Polytope of Type {4,4,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,6,6}*1152a
Also Known As : {{4,4|2},{4,6|2},{6,6|2}}. if this polytope has another name.
Group : SmallGroup(1152,134261)
Rank : 5
Schlafli Type : {4,4,6,6}
Number of vertices, edges, etc : 4, 8, 12, 18, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 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 : {2,4,6,6}*576a, {4,2,6,6}*576a
3-fold quotients : {4,4,2,6}*384, {4,4,6,2}*384
4-fold quotients : {2,2,6,6}*288a
6-fold quotients : {4,4,2,3}*192, {2,4,2,6}*192, {2,4,6,2}*192a, {4,2,2,6}*192, {4,2,6,2}*192
9-fold quotients : {4,4,2,2}*128
12-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96, {4,2,3,2}*96, {2,2,2,6}*96, {2,2,6,2}*96
18-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
24-fold quotients : {2,2,2,3}*48, {2,2,3,2}*48
36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)( 24,312)
( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)
( 33,321)( 34,322)( 35,323)( 36,324)( 37,325)( 38,326)( 39,327)( 40,328)
( 41,329)( 42,330)( 43,331)( 44,332)( 45,333)( 46,334)( 47,335)( 48,336)
( 49,337)( 50,338)( 51,339)( 52,340)( 53,341)( 54,342)( 55,343)( 56,344)
( 57,345)( 58,346)( 59,347)( 60,348)( 61,349)( 62,350)( 63,351)( 64,352)
( 65,353)( 66,354)( 67,355)( 68,356)( 69,357)( 70,358)( 71,359)( 72,360)
( 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)( 91,379)( 92,380)( 93,381)( 94,382)( 95,383)( 96,384)
( 97,385)( 98,386)( 99,387)(100,388)(101,389)(102,390)(103,391)(104,392)
(105,393)(106,394)(107,395)(108,396)(109,397)(110,398)(111,399)(112,400)
(113,401)(114,402)(115,403)(116,404)(117,405)(118,406)(119,407)(120,408)
(121,409)(122,410)(123,411)(124,412)(125,413)(126,414)(127,415)(128,416)
(129,417)(130,418)(131,419)(132,420)(133,421)(134,422)(135,423)(136,424)
(137,425)(138,426)(139,427)(140,428)(141,429)(142,430)(143,431)(144,432)
(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)(163,451)(164,452)(165,453)(166,454)(167,455)(168,456)
(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)(176,464)
(177,465)(178,466)(179,467)(180,468)(181,469)(182,470)(183,471)(184,472)
(185,473)(186,474)(187,475)(188,476)(189,477)(190,478)(191,479)(192,480)
(193,481)(194,482)(195,483)(196,484)(197,485)(198,486)(199,487)(200,488)
(201,489)(202,490)(203,491)(204,492)(205,493)(206,494)(207,495)(208,496)
(209,497)(210,498)(211,499)(212,500)(213,501)(214,502)(215,503)(216,504)
(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)(235,523)(236,524)(237,525)(238,526)(239,527)(240,528)
(241,529)(242,530)(243,531)(244,532)(245,533)(246,534)(247,535)(248,536)
(249,537)(250,538)(251,539)(252,540)(253,541)(254,542)(255,543)(256,544)
(257,545)(258,546)(259,547)(260,548)(261,549)(262,550)(263,551)(264,552)
(265,553)(266,554)(267,555)(268,556)(269,557)(270,558)(271,559)(272,560)
(273,561)(274,562)(275,563)(276,564)(277,565)(278,566)(279,567)(280,568)
(281,569)(282,570)(283,571)(284,572)(285,573)(286,574)(287,575)(288,576);;
s1 := (145,154)(146,155)(147,156)(148,157)(149,158)(150,159)(151,160)(152,161)
(153,162)(163,172)(164,173)(165,174)(166,175)(167,176)(168,177)(169,178)
(170,179)(171,180)(181,190)(182,191)(183,192)(184,193)(185,194)(186,195)
(187,196)(188,197)(189,198)(199,208)(200,209)(201,210)(202,211)(203,212)
