,143)( 50,136)( 51,141)( 52,137)( 53,139)( 54,144)( 55,113)
( 56,115)( 57,111)( 58,116)( 59,109)( 60,114)( 61,110)( 62,112)( 63,117)
( 64,122)( 65,124)( 66,120)( 67,125)( 68,118)( 69,123)( 70,119)( 71,121)
( 72,126)(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)
(152,220)(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)
(160,227)(161,229)(162,234)(163,248)(164,250)(165,246)(166,251)(167,244)
(168,249)(169,245)(170,247)(171,252)(172,239)(173,241)(174,237)(175,242)
(176,235)(177,240)(178,236)(179,238)(180,243)(181,275)(182,277)(183,273)
(184,278)(185,271)(186,276)(187,272)(188,274)(189,279)(190,284)(191,286)
(192,282)(193,287)(194,280)(195,285)(196,281)(197,283)(198,288)(199,257)
(200,259)(201,255)(202,260)(203,253)(204,258)(205,254)(206,256)(207,261)
(208,266)(209,268)(210,264)(211,269)(212,262)(213,267)(214,263)(215,265)
(216,270)(289,401)(290,403)(291,399)(292,404)(293,397)(294,402)(295,398)
(296,400)(297,405)(298,410)(299,412)(300,408)(301,413)(302,406)(303,411)
(304,407)(305,409)(306,414)(307,428)(308,430)(309,426)(310,431)(311,424)
(312,429)(313,425)(314,427)(315,432)(316,419)(317,421)(318,417)(319,422)
(320,415)(321,420)(322,416)(323,418)(324,423)(325,365)(326,367)(327,363)
(328,368)(329,361)(330,366)(331,362)(332,364)(333,369)(334,374)(335,376)
(336,372)(337,377)(338,370)(339,375)(340,371)(341,373)(342,378)(343,392)
(344,394)(345,390)(346,395)(347,388)(348,393)(349,389)(350,391)(351,396)
(352,383)(353,385)(354,381)(355,386)(356,379)(357,384)(358,380)(359,382)
(360,387)(433,545)(434,547)(435,543)(436,548)(437,541)(438,546)(439,542)
(440,544)(441,549)(442,554)(443,556)(444,552)(445,557)(446,550)(447,555)
(448,551)(449,553)(450,558)(451,572)(452,574)(453,570)(454,575)(455,568)
(456,573)(457,569)(458,571)(459,576)(460,563)(461,565)(462,561)(463,566)
(464,559)(465,564)(466,560)(467,562)(468,567)(469,509)(470,511)(471,507)
(472,512)(473,505)(474,510)(475,506)(476,508)(477,513)(478,518)(479,520)
(480,516)(481,521)(482,514)(483,519)(484,515)(485,517)(486,522)(487,536)
(488,538)(489,534)(490,539)(491,532)(492,537)(493,533)(494,535)(495,540)
(496,527)(497,529)(498,525)(499,530)(500,523)(501,528)(502,524)(503,526)
(504,531);
s2 := Sym(576)!( 1,505)( 2,512)( 3,510)( 4,511)( 5,509)( 6,507)( 7,508)
( 8,506)( 9,513)( 10,514)( 11,521)( 12,519)( 13,520)( 14,518)( 15,516)
( 16,517)( 17,515)( 18,522)( 19,532)( 20,539)( 21,537)( 22,538)( 23,536)
( 24,534)( 25,535)( 26,533)( 27,540)( 28,523)( 29,530)( 30,528)( 31,529)
( 32,527)( 33,525)( 34,526)( 35,524)( 36,531)( 37,559)( 38,566)( 39,564)
( 40,565)( 41,563)( 42,561)( 43,562)( 44,560)( 45,567)( 46,568)( 47,575)
( 48,573)( 49,574)( 50,572)( 51,570)( 52,571)( 53,569)( 54,576)( 55,541)
( 56,548)( 57,546)( 58,547)( 59,545)( 60,543)( 61,544)( 62,542)( 63,549)
( 64,550)( 65,557)( 66,555)( 67,556)( 68,554)( 69,552)( 70,553)( 71,551)
( 72,558)( 73,433)( 74,440)( 75,438)( 76,439)( 77,437)( 78,435)( 79,436)
( 80,434)( 81,441)( 82,442)( 83,449)( 84,447)( 85,448)( 86,446)( 87,444)
( 88,445)( 89,443)( 90,450)( 91,460)( 92,467)( 93,465)( 94,466)( 95,464)
( 96,462)( 97,463)( 98,461)( 99,468)(100,451)(101,458)(102,456)(103,457)
(104,455)(105,453)(106,454)(107,452)(108,459)(109,487)(110,494)(111,492)
(112,493)(113,491)(114,489)(115,490)(116,488)(117,495)(118,496)(119,503)
(120,501)(121,502)(122,500)(123,498)(124,499)(125,497)(126,504)(127,469)
(128,476)(129,474)(130,475)(131,473)(132,471)(133,472)(134,470)(135,477)
(136,478)(137,485)(138,483)(139,484)(140,482)(141,480)(142,481)(143,479)
(144,486)(145,361)(146,368)(147,366)(148,367)(149,365)(150,363)(151,364)
(152,362)(153,369)(154,370)(155,377)(156,375)(157,376)(158,374)(159,372)
(160,373)(161,371)(162,378)(163,388)(164,395)(165,393)(166,394)(167,392)
(168,390)(169,391)(170,389)(171,396)(172,379)(173,386)(174,384)(175,385)
