Polytope of Type {12,6,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,10}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240195)
Rank : 4
Schlafli Type : {12,6,10}
Number of vertices, edges, etc : 16, 48, 40, 10
Order of s0s1s2s3 : 40
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 : {6,6,10}*960
4-fold quotients : {3,6,10}*480
5-fold quotients : {12,6,2}*384b
10-fold quotients : {12,3,2}*192, {6,6,2}*192
20-fold quotients : {3,6,2}*96, {6,3,2}*96
24-fold quotients : {2,2,10}*80
40-fold quotients : {3,3,2}*48
48-fold quotients : {2,2,5}*40
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)
( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 41, 81)
( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)( 49, 89)
( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 97)
( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)( 65,105)
( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)( 73,113)
( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)(121,122)
(125,128)(126,127)(129,130)(133,136)(134,135)(137,138)(141,144)(142,143)
(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)(161,202)(162,201)
(163,203)(164,204)(165,208)(166,207)(167,206)(168,205)(169,210)(170,209)
(171,211)(172,212)(173,216)(174,215)(175,214)(176,213)(177,218)(178,217)
(179,219)(180,220)(181,224)(182,223)(183,222)(184,221)(185,226)(186,225)
(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,234)(194,233)
(195,235)(196,236)(197,240)(198,239)(199,238)(200,237)(243,244)(245,247)
(246,248)(251,252)(253,255)(254,256)(259,260)(261,263)(262,264)(267,268)
(269,271)(270,272)(275,276)(277,279)(278,280)(281,321)(282,322)(283,324)
(284,323)(285,327)(286,328)(287,325)(288,326)(289,329)(290,330)(291,332)
(292,331)(293,335)(294,336)(295,333)(296,334)(297,337)(298,338)(299,340)
(300,339)(301,343)(302,344)(303,341)(304,342)(305,345)(306,346)(307,348)
(308,347)(309,351)(310,352)(311,349)(312,350)(313,353)(314,354)(315,356)
(316,355)(317,359)(318,360)(319,357)(320,358)(361,362)(365,368)(366,367)
(369,370)(373,376)(374,375)(377,378)(381,384)(382,383)(385,386)(389,392)
(390,391)(393,394)(397,400)(398,399)(401,442)(402,441)(403,443)(404,444)
(405,448)(406,447)(407,446)(408,445)(409,450)(410,449)(411,451)(412,452)
(413,456)(414,455)(415,454)(416,453)(417,458)(418,457)(419,459)(420,460)
(421,464)(422,463)(423,462)(424,461)(425,466)(426,465)(427,467)(428,468)
(429,472)(430,471)(431,470)(432,469)(433,474)(434,473)(435,475)(436,476)
(437,480)(438,479)(439,478)(440,477);;
s1 := ( 1,161)( 2,162)( 3,167)( 4,168)( 5,166)( 6,165)( 7,163)( 8,164)
( 9,169)( 10,170)( 11,175)( 12,176)( 13,174)( 14,173)( 15,171)( 16,172)
( 17,177)( 18,178)( 19,183)( 20,184)( 21,182)( 22,181)( 23,179)( 24,180)
( 25,185)( 26,186)( 27,191)( 28,192)( 29,190)( 30,189)( 31,187)( 32,188)
( 33,193)( 34,194)( 35,199)( 36,200)( 37,198)( 38,197)( 39,195)( 40,196)
( 41,121)( 42,122)( 43,127)( 44,128)( 45,126)( 46,125)( 47,123)( 48,124)
( 49,129)( 50,130)( 51,135)( 52,136)( 53,134)( 54,133)( 55,131)( 56,132)
( 57,137)( 58,138)( 59,143)( 60,144)( 61,142)( 62,141)( 63,139)( 64,140)
( 65,145)( 66,146)( 67,151)( 68,152)( 69,150)( 70,149)( 71,147)( 72,148)
( 73,153)( 74,154)( 75,159)( 76,160)( 77,158)( 78,157)( 79,155)( 80,156)
( 81,201)( 82,202)( 83,207)( 84,208)( 85,206)( 86,205)( 87,203)( 88,204)
( 89,209)( 90,210)( 91,215)( 92,216)( 93,214)( 94,213)( 95,211)( 96,212)