(204,213)(205,214)(206,215)(207,216)(217,226)(218,227)(219,228)(220,229)
(221,230)(222,231)(223,232)(224,233)(225,234)(235,244)(236,245)(237,246)
(238,247)(239,248)(240,249)(241,250)(242,251)(243,252)(253,262)(254,263)
(255,264)(256,265)(257,266)(258,267)(259,268)(260,269)(261,270)(271,280)
(272,281)(273,282)(274,283)(275,284)(276,285)(277,286)(278,287)(279,288)
(289,307)(290,308)(291,309)(292,310)(293,311)(294,312)(295,313)(296,314)
(297,315)(298,316)(299,317)(300,318)(301,319)(302,320)(303,321)(304,322)
(305,323)(306,324)(325,343)(326,344)(327,345)(328,346)(329,347)(330,348)
(331,349)(332,350)(333,351)(334,352)(335,353)(336,354)(337,355)(338,356)
(339,357)(340,358)(341,359)(342,360)(361,379)(362,380)(363,381)(364,382)
(365,383)(366,384)(367,385)(368,386)(369,387)(370,388)(371,389)(372,390)
(373,391)(374,392)(375,393)(376,394)(377,395)(378,396)(397,415)(398,416)
(399,417)(400,418)(401,419)(402,420)(403,421)(404,422)(405,423)(406,424)
(407,425)(408,426)(409,427)(410,428)(411,429)(412,430)(413,431)(414,432)
(433,460)(434,461)(435,462)(436,463)(437,464)(438,465)(439,466)(440,467)
(441,468)(442,451)(443,452)(444,453)(445,454)(446,455)(447,456)(448,457)
(449,458)(450,459)(469,496)(470,497)(471,498)(472,499)(473,500)(474,501)
(475,502)(476,503)(477,504)(478,487)(479,488)(480,489)(481,490)(482,491)
(483,492)(484,493)(485,494)(486,495)(505,532)(506,533)(507,534)(508,535)
(509,536)(510,537)(511,538)(512,539)(513,540)(514,523)(515,524)(516,525)
(517,526)(518,527)(519,528)(520,529)(521,530)(522,531)(541,568)(542,569)
(543,570)(544,571)(545,572)(546,573)(547,574)(548,575)(549,576)(550,559)
(551,560)(552,561)(553,562)(554,563)(555,564)(556,565)(557,566)(558,567);;
s2 := ( 1,181)( 2,186)( 3,188)( 4,184)( 5,189)( 6,182)( 7,187)( 8,183)
( 9,185)( 10,190)( 11,195)( 12,197)( 13,193)( 14,198)( 15,191)( 16,196)
( 17,192)( 18,194)( 19,199)( 20,204)( 21,206)( 22,202)( 23,207)( 24,200)
( 25,205)( 26,201)( 27,203)( 28,208)( 29,213)( 30,215)( 31,211)( 32,216)
( 33,209)( 34,214)( 35,210)( 36,212)( 37,145)( 38,150)( 39,152)( 40,148)
( 41,153)( 42,146)( 43,151)( 44,147)( 45,149)( 46,154)( 47,159)( 48,161)
( 49,157)( 50,162)( 51,155)( 52,160)( 53,156)( 54,158)( 55,163)( 56,168)
( 57,170)( 58,166)( 59,171)( 60,164)( 61,169)( 62,165)( 63,167)( 64,172)
( 65,177)( 66,179)( 67,175)( 68,180)( 69,173)( 70,178)( 71,174)( 72,176)
( 73,253)( 74,258)( 75,260)( 76,256)( 77,261)( 78,254)( 79,259)( 80,255)
( 81,257)( 82,262)( 83,267)( 84,269)( 85,265)( 86,270)( 87,263)( 88,268)
( 89,264)( 90,266)( 91,271)( 92,276)( 93,278)( 94,274)( 95,279)( 96,272)
( 97,277)( 98,273)( 99,275)(100,280)(101,285)(102,287)(103,283)(104,288)
(105,281)(106,286)(107,282)(108,284)(109,217)(110,222)(111,224)(112,220)
(113,225)(114,218)(115,223)(116,219)(117,221)(118,226)(119,231)(120,233)
(121,229)(122,234)(123,227)(124,232)(125,228)(126,230)(127,235)(128,240)
(129,242)(130,238)(131,243)(132,236)(133,241)(134,237)(135,239)(136,244)
(137,249)(138,251)(139,247)(140,252)(141,245)(142,250)(143,246)(144,248)
(289,469)(290,474)(291,476)(292,472)(293,477)(294,470)(295,475)(296,471)
(297,473)(298,478)(299,483)(300,485)(301,481)(302,486)(303,479)(304,484)
(305,480)(306,482)(307,487)(308,492)(309,494)(310,490)(311,495)(312,488)
(313,493)(314,489)(315,491)(316,496)(317,501)(318,503)(319,499)(320,504)