(176,383)(177,381)(178,382)(179,380)(180,387)(181,415)(182,422)(183,420)
(184,421)(185,419)(186,417)(187,418)(188,416)(189,423)(190,424)(191,431)
(192,429)(193,430)(194,428)(195,426)(196,427)(197,425)(198,432)(199,397)
(200,404)(201,402)(202,403)(203,401)(204,399)(205,400)(206,398)(207,405)
(208,406)(209,413)(210,411)(211,412)(212,410)(213,408)(214,409)(215,407)
(216,414)(217,289)(218,296)(219,294)(220,295)(221,293)(222,291)(223,292)
(224,290)(225,297)(226,298)(227,305)(228,303)(229,304)(230,302)(231,300)
(232,301)(233,299)(234,306)(235,316)(236,323)(237,321)(238,322)(239,320)
(240,318)(241,319)(242,317)(243,324)(244,307)(245,314)(246,312)(247,313)
(248,311)(249,309)(250,310)(251,308)(252,315)(253,343)(254,350)(255,348)
(256,349)(257,347)(258,345)(259,346)(260,344)(261,351)(262,352)(263,359)
(264,357)(265,358)(266,356)(267,354)(268,355)(269,353)(270,360)(271,325)
(272,332)(273,330)(274,331)(275,329)(276,327)(277,328)(278,326)(279,333)
(280,334)(281,341)(282,339)(283,340)(284,338)(285,336)(286,337)(287,335)
(288,342);
s3 := Sym(576)!( 1,220)( 2,218)( 3,225)( 4,217)( 5,224)( 6,222)( 7,223)
( 8,221)( 9,219)( 10,229)( 11,227)( 12,234)( 13,226)( 14,233)( 15,231)
( 16,232)( 17,230)( 18,228)( 19,238)( 20,236)( 21,243)( 22,235)( 23,242)
( 24,240)( 25,241)( 26,239)( 27,237)( 28,247)( 29,245)( 30,252)( 31,244)
( 32,251)( 33,249)( 34,250)( 35,248)( 36,246)( 37,256)( 38,254)( 39,261)
( 40,253)( 41,260)( 42,258)( 43,259)( 44,257)( 45,255)( 46,265)( 47,263)
( 48,270)( 49,262)( 50,269)( 51,267)( 52,268)( 53,266)( 54,264)( 55,274)
( 56,272)( 57,279)( 58,271)( 59,278)( 60,276)( 61,277)( 62,275)( 63,273)
( 64,283)( 65,281)( 66,288)( 67,280)( 68,287)( 69,285)( 70,286)( 71,284)
( 72,282)( 73,148)( 74,146)( 75,153)( 76,145)( 77,152)( 78,150)( 79,151)
( 80,149)( 81,147)( 82,157)( 83,155)( 84,162)( 85,154)( 86,161)( 87,159)
( 88,160)( 89,158)( 90,156)( 91,166)( 92,164)( 93,171)( 94,163)( 95,170)
( 96,168)( 97,169)( 98,167)( 99,165)(100,175)(101,173)(102,180)(103,172)
(104,179)(105,177)(106,178)(107,176)(108,174)(109,184)(110,182)(111,189)
(112,181)(113,188)(114,186)(115,187)(116,185)(117,183)(118,193)(119,191)
(120,198)(121,190)(122,197)(123,195)(124,196)(125,194)(126,192)(127,202)
(128,200)(129,207)(130,199)(131,206)(132,204)(133,205)(134,203)(135,201)
(136,211)(137,209)(138,216)(139,208)(140,215)(141,213)(142,214)(143,212)
(144,210)(289,508)(290,506)(291,513)(292,505)(293,512)(294,510)(295,511)
(296,509)(297,507)(298,517)(299,515)(300,522)(301,514)(302,521)(303,519)
(304,520)(305,518)(306,516)(307,526)(308,524)(309,531)(310,523)(311,530)
(312,528)(313,529)(314,527)(315,525)(316,535)(317,533)(318,540)(319,532)
(320,539)(321,537)(322,538)(323,536)(324,534)(325,544)(326,542)(327,549)
(328,541)(329,548)(330,546)(331,547)(332,545)(333,543)(334,553)(335,551)
(336,558)(337,550)(338,557)(339,555)(340,556)(341,554)(342,552)(343,562)
(344,560)(345,567)(346,559)(347,566)(348,564)(349,565)(350,563)(351,561)
(352,571)(353,569)(354,576)(355,568)(356,575)(357,573)(358,574)(359,572)
(360,570)(361,436)(362,434)(363,441)(364,433)(365,440)(366,438)(367,439)
(368,437)(369,435)(370,445)(371,443)(372,450)(373,442)(374,449)(375,447)
(376,448)(377,446)(378,444)(379,454)(380,452)(381,459)(382,451)(383,458)
(384,456)(385,457)(386,455)(387,453)(388,463)(389,461)(390,468)(391,460)
(392,467)(393,465)(394,466)(395,464)(396,462)(397,472)(398,470)(399,477)
(400,469)(401,476)(402,474)(403,475)(404,473)(405,471)(406,481)(407,479)
(408,486)(409,478)(410,485)(411,483)(412,484)(413,482)(414,480)(415,490)
(416,488)(417,495)(418,487)(419,494)(420,492)(421,493)(422,491)(423,489)
(424,499)(425,497)(426,504)(427,496)(428,503)(429,501)(430,502)(431,500)
(432,498);
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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope