Polytope of Type {6,6,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,4,4}*1152c
if this polytope has a name.
Group : SmallGroup(1152,134263)
Rank : 5
Schlafli Type : {6,6,4,4}
Number of vertices, edges, etc : 6, 18, 12, 8, 4
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 : {3,6,4,4}*576, {6,6,2,4}*576c, {6,6,4,2}*576c
3-fold quotients : {6,2,4,4}*384
4-fold quotients : {3,6,2,4}*288, {3,6,4,2}*288, {6,6,2,2}*288c
6-fold quotients : {3,2,4,4}*192, {6,2,2,4}*192, {6,2,4,2}*192
8-fold quotients : {3,6,2,2}*144
9-fold quotients : {2,2,4,4}*128
12-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96, {6,2,2,2}*96
18-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
24-fold quotients : {3,2,2,2}*48
36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 37)( 2, 39)( 3, 38)( 4, 43)( 5, 45)( 6, 44)( 7, 40)( 8, 42)
( 9, 41)( 10, 46)( 11, 48)( 12, 47)( 13, 52)( 14, 54)( 15, 53)( 16, 49)
( 17, 51)( 18, 50)( 19, 55)( 20, 57)( 21, 56)( 22, 61)( 23, 63)( 24, 62)
( 25, 58)( 26, 60)( 27, 59)( 28, 64)( 29, 66)( 30, 65)( 31, 70)( 32, 72)
( 33, 71)( 34, 67)( 35, 69)( 36, 68)( 73,109)( 74,111)( 75,110)( 76,115)
( 77,117)( 78,116)( 79,112)( 80,114)( 81,113)( 82,118)( 83,120)( 84,119)
( 85,124)( 86,126)( 87,125)( 88,121)( 89,123)( 90,122)( 91,127)( 92,129)
( 93,128)( 94,133)( 95,135)( 96,134)( 97,130)( 98,132)( 99,131)(100,136)
(101,138)(102,137)(103,142)(104,144)(105,143)(106,139)(107,141)(108,140)
(145,181)(146,183)(147,182)(148,187)(149,189)(150,188)(151,184)(152,186)
(153,185)(154,190)(155,192)(156,191)(157,196)(158,198)(159,197)(160,193)
(161,195)(162,194)(163,199)(164,201)(165,200)(166,205)(167,207)(168,206)
(169,202)(170,204)(171,203)(172,208)(173,210)(174,209)(175,214)(176,216)
(177,215)(178,211)(179,213)(180,212)(217,253)(218,255)(219,254)(220,259)
(221,261)(222,260)(223,256)(224,258)(225,257)(226,262)(227,264)(228,263)
(229,268)(230,270)(231,269)(232,265)(233,267)(234,266)(235,271)(236,273)
(237,272)(238,277)(239,279)(240,278)(241,274)(242,276)(243,275)(244,280)
(245,282)(246,281)(247,286)(248,288)(249,287)(250,283)(251,285)(252,284)
(289,325)(290,327)(291,326)(292,331)(293,333)(294,332)(295,328)(296,330)
(297,329)(298,334)(299,336)(300,335)(301,340)(302,342)(303,341)(304,337)
(305,339)(306,338)(307,343)(308,345)(309,344)(310,349)(311,351)(312,350)
(313,346)(314,348)(315,347)(316,352)(317,354)(318,353)(319,358)(320,360)
(321,359)(322,355)(323,357)(324,356)(361,397)(362,399)(363,398)(364,403)
(365,405)(366,404)(367,400)(368,402)(369,401)(370,406)(371,408)(372,407)
(373,412)(374,414)(375,413)(376,409)(377,411)(378,410)(379,415)(380,417)
(381,416)(382,421)(383,423)(384,422)(385,418)(386,420)(387,419)(388,424)
(389,426)(390,425)(391,430)(392,432)(393,431)(394,427)(395,429)(396,428)
(433,469)(434,471)(435,470)(436,475)(437,477)(438,476)(439,472)(440,474)
(441,473)(442,478)(443,480)(444,479)(445,484)(446,486)(447,485)(448,481)
(449,483)(450,482)(451,487)(452,489)(453,488)(454,493)(455,495)(456,494)
(457,490)(458,492)(459,491)(460,496)(461,498)(462,497)(463,502)(464,504)
(465,503)(466,499)(467,501)(468,500)(505,541)(506,543)(507,542)(508,547)
(509,549)(510,548)(511,544)(512,546)(513,545)(514,550)(515,552)(516,551)
(517,556)(518,558)(519,557)(520,553)(521,555)(522,554)(523,559)(524,561)
(525,560)(526,565)(527,567)(528,566)(529,562)(530,564)(531,563)(532,568)