(321,497)(322,502)(323,498)(324,500)(325,433)(326,438)(327,440)(328,436)
(329,441)(330,434)(331,439)(332,435)(333,437)(334,442)(335,447)(336,449)
(337,445)(338,450)(339,443)(340,448)(341,444)(342,446)(343,451)(344,456)
(345,458)(346,454)(347,459)(348,452)(349,457)(350,453)(351,455)(352,460)
(353,465)(354,467)(355,463)(356,468)(357,461)(358,466)(359,462)(360,464)
(361,541)(362,546)(363,548)(364,544)(365,549)(366,542)(367,547)(368,543)
(369,545)(370,550)(371,555)(372,557)(373,553)(374,558)(375,551)(376,556)
(377,552)(378,554)(379,559)(380,564)(381,566)(382,562)(383,567)(384,560)
(385,565)(386,561)(387,563)(388,568)(389,573)(390,575)(391,571)(392,576)
(393,569)(394,574)(395,570)(396,572)(397,505)(398,510)(399,512)(400,508)
(401,513)(402,506)(403,511)(404,507)(405,509)(406,514)(407,519)(408,521)
(409,517)(410,522)(411,515)(412,520)(413,516)(414,518)(415,523)(416,528)
(417,530)(418,526)(419,531)(420,524)(421,529)(422,525)(423,527)(424,532)
(425,537)(426,539)(427,535)(428,540)(429,533)(430,538)(431,534)(432,536);;
s3 := ( 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);;
s4 := ( 1,109)( 2,116)( 3,114)( 4,115)( 5,113)( 6,111)( 7,112)( 8,110)
( 9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)( 16,121)
( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)( 24,129)
( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)( 32,140)
( 33,138)( 34,139)( 35,137)( 36,144)( 37, 73)( 38, 80)( 39, 78)( 40, 79)
( 41, 77)( 42, 75)( 43, 76)( 44, 74)( 45, 81)( 46, 82)( 47, 89)( 48, 87)
( 49, 88)( 50, 86)( 51, 84)( 52, 85)( 53, 83)( 54, 90)( 55, 91)( 56, 98)
( 57, 96)( 58, 97)( 59, 95)( 60, 93)( 61, 94)( 62, 92)( 63, 99)( 64,100)
( 65,107)( 66,105)( 67,106)( 68,104)( 69,102)( 70,103)( 71,101)( 72,108)
(145,253)(146,260)(147,258)(148,259)(149,257)(150,255)(151,256)(152,254)
(153,261)(154,262)(155,269)(156,267)(157,268)(158,266)(159,264)(160,265)
(161,263)(162,270)(163,271)(164,278)(165,276)(166,277)(167,275)(168,273)
(169,274)(170,272)(171,279)(172,280)(173,287)(174,285)(175,286)(176,284)
(177,282)(178,283)(179,281)(180,288)(181,217)(182,224)(183,222)(184,223)
(185,221)(186,219)(187,220)(188,218)(189,225)(190,226)(191,233)(192,231)
(193,232)(194,230)(195,228)(196,229)(197,227)(198,234)(199,235)(200,242)
(201,240)(202,241)(203,239)(204,237)(205,238)(206,236)(207,243)(208,244)
(209,251)(210,249)(211,250)(212,248)(213,246)(214,247)(215,245)(216,252)
(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)(296,398)
(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)(304,409)
(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)(312,417)
(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)(320,428)
(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)(328,367)
(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)(336,375)
(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)(344,386)
(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)(352,388)
(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)(360,396)
(433,541)(434,548)(435,546)(436,547)(437,545)(438,543)(439,544)(440,542)
(441,549)(442,550)(443,557)(444,555)(445,556)(446,554)(447,552)(448,553)
(449,551)(450,558)(451,559)(452,566)(453,564)(454,565)(455,563)(456,561)
(457,562)(458,560)(459,567)(460,568)(461,575)(462,573)(463,574)(464,572)
