Polytope of Type {8,6,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,15}*1920
if this polytope has a name.
Group : SmallGroup(1920,238882)
Rank : 4
Schlafli Type : {8,6,15}
Number of vertices, edges, etc : 8, 32, 60, 20
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 : {4,6,15}*960
4-fold quotients : {2,6,15}*480
5-fold quotients : {8,6,3}*384
10-fold quotients : {4,6,3}*192
12-fold quotients : {8,2,5}*160
20-fold quotients : {2,6,3}*96
24-fold quotients : {4,2,5}*80
40-fold quotients : {2,3,3}*48
48-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)( 8,248)
( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,421)(122,422)(123,423)(124,424)(125,425)(126,426)(127,427)(128,428)
(129,429)(130,430)(131,431)(132,432)(133,433)(134,434)(135,435)(136,436)
(137,437)(138,438)(139,439)(140,440)(141,441)(142,442)(143,443)(144,444)
(145,445)(146,446)(147,447)(148,448)(149,449)(150,450)(151,451)(152,452)
(153,453)(154,454)(155,455)(156,456)(157,457)(158,458)(159,459)(160,460)
(161,461)(162,462)(163,463)(164,464)(165,465)(166,466)(167,467)(168,468)
(169,469)(170,470)(171,471)(172,472)(173,473)(174,474)(175,475)(176,476)
(177,477)(178,478)(179,479)(180,480)(181,361)(182,362)(183,363)(184,364)
(185,365)(186,366)(187,367)(188,368)(189,369)(190,370)(191,371)(192,372)
(193,373)(194,374)(195,375)(196,376)(197,377)(198,378)(199,379)(200,380)
(201,381)(202,382)(203,383)(204,384)(205,385)(206,386)(207,387)(208,388)
(209,389)(210,390)(211,391)(212,392)(213,393)(214,394)(215,395)(216,396)
(217,397)(218,398)(219,399)(220,400)(221,401)(222,402)(223,403)(224,404)
(225,405)(226,406)(227,407)(228,408)(229,409)(230,410)(231,411)(232,412)
(233,413)(234,414)(235,415)(236,416)(237,417)(238,418)(239,419)(240,420);;
s1 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)( 23, 44)
( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)( 31, 52)
( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)( 39, 60)
( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)( 82,102)
( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)( 90,110)
( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)( 98,118)
( 99,120)(100,119)(121,181)(122,182)(123,184)(124,183)(125,185)(126,186)
(127,188)(128,187)(129,189)(130,190)(131,192)(132,191)(133,193)(134,194)
(135,196)(136,195)(137,197)(138,198)(139,200)(140,199)(141,221)(142,222)
(143,224)(144,223)(145,225)(146,226)(147,228)(148,227)(149,229)(150,230)
(151,232)(152,231)(153,233)(154,234)(155,236)(156,235)(157,237)(158,238)
(159,240)(160,239)(161,201)(162,202)(163,204)(164,203)(165,205)(166,206)
(167,208)(168,207)(169,209)(170,210)(171,212)(172,211)(173,213)(174,214)
(175,216)(176,215)(177,217)(178,218)(179,220)(180,219)(241,361)(242,362)
(243,364)(244,363)(245,365)(246,366)(247,368)(248,367)(249,369)(250,370)
(251,372)(252,371)(253,373)(254,374)(255,376)(256,375)(257,377)(258,378)
(259,380)(260,379)(261,401)(262,402)(263,404)(264,403)(265,405)(266,406)
(267,408)(268,407)(269,409)(270,410)(271,412)(272,411)(273,413)(274,414)
(275,416)(276,415)(277,417)(278,418)(279,420)(280,419)(281,381)(282,382)
(283,384)(284,383)(285,385)(286,386)(287,388)(288,387)(289,389)(290,390)
(291,392)(292,391)(293,393)(294,394)(295,396)(296,395)(297,397)(298,398)