( 97,217)( 98,218)( 99,223)(100,224)(101,222)(102,221)(103,219)(104,220)
(105,225)(106,226)(107,231)(108,232)(109,230)(110,229)(111,227)(112,228)
(113,233)(114,234)(115,239)(116,240)(117,238)(118,237)(119,235)(120,236)
(241,401)(242,402)(243,407)(244,408)(245,406)(246,405)(247,403)(248,404)
(249,409)(250,410)(251,415)(252,416)(253,414)(254,413)(255,411)(256,412)
(257,417)(258,418)(259,423)(260,424)(261,422)(262,421)(263,419)(264,420)
(265,425)(266,426)(267,431)(268,432)(269,430)(270,429)(271,427)(272,428)
(273,433)(274,434)(275,439)(276,440)(277,438)(278,437)(279,435)(280,436)
(281,361)(282,362)(283,367)(284,368)(285,366)(286,365)(287,363)(288,364)
(289,369)(290,370)(291,375)(292,376)(293,374)(294,373)(295,371)(296,372)
(297,377)(298,378)(299,383)(300,384)(301,382)(302,381)(303,379)(304,380)
(305,385)(306,386)(307,391)(308,392)(309,390)(310,389)(311,387)(312,388)
(313,393)(314,394)(315,399)(316,400)(317,398)(318,397)(319,395)(320,396)
(321,441)(322,442)(323,447)(324,448)(325,446)(326,445)(327,443)(328,444)
(329,449)(330,450)(331,455)(332,456)(333,454)(334,453)(335,451)(336,452)
(337,457)(338,458)(339,463)(340,464)(341,462)(342,461)(343,459)(344,460)
(345,465)(346,466)(347,471)(348,472)(349,470)(350,469)(351,467)(352,468)
(353,473)(354,474)(355,479)(356,480)(357,478)(358,477)(359,475)(360,476);;
s2 := ( 1,123)( 2,124)( 3,121)( 4,122)( 5,126)( 6,125)( 7,127)( 8,128)
( 9,155)( 10,156)( 11,153)( 12,154)( 13,158)( 14,157)( 15,159)( 16,160)
( 17,147)( 18,148)( 19,145)( 20,146)( 21,150)( 22,149)( 23,151)( 24,152)
( 25,139)( 26,140)( 27,137)( 28,138)( 29,142)( 30,141)( 31,143)( 32,144)
( 33,131)( 34,132)( 35,129)( 36,130)( 37,134)( 38,133)( 39,135)( 40,136)
( 41,203)( 42,204)( 43,201)( 44,202)( 45,206)( 46,205)( 47,207)( 48,208)
( 49,235)( 50,236)( 51,233)( 52,234)( 53,238)( 54,237)( 55,239)( 56,240)
( 57,227)( 58,228)( 59,225)( 60,226)( 61,230)( 62,229)( 63,231)( 64,232)
( 65,219)( 66,220)( 67,217)( 68,218)( 69,222)( 70,221)( 71,223)( 72,224)
( 73,211)( 74,212)( 75,209)( 76,210)( 77,214)( 78,213)( 79,215)( 80,216)
( 81,163)( 82,164)( 83,161)( 84,162)( 85,166)( 86,165)( 87,167)( 88,168)
( 89,195)( 90,196)( 91,193)( 92,194)( 93,198)( 94,197)( 95,199)( 96,200)
( 97,187)( 98,188)( 99,185)(100,186)(101,190)(102,189)(103,191)(104,192)
(105,179)(106,180)(107,177)(108,178)(109,182)(110,181)(111,183)(112,184)
(113,171)(114,172)(115,169)(116,170)(117,174)(118,173)(119,175)(120,176)
(241,363)(242,364)(243,361)(244,362)(245,366)(246,365)(247,367)(248,368)
(249,395)(250,396)(251,393)(252,394)(253,398)(254,397)(255,399)(256,400)
(257,387)(258,388)(259,385)(260,386)(261,390)(262,389)(263,391)(264,392)
(265,379)(266,380)(267,377)(268,378)(269,382)(270,381)(271,383)(272,384)
(273,371)(274,372)(275,369)(276,370)(277,374)(278,373)(279,375)(280,376)
(281,443)(282,444)(283,441)(284,442)(285,446)(286,445)(287,447)(288,448)
(289,475)(290,476)(291,473)(292,474)(293,478)(294,477)(295,479)(296,480)
(297,467)(298,468)(299,465)(300,466)(301,470)(302,469)(303,471)(304,472)
(305,459)(306,460)(307,457)(308,458)(309,462)(310,461)(311,463)(312,464)
(313,451)(314,452)(315,449)(316,450)(317,454)(318,453)(319,455)(320,456)
(321,403)(322,404)(323,401)(324,402)(325,406)(326,405)(327,407)(328,408)
(329,435)(330,436)(331,433)(332,434)(333,438)(334,437)(335,439)(336,440)
(337,427)(338,428)(339,425)(340,426)(341,430)(342,429)(343,431)(344,432)
(345,419)(346,420)(347,417)(348,418)(349,422)(350,421)(351,423)(352,424)
(353,411)(354,412)(355,409)(356,410)(357,414)(358,413)(359,415)(360,416);;
s3 := ( 1,249)( 2,250)( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)( 8,256)
( 9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)( 16,248)
( 17,273)( 18,274)( 19,275)( 20,276)( 21,277)( 22,278)( 23,279)( 24,280)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)( 40,264)
( 41,289)( 42,290)( 43,291)( 44,292)( 45,293)( 46,294)( 47,295)( 48,296)
( 49,281)( 50,282)( 51,283)( 52,284)( 53,285)( 54,286)( 55,287)( 56,288)
( 57,313)( 58,314)( 59,315)( 60,316)( 61,317)( 62,318)( 63,319)( 64,320)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)( 80,304)
( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)
( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)( 96,328)
( 97,353)( 98,354)( 99,355)(100,356)(101,357)(102,358)(103,359)(104,360)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)
(121,369)(122,370)(123,371)(124,372)(125,373)(126,374)(127,375)(128,376)
(129,361)(130,362)(131,363)(132,364)(133,365)(134,366)(135,367)(136,368)
(137,393)(138,394)(139,395)(140,396)(141,397)(142,398)(143,399)(144,400)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)(160,384)
(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)
(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)
(177,433)(178,434)(179,435)(180,436)(181,437)(182,438)(183,439)(184,440)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)(200,424)
(201,449)(202,450)(203,451)(204,452)(205,453)(206,454)(207,455)(208,456)
(209,441)(210,442)(211,443)(212,444)(213,445)(214,446)(215,447)(216,448)
(217,473)(218,474)(219,475)(220,476)(221,477)(222,478)(223,479)(224,480)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,457)(234,458)(235,459)(236,460)(237,461)(238,462)(239,463)(240,464);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
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(480)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)
( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)
( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)
( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)
( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)
( 65,105)( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)
( 73,113)( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)
(121,122)(125,128)(126,127)(129,130)(133,136)(134,135)(137,138)(141,144)
(142,143)(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)(161,202)
(162,201)(163,203)(164,204)(165,208)(166,207)(167,206)(168,205)(169,210)
(170,209)(171,211)(172,212)(173,216)(174,215)(175,214)(176,213)(177,218)
(178,217)(179,219)(180,220)(181,224)(182,223)(183,222)(184,221)(185,226)
(186,225)(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,234)
(194,233)(195,235)(196,236)(197,240)(198,239)(199,238)(200,237)(243,244)
(245,247)(246,248)(251,252)(253,255)(254,256)(259,260)(261,263)(262,264)
(267,268)(269,271)(270,272)(275,276)(277,279)(278,280)(281,321)(282,322)
(283,324)(284,323)(285,327)(286,328)(287,325)(288,326)(289,329)(290,330)
(291,332)(292,331)(293,335)(294,336)(295,333)(296,334)(297,337)(298,338)
(299,340)(300,339)(301,343)(302,344)(303,341)(304,342)(305,345)(306,346)
(307,348)(308,347)(309,351)(310,352)(311,349)(312,350)(313,353)(314,354)
(315,356)(316,355)(317,359)(318,360)(319,357)(320,358)(361,362)(365,368)
(366,367)(369,370)(373,376)(374,375)(377,378)(381,384)(382,383)(385,386)