(465,570)(466,571)(467,569)(468,576)(469,505)(470,512)(471,510)(472,511)
(473,509)(474,507)(475,508)(476,506)(477,513)(478,514)(479,521)(480,519)
(481,520)(482,518)(483,516)(484,517)(485,515)(486,522)(487,523)(488,530)
(489,528)(490,529)(491,527)(492,525)(493,526)(494,524)(495,531)(496,532)
(497,539)(498,537)(499,538)(500,536)(501,534)(502,535)(503,533)(504,540);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)
( 24,312)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)
( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 37,325)( 38,326)( 39,327)
( 40,328)( 41,329)( 42,330)( 43,331)( 44,332)( 45,333)( 46,334)( 47,335)
( 48,336)( 49,337)( 50,338)( 51,339)( 52,340)( 53,341)( 54,342)( 55,343)
( 56,344)( 57,345)( 58,346)( 59,347)( 60,348)( 61,349)( 62,350)( 63,351)
( 64,352)( 65,353)( 66,354)( 67,355)( 68,356)( 69,357)( 70,358)( 71,359)
( 72,360)( 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)( 91,379)( 92,380)( 93,381)( 94,382)( 95,383)
( 96,384)( 97,385)( 98,386)( 99,387)(100,388)(101,389)(102,390)(103,391)
(104,392)(105,393)(106,394)(107,395)(108,396)(109,397)(110,398)(111,399)
(112,400)(113,401)(114,402)(115,403)(116,404)(117,405)(118,406)(119,407)
(120,408)(121,409)(122,410)(123,411)(124,412)(125,413)(126,414)(127,415)
(128,416)(129,417)(130,418)(131,419)(132,420)(133,421)(134,422)(135,423)
(136,424)(137,425)(138,426)(139,427)(140,428)(141,429)(142,430)(143,431)
(144,432)(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)(163,451)(164,452)(165,453)(166,454)(167,455)
(168,456)(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)
(176,464)(177,465)(178,466)(179,467)(180,468)(181,469)(182,470)(183,471)
(184,472)(185,473)(186,474)(187,475)(188,476)(189,477)(190,478)(191,479)
(192,480)(193,481)(194,482)(195,483)(196,484)(197,485)(198,486)(199,487)
(200,488)(201,489)(202,490)(203,491)(204,492)(205,493)(206,494)(207,495)
(208,496)(209,497)(210,498)(211,499)(212,500)(213,501)(214,502)(215,503)
(216,504)(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)(235,523)(236,524)(237,525)(238,526)(239,527)
(240,528)(241,529)(242,530)(243,531)(244,532)(245,533)(246,534)(247,535)
(248,536)(249,537)(250,538)(251,539)(252,540)(253,541)(254,542)(255,543)
(256,544)(257,545)(258,546)(259,547)(260,548)(261,549)(262,550)(263,551)
(264,552)(265,553)(266,554)(267,555)(268,556)(269,557)(270,558)(271,559)
(272,560)(273,561)(274,562)(275,563)(276,564)(277,565)(278,566)(279,567)
(280,568)(281,569)(282,570)(283,571)(284,572)(285,573)(286,574)(287,575)
(288,576);
s1 := Sym(576)!(145,154)(146,155)(147,156)(148,157)(149,158)(150,159)(151,160)
(152,161)(153,162)(163,172)(164,173)(165,174)(166,175)(167,176)(168,177)
(169,178)(170,179)(171,180)(181,190)(182,191)(183,192)(184,193)(185,194)
(186,195)(187,196)(188,197)(189,198)(199,208)(200,209)(201,210)(202,211)
(203,212)(204,213)(205,214)(206,215)(207,216)(217,226)(218,227)(219,228)
(220,229)(221,230)(222,231)(223,232)(224,233)(225,234)(235,244)(236,245)
(237,246)(238,247)(239,248)(240,249)(241,250)(242,251)(243,252)(253,262)
(254,263)(255,264)(256,265)(257,266)(258,267)(259,268)(260,269)(261,270)
(271,280)(272,281)(273,282)(274,283)(275,284)(276,285)(277,286)(278,287)
(279,288)(289,307)(290,308)(291,309)(292,310)(293,311)(294,312)(295,313)
(296,314)(297,315)(298,316)(299,317)(300,318)(301,319)(302,320)(303,321)
(304,322)(305,323)(306,324)(325,343)(326,344)(327,345)(328,346)(329,347)
(330,348)(331,349)(332,350)(333,351)(334,352)(335,353)(336,354)(337,355)
(338,356)(339,357)(340,358)(341,359)(342,360)(361,379)(362,380)(363,381)
(364,382)(365,383)(366,384)(367,385)(368,386)(369,387)(370,388)(371,389)
(372,390)(373,391)(374,392)(375,393)(376,394)(377,395)(378,396)(397,415)
(398,416)(399,417)(400,418)(401,419)(402,420)(403,421)(404,422)(405,423)
(406,424)(407,425)(408,426)(409,427)(410,428)(411,429)(412,430)(413,431)
(414,432)(433,460)(434,461)(435,462)(436,463)(437,464)(438,465)(439,466)
(440,467)(441,468)(442,451)(443,452)(444,453)(445,454)(446,455)(447,456)
(448,457)(449,458)(450,459)(469,496)(470,497)(471,498)(472,499)(473,500)
(474,501)(475,502)(476,503)(477,504)(478,487)(479,488)(480,489)(481,490)
(482,491)(483,492)(484,493)(485,494)(486,495)(505,532)(506,533)(507,534)
(508,535)(509,536)(510,537)(511,538)(512,539)(513,540)(514,523)(515,524)
(516,525)(517,526)(518,527)(519,528)(520,529)(521,530)(522,531)(541,568)
(542,569)(543,570)(544,571)(545,572)(546,573)(547,574)(548,575)(549,576)
(550,559)(551,560)(552,561)(553,562)(554,563)(555,564)(556,565)(557,566)
(558,567);
s2 := Sym(576)!( 1,181)( 2,186)( 3,188)( 4,184)( 5,189)( 6,182)( 7,187)
( 8,183)( 9,185)( 10,190)( 11,195)( 12,197)( 13,193)( 14,198)( 15,191)
( 16,196)( 17,192)( 18,194)( 19,199)( 20,204)( 21,206)( 22,202)( 23,207)
( 24,200)( 25,205)( 26,201)( 27,203)( 28,208)( 29,213)( 30,215)( 31,211)
( 32,216)( 33,209)( 34,214)( 35,210)( 36,212)( 37,145)( 38,150)( 39,152)
( 40,148)( 41,153)( 42,146)( 43,151)( 44,147)( 45,149)( 46,154)( 47,159)
( 48,161)( 49,157)( 50,162)( 51,155)( 52,160)( 53,156)( 54,158)( 55,163)
( 56,168)( 57,170)( 58,166)( 59,171)( 60,164)( 61,169)( 62,165)( 63,167)
( 64,172)( 65,177)( 66,179)( 67,175)( 68,180)( 69,173)( 70,178)( 71,174)
( 72,176)( 73,253)( 74,258)( 75,260)( 76,256)( 77,261)( 78,254)( 79,259)
( 80,255)( 81,257)( 82,262)( 83,267)( 84,269)( 85,265)( 86,270)( 87,263)
( 88,268)( 89,264)( 90,266)( 91,271)( 92,276)( 93,278)( 94,274)( 95,279)
( 96,272)( 97,277)( 98,273)( 99,275)(100,280)(101,285)(102,287)(103,283)
(104,288)(105,281)(106,286)(107,282)(108,284)(109,217)(110,222)(111,224)
(112,220)(113,225)(114,218)(115,223)(116,219)(117,221)(118,226)(119,231)
(120,233)(121,229)(122,234)(123,227)(124,232)(125,228)(126,230)(127,235)
(128,240)(129,242)(130,238)(131,243)(132,236)(133,241)(134,237)(135,239)
(136,244)(137,249)(138,251)(139,247)(140,252)(141,245)(142,250)(143,246)
(144,248)(289,469)(290,474)(291,476)(292,472)(293,477)(294,470)(295,475)
(296,471)(297,473)(298,478)(299,483)(300,485)(301,481)(302,486)(303,479)
(304,484)(305,480)(306,482)(307,487)(308,492)(309,494)(310,490)(311,495)
(312,488)(313,493)(314,489)(315,491)(316,496)(317,501)(318,503)(319,499)
(320,504)(321,497)(322,502)(323,498)(324,500)(325,433)(326,438)(327,440)
(328,436)(329,441)(330,434)(331,439)(332,435)(333,437)(334,442)(335,447)
(336,449)(337,445)(338,450)(339,443)(340,448)(341,444)(342,446)(343,451)
(344,456)(345,458)(346,454)(347,459)(348,452)(349,457)(350,453)(351,455)
(352,460)(353,465)(354,467)(355,463)(356,468)(357,461)(358,466)(359,462)
(360,464)(361,541)(362,546)(363,548)(364,544)(365,549)(366,542)(367,547)
(368,543)(369,545)(370,550)(371,555)(372,557)(373,553)(374,558)(375,551)