(299,400)(300,399)(301,421)(302,422)(303,424)(304,423)(305,425)(306,426)
(307,428)(308,427)(309,429)(310,430)(311,432)(312,431)(313,433)(314,434)
(315,436)(316,435)(317,437)(318,438)(319,440)(320,439)(321,461)(322,462)
(323,464)(324,463)(325,465)(326,466)(327,468)(328,467)(329,469)(330,470)
(331,472)(332,471)(333,473)(334,474)(335,476)(336,475)(337,477)(338,478)
(339,480)(340,479)(341,441)(342,442)(343,444)(344,443)(345,445)(346,446)
(347,448)(348,447)(349,449)(350,450)(351,452)(352,451)(353,453)(354,454)
(355,456)(356,455)(357,457)(358,458)(359,460)(360,459);;
s2 := ( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 37)( 6, 40)( 7, 39)( 8, 38)
( 9, 33)( 10, 36)( 11, 35)( 12, 34)( 13, 29)( 14, 32)( 15, 31)( 16, 30)
( 17, 25)( 18, 28)( 19, 27)( 20, 26)( 42, 44)( 45, 57)( 46, 60)( 47, 59)
( 48, 58)( 49, 53)( 50, 56)( 51, 55)( 52, 54)( 61, 81)( 62, 84)( 63, 83)
( 64, 82)( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69, 93)( 70, 96)( 71, 95)
( 72, 94)( 73, 89)( 74, 92)( 75, 91)( 76, 90)( 77, 85)( 78, 88)( 79, 87)
( 80, 86)(102,104)(105,117)(106,120)(107,119)(108,118)(109,113)(110,116)
(111,115)(112,114)(121,141)(122,144)(123,143)(124,142)(125,157)(126,160)
(127,159)(128,158)(129,153)(130,156)(131,155)(132,154)(133,149)(134,152)
(135,151)(136,150)(137,145)(138,148)(139,147)(140,146)(162,164)(165,177)
(166,180)(167,179)(168,178)(169,173)(170,176)(171,175)(172,174)(181,201)
(182,204)(183,203)(184,202)(185,217)(186,220)(187,219)(188,218)(189,213)
(190,216)(191,215)(192,214)(193,209)(194,212)(195,211)(196,210)(197,205)
(198,208)(199,207)(200,206)(222,224)(225,237)(226,240)(227,239)(228,238)
(229,233)(230,236)(231,235)(232,234)(241,261)(242,264)(243,263)(244,262)
(245,277)(246,280)(247,279)(248,278)(249,273)(250,276)(251,275)(252,274)
(253,269)(254,272)(255,271)(256,270)(257,265)(258,268)(259,267)(260,266)
(282,284)(285,297)(286,300)(287,299)(288,298)(289,293)(290,296)(291,295)
(292,294)(301,321)(302,324)(303,323)(304,322)(305,337)(306,340)(307,339)
(308,338)(309,333)(310,336)(311,335)(312,334)(313,329)(314,332)(315,331)
(316,330)(317,325)(318,328)(319,327)(320,326)(342,344)(345,357)(346,360)
(347,359)(348,358)(349,353)(350,356)(351,355)(352,354)(361,381)(362,384)
(363,383)(364,382)(365,397)(366,400)(367,399)(368,398)(369,393)(370,396)
(371,395)(372,394)(373,389)(374,392)(375,391)(376,390)(377,385)(378,388)
(379,387)(380,386)(402,404)(405,417)(406,420)(407,419)(408,418)(409,413)
(410,416)(411,415)(412,414)(421,441)(422,444)(423,443)(424,442)(425,457)
(426,460)(427,459)(428,458)(429,453)(430,456)(431,455)(432,454)(433,449)
(434,452)(435,451)(436,450)(437,445)(438,448)(439,447)(440,446)(462,464)
(465,477)(466,480)(467,479)(468,478)(469,473)(470,476)(471,475)(472,474);;
s3 := ( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9, 18)( 10, 17)( 11, 19)( 12, 20)
( 13, 14)( 21, 46)( 22, 45)( 23, 47)( 24, 48)( 25, 42)( 26, 41)( 27, 43)
( 28, 44)( 29, 58)( 30, 57)( 31, 59)( 32, 60)( 33, 54)( 34, 53)( 35, 55)
( 36, 56)( 37, 50)( 38, 49)( 39, 51)( 40, 52)( 61, 66)( 62, 65)( 63, 67)
( 64, 68)( 69, 78)( 70, 77)( 71, 79)( 72, 80)( 73, 74)( 81,106)( 82,105)
( 83,107)( 84,108)( 85,102)( 86,101)( 87,103)( 88,104)( 89,118)( 90,117)
( 91,119)( 92,120)( 93,114)( 94,113)( 95,115)( 96,116)( 97,110)( 98,109)
( 99,111)(100,112)(121,126)(122,125)(123,127)(124,128)(129,138)(130,137)
(131,139)(132,140)(133,134)(141,166)(142,165)(143,167)(144,168)(145,162)
(146,161)(147,163)(148,164)(149,178)(150,177)(151,179)(152,180)(153,174)
(154,173)(155,175)(156,176)(157,170)(158,169)(159,171)(160,172)(181,186)
(182,185)(183,187)(184,188)(189,198)(190,197)(191,199)(192,200)(193,194)
(201,226)(202,225)(203,227)(204,228)(205,222)(206,221)(207,223)(208,224)
(209,238)(210,237)(211,239)(212,240)(213,234)(214,233)(215,235)(216,236)
(217,230)(218,229)(219,231)(220,232)(241,246)(242,245)(243,247)(244,248)
(249,258)(250,257)(251,259)(252,260)(253,254)(261,286)(262,285)(263,287)
(264,288)(265,282)(266,281)(267,283)(268,284)(269,298)(270,297)(271,299)
(272,300)(273,294)(274,293)(275,295)(276,296)(277,290)(278,289)(279,291)
(280,292)(301,306)(302,305)(303,307)(304,308)(309,318)(310,317)(311,319)
(312,320)(313,314)(321,346)(322,345)(323,347)(324,348)(325,342)(326,341)
(327,343)(328,344)(329,358)(330,357)(331,359)(332,360)(333,354)(334,353)
(335,355)(336,356)(337,350)(338,349)(339,351)(340,352)(361,366)(362,365)
(363,367)(364,368)(369,378)(370,377)(371,379)(372,380)(373,374)(381,406)
(382,405)(383,407)(384,408)(385,402)(386,401)(387,403)(388,404)(389,418)
(390,417)(391,419)(392,420)(393,414)(394,413)(395,415)(396,416)(397,410)
(398,409)(399,411)(400,412)(421,426)(422,425)(423,427)(424,428)(429,438)
(430,437)(431,439)(432,440)(433,434)(441,466)(442,465)(443,467)(444,468)
(445,462)(446,461)(447,463)(448,464)(449,478)(450,477)(451,479)(452,480)
(453,474)(454,473)(455,475)(456,476)(457,470)(458,469)(459,471)(460,472);;
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*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3,
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)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,246)( 7,247)
( 8,248)( 9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,421)(122,422)(123,423)(124,424)(125,425)(126,426)(127,427)
(128,428)(129,429)(130,430)(131,431)(132,432)(133,433)(134,434)(135,435)
(136,436)(137,437)(138,438)(139,439)(140,440)(141,441)(142,442)(143,443)
(144,444)(145,445)(146,446)(147,447)(148,448)(149,449)(150,450)(151,451)
(152,452)(153,453)(154,454)(155,455)(156,456)(157,457)(158,458)(159,459)
(160,460)(161,461)(162,462)(163,463)(164,464)(165,465)(166,466)(167,467)
(168,468)(169,469)(170,470)(171,471)(172,472)(173,473)(174,474)(175,475)
(176,476)(177,477)(178,478)(179,479)(180,480)(181,361)(182,362)(183,363)
(184,364)(185,365)(186,366)(187,367)(188,368)(189,369)(190,370)(191,371)
(192,372)(193,373)(194,374)(195,375)(196,376)(197,377)(198,378)(199,379)
(200,380)(201,381)(202,382)(203,383)(204,384)(205,385)(206,386)(207,387)
(208,388)(209,389)(210,390)(211,391)(212,392)(213,393)(214,394)(215,395)
(216,396)(217,397)(218,398)(219,399)(220,400)(221,401)(222,402)(223,403)
(224,404)(225,405)(226,406)(227,407)(228,408)(229,409)(230,410)(231,411)
(232,412)(233,413)(234,414)(235,415)(236,416)(237,417)(238,418)(239,419)
(240,420);
s1 := Sym(480)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)
( 23, 44)( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)
( 31, 52)( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)
( 39, 60)( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)
( 82,102)( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)
( 90,110)( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)
( 98,118)( 99,120)(100,119)(121,181)(122,182)(123,184)(124,183)(125,185)
(126,186)(127,188)(128,187)(129,189)(130,190)(131,192)(132,191)(133,193)
(134,194)(135,196)(136,195)(137,197)(138,198)(139,200)(140,199)(141,221)
(142,222)(143,224)(144,223)(145,225)(146,226)(147,228)(148,227)(149,229)
(150,230)(151,232)(152,231)(153,233)(154,234)(155,236)(156,235)(157,237)
(158,238)(159,240)(160,239)(161,201)(162,202)(163,204)(164,203)(165,205)
(166,206)(167,208)(168,207)(169,209)(170,210)(171,212)(172,211)(173,213)
(174,214)(175,216)(176,215)(177,217)(178,218)(179,220)(180,219)(241,361)
(242,362)(243,364)(244,363)(245,365)(246,366)(247,368)(248,367)(249,369)
(250,370)(251,372)(252,371)(253,373)(254,374)(255,376)(256,375)(257,377)
(258,378)(259,380)(260,379)(261,401)(262,402)(263,404)(264,403)(265,405)
(266,406)(267,408)(268,407)(269,409)(270,410)(271,412)(272,411)(273,413)
(274,414)(275,416)(276,415)(277,417)(278,418)(279,420)(280,419)(281,381)
(282,382)(283,384)(284,383)(285,385)(286,386)(287,388)(288,387)(289,389)
(290,390)(291,392)(292,391)(293,393)(294,394)(295,396)(296,395)(297,397)
(298,398)(299,400)(300,399)(301,421)(302,422)(303,424)(304,423)(305,425)
(306,426)(307,428)(308,427)(309,429)(310,430)(311,432)(312,431)(313,433)
(314,434)(315,436)(316,435)(317,437)(318,438)(319,440)(320,439)(321,461)
(322,462)(323,464)(324,463)(325,465)(326,466)(327,468)(328,467)(329,469)
(330,470)(331,472)(332,471)(333,473)(334,474)(335,476)(336,475)(337,477)
(338,478)(339,480)(340,479)(341,441)(342,442)(343,444)(344,443)(345,445)
(346,446)(347,448)(348,447)(349,449)(350,450)(351,452)(352,451)(353,453)
(354,454)(355,456)(356,455)(357,457)(358,458)(359,460)(360,459);
s2 := Sym(480)!( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 37)( 6, 40)( 7, 39)
( 8, 38)( 9, 33)( 10, 36)( 11, 35)( 12, 34)( 13, 29)( 14, 32)( 15, 31)
( 16, 30)( 17, 25)( 18, 28)( 19, 27)( 20, 26)( 42, 44)( 45, 57)( 46, 60)
( 47, 59)( 48, 58)( 49, 53)( 50, 56)( 51, 55)( 52, 54)( 61, 81)( 62, 84)
( 63, 83)( 64, 82)( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69, 93)( 70, 96)
( 71, 95)( 72, 94)( 73, 89)( 74, 92)( 75, 91)( 76, 90)( 77, 85)( 78, 88)
( 79, 87)( 80, 86)(102,104)(105,117)(106,120)(107,119)(108,118)(109,113)
(110,116)(111,115)(112,114)(121,141)(122,144)(123,143)(124,142)(125,157)
(126,160)(127,159)(128,158)(129,153)(130,156)(131,155)(132,154)(133,149)
(134,152)(135,151)(136,150)(137,145)(138,148)(139,147)(140,146)(162,164)
(165,177)(166,180)(167,179)(168,178)(169,173)(170,176)(171,175)(172,174)
(181,201)(182,204)(183,203)(184,202)(185,217)(186,220)(187,219)(188,218)
(189,213)(190,216)(191,215)(192,214)(193,209)(194,212)(195,211)(196,210)
(197,205)(198,208)(199,207)(200,206)(222,224)(225,237)(226,240)(227,239)
(228,238)(229,233)(230,236)(231,235)(232,234)(241,261)(242,264)(243,263)
(244,262)(245,277)(246,280)(247,279)(248,278)(249,273)(250,276)(251,275)