(389,392)(390,391)(393,394)(397,400)(398,399)(401,442)(402,441)(403,443)
(404,444)(405,448)(406,447)(407,446)(408,445)(409,450)(410,449)(411,451)
(412,452)(413,456)(414,455)(415,454)(416,453)(417,458)(418,457)(419,459)
(420,460)(421,464)(422,463)(423,462)(424,461)(425,466)(426,465)(427,467)
(428,468)(429,472)(430,471)(431,470)(432,469)(433,474)(434,473)(435,475)
(436,476)(437,480)(438,479)(439,478)(440,477);
s1 := Sym(480)!( 1,161)( 2,162)( 3,167)( 4,168)( 5,166)( 6,165)( 7,163)
( 8,164)( 9,169)( 10,170)( 11,175)( 12,176)( 13,174)( 14,173)( 15,171)
( 16,172)( 17,177)( 18,178)( 19,183)( 20,184)( 21,182)( 22,181)( 23,179)
( 24,180)( 25,185)( 26,186)( 27,191)( 28,192)( 29,190)( 30,189)( 31,187)
( 32,188)( 33,193)( 34,194)( 35,199)( 36,200)( 37,198)( 38,197)( 39,195)
( 40,196)( 41,121)( 42,122)( 43,127)( 44,128)( 45,126)( 46,125)( 47,123)
( 48,124)( 49,129)( 50,130)( 51,135)( 52,136)( 53,134)( 54,133)( 55,131)
( 56,132)( 57,137)( 58,138)( 59,143)( 60,144)( 61,142)( 62,141)( 63,139)
( 64,140)( 65,145)( 66,146)( 67,151)( 68,152)( 69,150)( 70,149)( 71,147)
( 72,148)( 73,153)( 74,154)( 75,159)( 76,160)( 77,158)( 78,157)( 79,155)
( 80,156)( 81,201)( 82,202)( 83,207)( 84,208)( 85,206)( 86,205)( 87,203)
( 88,204)( 89,209)( 90,210)( 91,215)( 92,216)( 93,214)( 94,213)( 95,211)
( 96,212)( 97,217)( 98,218)( 99,223)(100,224)(101,222)(102,221)(103,219)
(104,220)(105,225)(106,226)(107,231)(108,232)(109,230)(110,229)(111,227)
(112,228)(113,233)(114,234)(115,239)(116,240)(117,238)(118,237)(119,235)
(120,236)(241,401)(242,402)(243,407)(244,408)(245,406)(246,405)(247,403)
(248,404)(249,409)(250,410)(251,415)(252,416)(253,414)(254,413)(255,411)
(256,412)(257,417)(258,418)(259,423)(260,424)(261,422)(262,421)(263,419)
(264,420)(265,425)(266,426)(267,431)(268,432)(269,430)(270,429)(271,427)
(272,428)(273,433)(274,434)(275,439)(276,440)(277,438)(278,437)(279,435)
(280,436)(281,361)(282,362)(283,367)(284,368)(285,366)(286,365)(287,363)
(288,364)(289,369)(290,370)(291,375)(292,376)(293,374)(294,373)(295,371)
(296,372)(297,377)(298,378)(299,383)(300,384)(301,382)(302,381)(303,379)
(304,380)(305,385)(306,386)(307,391)(308,392)(309,390)(310,389)(311,387)
(312,388)(313,393)(314,394)(315,399)(316,400)(317,398)(318,397)(319,395)
(320,396)(321,441)(322,442)(323,447)(324,448)(325,446)(326,445)(327,443)
(328,444)(329,449)(330,450)(331,455)(332,456)(333,454)(334,453)(335,451)
(336,452)(337,457)(338,458)(339,463)(340,464)(341,462)(342,461)(343,459)
(344,460)(345,465)(346,466)(347,471)(348,472)(349,470)(350,469)(351,467)
(352,468)(353,473)(354,474)(355,479)(356,480)(357,478)(358,477)(359,475)
(360,476);
s2 := Sym(480)!( 1,123)( 2,124)( 3,121)( 4,122)( 5,126)( 6,125)( 7,127)
( 8,128)( 9,155)( 10,156)( 11,153)( 12,154)( 13,158)( 14,157)( 15,159)
( 16,160)( 17,147)( 18,148)( 19,145)( 20,146)( 21,150)( 22,149)( 23,151)
( 24,152)( 25,139)( 26,140)( 27,137)( 28,138)( 29,142)( 30,141)( 31,143)
( 32,144)( 33,131)( 34,132)( 35,129)( 36,130)( 37,134)( 38,133)( 39,135)
( 40,136)( 41,203)( 42,204)( 43,201)( 44,202)( 45,206)( 46,205)( 47,207)
( 48,208)( 49,235)( 50,236)( 51,233)( 52,234)( 53,238)( 54,237)( 55,239)
( 56,240)( 57,227)( 58,228)( 59,225)( 60,226)( 61,230)( 62,229)( 63,231)
( 64,232)( 65,219)( 66,220)( 67,217)( 68,218)( 69,222)( 70,221)( 71,223)
( 72,224)( 73,211)( 74,212)( 75,209)( 76,210)( 77,214)( 78,213)( 79,215)