(533,570)(534,569)(535,574)(536,576)(537,575)(538,571)(539,573)(540,572);;
s1 := ( 1,110)( 2,109)( 3,111)( 4,116)( 5,115)( 6,117)( 7,113)( 8,112)
( 9,114)( 10,119)( 11,118)( 12,120)( 13,125)( 14,124)( 15,126)( 16,122)
( 17,121)( 18,123)( 19,128)( 20,127)( 21,129)( 22,134)( 23,133)( 24,135)
( 25,131)( 26,130)( 27,132)( 28,137)( 29,136)( 30,138)( 31,143)( 32,142)
( 33,144)( 34,140)( 35,139)( 36,141)( 37, 74)( 38, 73)( 39, 75)( 40, 80)
( 41, 79)( 42, 81)( 43, 77)( 44, 76)( 45, 78)( 46, 83)( 47, 82)( 48, 84)
( 49, 89)( 50, 88)( 51, 90)( 52, 86)( 53, 85)( 54, 87)( 55, 92)( 56, 91)
( 57, 93)( 58, 98)( 59, 97)( 60, 99)( 61, 95)( 62, 94)( 63, 96)( 64,101)
( 65,100)( 66,102)( 67,107)( 68,106)( 69,108)( 70,104)( 71,103)( 72,105)
(145,254)(146,253)(147,255)(148,260)(149,259)(150,261)(151,257)(152,256)
(153,258)(154,263)(155,262)(156,264)(157,269)(158,268)(159,270)(160,266)
(161,265)(162,267)(163,272)(164,271)(165,273)(166,278)(167,277)(168,279)
(169,275)(170,274)(171,276)(172,281)(173,280)(174,282)(175,287)(176,286)
(177,288)(178,284)(179,283)(180,285)(181,218)(182,217)(183,219)(184,224)
(185,223)(186,225)(187,221)(188,220)(189,222)(190,227)(191,226)(192,228)
(193,233)(194,232)(195,234)(196,230)(197,229)(198,231)(199,236)(200,235)
(201,237)(202,242)(203,241)(204,243)(205,239)(206,238)(207,240)(208,245)
(209,244)(210,246)(211,251)(212,250)(213,252)(214,248)(215,247)(216,249)
(289,398)(290,397)(291,399)(292,404)(293,403)(294,405)(295,401)(296,400)
(297,402)(298,407)(299,406)(300,408)(301,413)(302,412)(303,414)(304,410)
(305,409)(306,411)(307,416)(308,415)(309,417)(310,422)(311,421)(312,423)
(313,419)(314,418)(315,420)(316,425)(317,424)(318,426)(319,431)(320,430)
(321,432)(322,428)(323,427)(324,429)(325,362)(326,361)(327,363)(328,368)
(329,367)(330,369)(331,365)(332,364)(333,366)(334,371)(335,370)(336,372)
(337,377)(338,376)(339,378)(340,374)(341,373)(342,375)(343,380)(344,379)
(345,381)(346,386)(347,385)(348,387)(349,383)(350,382)(351,384)(352,389)
(353,388)(354,390)(355,395)(356,394)(357,396)(358,392)(359,391)(360,393)
(433,542)(434,541)(435,543)(436,548)(437,547)(438,549)(439,545)(440,544)
(441,546)(442,551)(443,550)(444,552)(445,557)(446,556)(447,558)(448,554)
(449,553)(450,555)(451,560)(452,559)(453,561)(454,566)(455,565)(456,567)
(457,563)(458,562)(459,564)(460,569)(461,568)(462,570)(463,575)(464,574)
(465,576)(466,572)(467,571)(468,573)(469,506)(470,505)(471,507)(472,512)
(473,511)(474,513)(475,509)(476,508)(477,510)(478,515)(479,514)(480,516)
(481,521)(482,520)(483,522)(484,518)(485,517)(486,519)(487,524)(488,523)
(489,525)(490,530)(491,529)(492,531)(493,527)(494,526)(495,528)(496,533)
(497,532)(498,534)(499,539)(500,538)(501,540)(502,536)(503,535)(504,537);;
s2 := ( 1,145)( 2,150)( 3,152)( 4,148)( 5,153)( 6,146)( 7,151)( 8,147)
( 9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)( 16,160)
( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)( 24,164)
( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)( 32,180)
( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)( 40,184)
( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)( 48,197)
( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)( 56,204)
( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)( 64,208)
( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)( 72,212)
( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)( 80,219)
( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)( 88,232)
( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)( 96,236)
( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)(104,252)
(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)(112,256)
(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)(120,269)
(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)(128,276)
(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)(136,280)
(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)(144,284)
(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)(296,435)
(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)(304,448)
(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)(312,452)
(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)(320,468)
(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)(328,472)
(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)(336,485)
(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)(344,492)
(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)(352,496)
(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)(360,500)
(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)(368,507)
(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)(376,520)
(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)(384,524)
(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)(392,540)
(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)(400,544)
(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)(408,557)
(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)(416,564)
(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)(424,568)
(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)(432,572);;
s3 := (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);;
s4 := ( 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);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1, 37)( 2, 39)( 3, 38)( 4, 43)( 5, 45)( 6, 44)( 7, 40)
( 8, 42)( 9, 41)( 10, 46)( 11, 48)( 12, 47)( 13, 52)( 14, 54)( 15, 53)
( 16, 49)( 17, 51)( 18, 50)( 19, 55)( 20, 57)( 21, 56)( 22, 61)( 23, 63)
( 24, 62)( 25, 58)( 26, 60)( 27, 59)( 28, 64)( 29, 66)( 30, 65)( 31, 70)
( 32, 72)( 33, 71)( 34, 67)( 35, 69)( 36, 68)( 73,109)( 74,111)( 75,110)
( 76,115)( 77,117)( 78,116)( 79,112)( 80,114)( 81,113)( 82,118)( 83,120)
( 84,119)( 85,124)( 86,126)( 87,125)( 88,121)( 89,123)( 90,122)( 91,127)
( 92,129)( 93,128)( 94,133)( 95,135)( 96,134)( 97,130)( 98,132)( 99,131)
(100,136)(101,138)(102,137)(103,142)(104,144)(105,143)(106,139)(107,141)
(108,140)(145,181)(146,183)(147,182)(148,187)(149,189)(150,188)(151,184)
(152,186)(153,185)(154,190)(155,192)(156,191)(157,196)(158,198)(159,197)
(160,193)(161,195)(162,194)(163,199)(164,201)(165,200)(166,205)(167,207)
(168,206)(169,202)(170,204)(171,203)(172,208)(173,210)(174,209)(175,214)
(176,216)(177,215)(178,211)(179,213)(180,212)(217,253)(218,255)(219,254)
(220,259)(221,261)(222,260)(223,256)(224,258)(225,257)(226,262)(227,264)
(228,263)(229,268)(230,270)(231,269)(232,265)(233,267)(234,266)(235,271)
(236,273)(237,272)(238,277)(239,279)(240,278)(241,274)(242,276)(243,275)
(244,280)(245,282)(246,281)(247,286)(248,288)(249,287)(250,283)(251,285)
(252,284)(289,325)(290,327)(291,326)(292,331)(293,333)(294,332)(295,328)
(296,330)(297,329)(298,334)(299,336)(300,335)(301,340)(302,342)(303,341)
(304,337)(305,339)(306,338)(307,343)(308,345)(309,344)(310,349)(311,351)
(312,350)(313,346)(314,348)(315,347)(316,352)(317,354)(318,353)(319,358)
(320,360)(321,359)(322,355)(323,357)(324,356)(361,397)(362,399)(363,398)
(364,403)(365,405)(366,404)(367,400)(368,402)(369,401)(370,406)(371,408)
(372,407)(373,412)(374,414)(375,413)(376,409)(377,411)(378,410)(379,415)
(380,417)(381,416)(382,421)(383,423)(384,422)(385,418)(386,420)(387,419)
(388,424)(389,426)(390,425)(391,430)(392,432)(393,431)(394,427)(395,429)
(396,428)(433,469)(434,471)(435,470)(436,475)(437,477)(438,476)(439,472)
(440,474)(441,473)(442,478)(443,480)(444,479)(445,484)(446,486)(447,485)
(448,481)(449,483)(450,482)(451,487)(452,489)(453,488)(454,493)(455,495)
(456,494)(457,490)(458,492)(459,491)(460,496)(461,498)(462,497)(463,502)
(464,504)(465,503)(466,499)(467,501)(468,500)(505,541)(506,543)(507,542)
(508,547)(509,549)(510,548)(511,544)(512,546)(513,545)(514,550)(515,552)
(516,551)(517,556)(518,558)(519,557)(520,553)(521,555)(522,554)(523,559)
(524,561)(525,560)(526,565)(527,567)(528,566)(529,562)(530,564)(531,563)
(532,568)(533,570)(534,569)(535,574)(536,576)(537,575)(538,571)(539,573)
(540,572);
s1 := Sym(576)!( 1,110)( 2,109)( 3,111)( 4,116)( 5,115)( 6,117)( 7,113)
( 8,112)( 9,114)( 10,119)( 11,118)( 12,120)( 13,125)( 14,124)( 15,126)
( 16,122)( 17,121)( 18,123)( 19,128)( 20,127)( 21,129)( 22,134)( 23,133)
( 24,135)( 25,131)( 26,130)( 27,132)( 28,137)( 29,136)( 30,138)( 31,143)
( 32,142)( 33,144)( 34,140)( 35,139)( 36,141)( 37, 74)( 38, 73)( 39, 75)
( 40, 80)( 41, 79)( 42, 81)( 43, 77)( 44, 76)( 45, 78)( 46, 83)( 47, 82)
( 48, 84)( 49, 89)( 50, 88)( 51, 90)( 52, 86)( 53, 85)( 54, 87)( 55, 92)
( 56, 91)( 57, 93)( 58, 98)( 59, 97)( 60, 99)( 61, 95)( 62, 94)( 63, 96)
( 64,101)( 65,100)( 66,102)( 67,107)( 68,106)( 69,108)( 70,104)( 71,103)
( 72,105)(145,254)(146,253)(147,255)(148,260)(149,259)(150,261)(151,257)
(152,256)(153,258)(154,263)(155,262)(156,264)(157,269)(158,268)(159,270)
(160,266)(161,265)(162,267)(163,272)(164,271)(165,273)(166,278)(167,277)
(168,279)(169,275)(170,274)(171,276)(172,281)(173,280)(174,282)(175,287)
(176,286)(177,288)(178,284)(179,283)(180,285)(181,218)(182,217)(183,219)
(184,224)(185,223)(186,225)(187,221)(188,220)(189,222)(190,227)(191,226)
(192,228)(193,233)(194,232)(195,234)(196,230)(197,229)(198,231)(199,236)
(200,235)(201,237)(202,242)(203,241)(204,243)(205,239)(206,238)(207,240)
(208,245)(209,244)(210,246)(211,251)(212,250)(213,252)(214,248)(215,247)
(216,249)(289,398)(290,397)(291,399)(292,404)(293,403)(294,405)(295,401)
(296,400)(297,402)(298,407)(299,406)(300,408)(301,413)(302,412)(303,414)
(304,410)(305,409)(306,411)(307,416)(308,415)(309,417)(310,422)(311,421)
(312,423)(313,419)(314,418)(315,420)(316,425)(317,424)(318,426)(319,431)
(320,430)(321,432)(322,428)(323,427)(324,429)(325,362)(326,361)(327,363)
(328,368)(329,367)(330,369)(331,365)(332,364)(333,366)(334,371)(335,370)
(336,372)(337,377)(338,376)(339,378)(340,374)(341,373)(342,375)(343,380)
(344,379)(345,381)(346,386)(347,385)(348,387)(349,383)(350,382)(351,384)
(352,389)(353,388)(354,390)(355,395)(356,394)(357,396)(358,392)(359,391)
(360,393)(433,542)(434,541)(435,543)(436,548)(437,547)(438,549)(439,545)
