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