( 80,216)( 81,163)( 82,164)( 83,161)( 84,162)( 85,166)( 86,165)( 87,167)
( 88,168)( 89,195)( 90,196)( 91,193)( 92,194)( 93,198)( 94,197)( 95,199)
( 96,200)( 97,187)( 98,188)( 99,185)(100,186)(101,190)(102,189)(103,191)
(104,192)(105,179)(106,180)(107,177)(108,178)(109,182)(110,181)(111,183)
(112,184)(113,171)(114,172)(115,169)(116,170)(117,174)(118,173)(119,175)
(120,176)(241,363)(242,364)(243,361)(244,362)(245,366)(246,365)(247,367)
(248,368)(249,395)(250,396)(251,393)(252,394)(253,398)(254,397)(255,399)
(256,400)(257,387)(258,388)(259,385)(260,386)(261,390)(262,389)(263,391)
(264,392)(265,379)(266,380)(267,377)(268,378)(269,382)(270,381)(271,383)
(272,384)(273,371)(274,372)(275,369)(276,370)(277,374)(278,373)(279,375)
(280,376)(281,443)(282,444)(283,441)(284,442)(285,446)(286,445)(287,447)
(288,448)(289,475)(290,476)(291,473)(292,474)(293,478)(294,477)(295,479)
(296,480)(297,467)(298,468)(299,465)(300,466)(301,470)(302,469)(303,471)
(304,472)(305,459)(306,460)(307,457)(308,458)(309,462)(310,461)(311,463)
(312,464)(313,451)(314,452)(315,449)(316,450)(317,454)(318,453)(319,455)
(320,456)(321,403)(322,404)(323,401)(324,402)(325,406)(326,405)(327,407)
(328,408)(329,435)(330,436)(331,433)(332,434)(333,438)(334,437)(335,439)
(336,440)(337,427)(338,428)(339,425)(340,426)(341,430)(342,429)(343,431)
(344,432)(345,419)(346,420)(347,417)(348,418)(349,422)(350,421)(351,423)
(352,424)(353,411)(354,412)(355,409)(356,410)(357,414)(358,413)(359,415)
(360,416);
s3 := Sym(480)!( 1,249)( 2,250)( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)
( 8,256)( 9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)
( 16,248)( 17,273)( 18,274)( 19,275)( 20,276)( 21,277)( 22,278)( 23,279)
( 24,280)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)
( 40,264)( 41,289)( 42,290)( 43,291)( 44,292)( 45,293)( 46,294)( 47,295)
( 48,296)( 49,281)( 50,282)( 51,283)( 52,284)( 53,285)( 54,286)( 55,287)
( 56,288)( 57,313)( 58,314)( 59,315)( 60,316)( 61,317)( 62,318)( 63,319)
( 64,320)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)
( 80,304)( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)
( 88,336)( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)
( 96,328)( 97,353)( 98,354)( 99,355)(100,356)(101,357)(102,358)(103,359)
(104,360)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)
(120,344)(121,369)(122,370)(123,371)(124,372)(125,373)(126,374)(127,375)
(128,376)(129,361)(130,362)(131,363)(132,364)(133,365)(134,366)(135,367)
(136,368)(137,393)(138,394)(139,395)(140,396)(141,397)(142,398)(143,399)
(144,400)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)
(160,384)(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)
(168,416)(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)
(176,408)(177,433)(178,434)(179,435)(180,436)(181,437)(182,438)(183,439)
(184,440)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)
(200,424)(201,449)(202,450)(203,451)(204,452)(205,453)(206,454)(207,455)
(208,456)(209,441)(210,442)(211,443)(212,444)(213,445)(214,446)(215,447)
(216,448)(217,473)(218,474)(219,475)(220,476)(221,477)(222,478)(223,479)
(224,480)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,457)(234,458)(235,459)(236,460)(237,461)(238,462)(239,463)
(240,464);
poly := sub<Sym(480)|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,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
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