(440,544)(441,546)(442,551)(443,550)(444,552)(445,557)(446,556)(447,558)
(448,554)(449,553)(450,555)(451,560)(452,559)(453,561)(454,566)(455,565)
(456,567)(457,563)(458,562)(459,564)(460,569)(461,568)(462,570)(463,575)
(464,574)(465,576)(466,572)(467,571)(468,573)(469,506)(470,505)(471,507)
(472,512)(473,511)(474,513)(475,509)(476,508)(477,510)(478,515)(479,514)
(480,516)(481,521)(482,520)(483,522)(484,518)(485,517)(486,519)(487,524)
(488,523)(489,525)(490,530)(491,529)(492,531)(493,527)(494,526)(495,528)
(496,533)(497,532)(498,534)(499,539)(500,538)(501,540)(502,536)(503,535)
(504,537);
s2 := Sym(576)!( 1,145)( 2,150)( 3,152)( 4,148)( 5,153)( 6,146)( 7,151)
( 8,147)( 9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)
( 16,160)( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)
( 24,164)( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)
( 32,180)( 33,173)( 34,178)( 35,174)( 36,176)( 37,181)( 38,186)( 39,188)
( 40,184)( 41,189)( 42,182)( 43,187)( 44,183)( 45,185)( 46,190)( 47,195)
( 48,197)( 49,193)( 50,198)( 51,191)( 52,196)( 53,192)( 54,194)( 55,199)
( 56,204)( 57,206)( 58,202)( 59,207)( 60,200)( 61,205)( 62,201)( 63,203)
( 64,208)( 65,213)( 66,215)( 67,211)( 68,216)( 69,209)( 70,214)( 71,210)
( 72,212)( 73,217)( 74,222)( 75,224)( 76,220)( 77,225)( 78,218)( 79,223)
( 80,219)( 81,221)( 82,226)( 83,231)( 84,233)( 85,229)( 86,234)( 87,227)
( 88,232)( 89,228)( 90,230)( 91,235)( 92,240)( 93,242)( 94,238)( 95,243)
( 96,236)( 97,241)( 98,237)( 99,239)(100,244)(101,249)(102,251)(103,247)
(104,252)(105,245)(106,250)(107,246)(108,248)(109,253)(110,258)(111,260)
(112,256)(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)
(120,269)(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)
(128,276)(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)
(136,280)(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)
(144,284)(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)
(296,435)(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)
(304,448)(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)
(312,452)(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)
(320,468)(321,461)(322,466)(323,462)(324,464)(325,469)(326,474)(327,476)
(328,472)(329,477)(330,470)(331,475)(332,471)(333,473)(334,478)(335,483)
(336,485)(337,481)(338,486)(339,479)(340,484)(341,480)(342,482)(343,487)
(344,492)(345,494)(346,490)(347,495)(348,488)(349,493)(350,489)(351,491)
(352,496)(353,501)(354,503)(355,499)(356,504)(357,497)(358,502)(359,498)
(360,500)(361,505)(362,510)(363,512)(364,508)(365,513)(366,506)(367,511)
(368,507)(369,509)(370,514)(371,519)(372,521)(373,517)(374,522)(375,515)
(376,520)(377,516)(378,518)(379,523)(380,528)(381,530)(382,526)(383,531)
(384,524)(385,529)(386,525)(387,527)(388,532)(389,537)(390,539)(391,535)
(392,540)(393,533)(394,538)(395,534)(396,536)(397,541)(398,546)(399,548)
(400,544)(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)
(408,557)(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)
(416,564)(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)
(424,568)(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)
(432,572);
s3 := 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);
s4 := 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);
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 >;
References : None.
to this polytope