(376,556)(377,552)(378,554)(379,559)(380,564)(381,566)(382,562)(383,567)
(384,560)(385,565)(386,561)(387,563)(388,568)(389,573)(390,575)(391,571)
(392,576)(393,569)(394,574)(395,570)(396,572)(397,505)(398,510)(399,512)
(400,508)(401,513)(402,506)(403,511)(404,507)(405,509)(406,514)(407,519)
(408,521)(409,517)(410,522)(411,515)(412,520)(413,516)(414,518)(415,523)
(416,528)(417,530)(418,526)(419,531)(420,524)(421,529)(422,525)(423,527)
(424,532)(425,537)(426,539)(427,535)(428,540)(429,533)(430,538)(431,534)
(432,536);
s3 := 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);
s4 := Sym(576)!( 1,109)( 2,116)( 3,114)( 4,115)( 5,113)( 6,111)( 7,112)
( 8,110)( 9,117)( 10,118)( 11,125)( 12,123)( 13,124)( 14,122)( 15,120)
( 16,121)( 17,119)( 18,126)( 19,127)( 20,134)( 21,132)( 22,133)( 23,131)
( 24,129)( 25,130)( 26,128)( 27,135)( 28,136)( 29,143)( 30,141)( 31,142)
( 32,140)( 33,138)( 34,139)( 35,137)( 36,144)( 37, 73)( 38, 80)( 39, 78)
( 40, 79)( 41, 77)( 42, 75)( 43, 76)( 44, 74)( 45, 81)( 46, 82)( 47, 89)
( 48, 87)( 49, 88)( 50, 86)( 51, 84)( 52, 85)( 53, 83)( 54, 90)( 55, 91)
( 56, 98)( 57, 96)( 58, 97)( 59, 95)( 60, 93)( 61, 94)( 62, 92)( 63, 99)
( 64,100)( 65,107)( 66,105)( 67,106)( 68,104)( 69,102)( 70,103)( 71,101)
( 72,108)(145,253)(146,260)(147,258)(148,259)(149,257)(150,255)(151,256)
(152,254)(153,261)(154,262)(155,269)(156,267)(157,268)(158,266)(159,264)
(160,265)(161,263)(162,270)(163,271)(164,278)(165,276)(166,277)(167,275)
(168,273)(169,274)(170,272)(171,279)(172,280)(173,287)(174,285)(175,286)
(176,284)(177,282)(178,283)(179,281)(180,288)(181,217)(182,224)(183,222)
(184,223)(185,221)(186,219)(187,220)(188,218)(189,225)(190,226)(191,233)
(192,231)(193,232)(194,230)(195,228)(196,229)(197,227)(198,234)(199,235)
(200,242)(201,240)(202,241)(203,239)(204,237)(205,238)(206,236)(207,243)
(208,244)(209,251)(210,249)(211,250)(212,248)(213,246)(214,247)(215,245)
(216,252)(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)
(296,398)(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)
(304,409)(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)
(312,417)(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)
(320,428)(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)
(328,367)(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)
(336,375)(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)
(344,386)(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)
(352,388)(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)
(360,396)(433,541)(434,548)(435,546)(436,547)(437,545)(438,543)(439,544)
(440,542)(441,549)(442,550)(443,557)(444,555)(445,556)(446,554)(447,552)
(448,553)(449,551)(450,558)(451,559)(452,566)(453,564)(454,565)(455,563)
(456,561)(457,562)(458,560)(459,567)(460,568)(461,575)(462,573)(463,574)
(464,572)(465,570)(466,571)(467,569)(468,576)(469,505)(470,512)(471,510)
(472,511)(473,509)(474,507)(475,508)(476,506)(477,513)(478,514)(479,521)
(480,519)(481,520)(482,518)(483,516)(484,517)(485,515)(486,522)(487,523)
(488,530)(489,528)(490,529)(491,527)(492,525)(493,526)(494,524)(495,531)
(496,532)(497,539)(498,537)(499,538)(500,536)(501,534)(502,535)(503,533)
(504,540);
poly := sub<Sym(576)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
References : None.
to this polytope