(252,274)(253,269)(254,272)(255,271)(256,270)(257,265)(258,268)(259,267)
(260,266)(282,284)(285,297)(286,300)(287,299)(288,298)(289,293)(290,296)
(291,295)(292,294)(301,321)(302,324)(303,323)(304,322)(305,337)(306,340)
(307,339)(308,338)(309,333)(310,336)(311,335)(312,334)(313,329)(314,332)
(315,331)(316,330)(317,325)(318,328)(319,327)(320,326)(342,344)(345,357)
(346,360)(347,359)(348,358)(349,353)(350,356)(351,355)(352,354)(361,381)
(362,384)(363,383)(364,382)(365,397)(366,400)(367,399)(368,398)(369,393)
(370,396)(371,395)(372,394)(373,389)(374,392)(375,391)(376,390)(377,385)
(378,388)(379,387)(380,386)(402,404)(405,417)(406,420)(407,419)(408,418)
(409,413)(410,416)(411,415)(412,414)(421,441)(422,444)(423,443)(424,442)
(425,457)(426,460)(427,459)(428,458)(429,453)(430,456)(431,455)(432,454)
(433,449)(434,452)(435,451)(436,450)(437,445)(438,448)(439,447)(440,446)
(462,464)(465,477)(466,480)(467,479)(468,478)(469,473)(470,476)(471,475)
(472,474);
s3 := Sym(480)!( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9, 18)( 10, 17)( 11, 19)
( 12, 20)( 13, 14)( 21, 46)( 22, 45)( 23, 47)( 24, 48)( 25, 42)( 26, 41)
( 27, 43)( 28, 44)( 29, 58)( 30, 57)( 31, 59)( 32, 60)( 33, 54)( 34, 53)
( 35, 55)( 36, 56)( 37, 50)( 38, 49)( 39, 51)( 40, 52)( 61, 66)( 62, 65)
( 63, 67)( 64, 68)( 69, 78)( 70, 77)( 71, 79)( 72, 80)( 73, 74)( 81,106)
( 82,105)( 83,107)( 84,108)( 85,102)( 86,101)( 87,103)( 88,104)( 89,118)
( 90,117)( 91,119)( 92,120)( 93,114)( 94,113)( 95,115)( 96,116)( 97,110)
( 98,109)( 99,111)(100,112)(121,126)(122,125)(123,127)(124,128)(129,138)
(130,137)(131,139)(132,140)(133,134)(141,166)(142,165)(143,167)(144,168)
(145,162)(146,161)(147,163)(148,164)(149,178)(150,177)(151,179)(152,180)
(153,174)(154,173)(155,175)(156,176)(157,170)(158,169)(159,171)(160,172)
(181,186)(182,185)(183,187)(184,188)(189,198)(190,197)(191,199)(192,200)
(193,194)(201,226)(202,225)(203,227)(204,228)(205,222)(206,221)(207,223)
(208,224)(209,238)(210,237)(211,239)(212,240)(213,234)(214,233)(215,235)
(216,236)(217,230)(218,229)(219,231)(220,232)(241,246)(242,245)(243,247)
(244,248)(249,258)(250,257)(251,259)(252,260)(253,254)(261,286)(262,285)
(263,287)(264,288)(265,282)(266,281)(267,283)(268,284)(269,298)(270,297)
(271,299)(272,300)(273,294)(274,293)(275,295)(276,296)(277,290)(278,289)
(279,291)(280,292)(301,306)(302,305)(303,307)(304,308)(309,318)(310,317)
(311,319)(312,320)(313,314)(321,346)(322,345)(323,347)(324,348)(325,342)
(326,341)(327,343)(328,344)(329,358)(330,357)(331,359)(332,360)(333,354)
(334,353)(335,355)(336,356)(337,350)(338,349)(339,351)(340,352)(361,366)
(362,365)(363,367)(364,368)(369,378)(370,377)(371,379)(372,380)(373,374)
(381,406)(382,405)(383,407)(384,408)(385,402)(386,401)(387,403)(388,404)
(389,418)(390,417)(391,419)(392,420)(393,414)(394,413)(395,415)(396,416)
(397,410)(398,409)(399,411)(400,412)(421,426)(422,425)(423,427)(424,428)
(429,438)(430,437)(431,439)(432,440)(433,434)(441,466)(442,465)(443,467)
(444,468)(445,462)(446,461)(447,463)(448,464)(449,478)(450,477)(451,479)
(452,480)(453,474)(454,473)(455,475)(456,476)(457,470)(458,469)(459,471)
(460,472);
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*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope