Polytope of Type {20,8,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8,3}*1920
if this polytope has a name.
Group : SmallGroup(1920,238596)
Rank : 4
Schlafli Type : {20,8,3}
Number of vertices, edges, etc : 20, 160, 24, 6
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 : {20,4,3}*960, {10,8,3}*960
4-fold quotients : {10,4,3}*480
5-fold quotients : {4,8,3}*384
8-fold quotients : {20,2,3}*240
10-fold quotients : {4,4,3}*192b, {2,8,3}*192
16-fold quotients : {10,2,3}*120
20-fold quotients : {2,4,3}*96
32-fold quotients : {5,2,3}*60
40-fold quotients : {4,2,3}*48, {2,4,3}*48
80-fold quotients : {2,2,3}*24
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)
(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)
(249,393)(250,394)(251,395)(252,396)(253,397)(254,398)(255,399)(256,400)
(257,385)(258,386)(259,387)(260,388)(261,389)(262,390)(263,391)(264,392)
(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)(272,384)
(273,369)(274,370)(275,371)(276,372)(277,373)(278,374)(279,375)(280,376)
(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,407)(288,408)
(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)(296,440)
(297,425)(298,426)(299,427)(300,428)(301,429)(302,430)(303,431)(304,432)
(305,417)(306,418)(307,419)(308,420)(309,421)(310,422)(311,423)(312,424)
(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)(320,416)
(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)(328,448)
(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)(336,480)
(337,465)(338,466)(339,467)(340,468)(341,469)(342,470)(343,471)(344,472)
(345,457)(346,458)(347,459)(348,460)(349,461)(350,462)(351,463)(352,464)
(353,449)(354,450)(355,451)(356,452)(357,453)(358,454)(359,455)(360,456);;
s1 := ( 1,253)( 2,254)( 3,256)( 4,255)( 5,250)( 6,249)( 7,251)( 8,252)
( 9,245)( 10,246)( 11,248)( 12,247)( 13,242)( 14,241)( 15,243)( 16,244)
( 17,277)( 18,278)( 19,280)( 20,279)( 21,274)( 22,273)( 23,275)( 24,276)
( 25,269)( 26,270)( 27,272)( 28,271)( 29,266)( 30,265)( 31,267)( 32,268)
( 33,261)( 34,262)( 35,264)( 36,263)( 37,258)( 38,257)( 39,259)( 40,260)
( 41,293)( 42,294)( 43,296)( 44,295)( 45,290)( 46,289)( 47,291)( 48,292)
( 49,285)( 50,286)( 51,288)( 52,287)( 53,282)( 54,281)( 55,283)( 56,284)
( 57,317)( 58,318)( 59,320)( 60,319)( 61,314)( 62,313)( 63,315)( 64,316)
( 65,309)( 66,310)( 67,312)( 68,311)( 69,306)( 70,305)( 71,307)( 72,308)
( 73,301)( 74,302)( 75,304)( 76,303)( 77,298)( 78,297)( 79,299)( 80,300)
( 81,333)( 82,334)( 83,336)( 84,335)( 85,330)( 86,329)( 87,331)( 88,332)
( 89,325)( 90,326)( 91,328)( 92,327)( 93,322)( 94,321)( 95,323)( 96,324)
( 97,357)( 98,358)( 99,360)(100,359)(101,354)(102,353)(103,355)(104,356)
(105,349)(106,350)(107,352)(108,351)(109,346)(110,345)(111,347)(112,348)
(113,341)(114,342)(115,344)(116,343)(117,338)(118,337)(119,339)(120,340)
(121,373)(122,374)(123,376)(124,375)(125,370)(126,369)(127,371)(128,372)
(129,365)(130,366)(131,368)(132,367)(133,362)(134,361)(135,363)(136,364)
(137,397)(138,398)(139,400)(140,399)(141,394)(142,393)(143,395)(144,396)
(145,389)(146,390)(147,392)(148,391)(149,386)(150,385)(151,387)(152,388)
(153,381)(154,382)(155,384)(156,383)(157,378)(158,377)(159,379)(160,380)
(161,413)(162,414)(163,416)(164,415)(165,410)(166,409)(167,411)(168,412)
(169,405)(170,406)(171,408)(172,407)(173,402)(174,401)(175,403)(176,404)
(177,437)(178,438)(179,440)(180,439)(181,434)(182,433)(183,435)(184,436)
(185,429)(186,430)(187,432)(188,431)(189,426)(190,425)(191,427)(192,428)
(193,421)(194,422)(195,424)(196,423)(197,418)(198,417)(199,419)(200,420)
(201,453)(202,454)(203,456)(204,455)(205,450)(206,449)(207,451)(208,452)
(209,445)(210,446)(211,448)(212,447)(213,442)(214,441)(215,443)(216,444)
(217,477)(218,478)(219,480)(220,479)(221,474)(222,473)(223,475)(224,476)
(225,469)(226,470)(227,472)(228,471)(229,466)(230,465)(231,467)(232,468)
(233,461)(234,462)(235,464)(236,463)(237,458)(238,457)(239,459)(240,460);;
s2 := ( 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)(123,124)
(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)(142,144)
(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(161,201)(162,202)
(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)
(171,212)(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)(178,218)
(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)(186,226)
(187,228)(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)
(195,236)(196,235)(197,239)(198,240)(199,237)(200,238)(241,242)(245,248)
(246,247)(249,250)(253,256)(254,255)(257,258)(261,264)(262,263)(265,266)
(269,272)(270,271)(273,274)(277,280)(278,279)(281,322)(282,321)(283,323)
(284,324)(285,328)(286,327)(287,326)(288,325)(289,330)(290,329)(291,331)
(292,332)(293,336)(294,335)(295,334)(296,333)(297,338)(298,337)(299,339)
(300,340)(301,344)(302,343)(303,342)(304,341)(305,346)(306,345)(307,347)
(308,348)(309,352)(310,351)(311,350)(312,349)(313,354)(314,353)(315,355)
(316,356)(317,360)(318,359)(319,358)(320,357)(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);;
s3 := ( 1, 41)( 2, 42)( 3, 47)( 4, 48)( 5, 46)( 6, 45)( 7, 43)( 8, 44)
( 9, 49)( 10, 50)( 11, 55)( 12, 56)( 13, 54)( 14, 53)( 15, 51)( 16, 52)
( 17, 57)( 18, 58)( 19, 63)( 20, 64)( 21, 62)( 22, 61)( 23, 59)( 24, 60)
( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)( 32, 68)
( 33, 73)( 34, 74)( 35, 79)( 36, 80)( 37, 78)( 38, 77)( 39, 75)( 40, 76)
( 83, 87)( 84, 88)( 85, 86)( 91, 95)( 92, 96)( 93, 94)( 99,103)(100,104)
(101,102)(107,111)(108,112)(109,110)(115,119)(116,120)(117,118)(121,161)
(122,162)(123,167)(124,168)(125,166)(126,165)(127,163)(128,164)(129,169)
(130,170)(131,175)(132,176)(133,174)(134,173)(135,171)(136,172)(137,177)
(138,178)(139,183)(140,184)(141,182)(142,181)(143,179)(144,180)(145,185)
(146,186)(147,191)(148,192)(149,190)(150,189)(151,187)(152,188)(153,193)
(154,194)(155,199)(156,200)(157,198)(158,197)(159,195)(160,196)(203,207)
(204,208)(205,206)(211,215)(212,216)(213,214)(219,223)(220,224)(221,222)
(227,231)(228,232)(229,230)(235,239)(236,240)(237,238)(241,282)(242,281)
(243,288)(244,287)(245,285)(246,286)(247,284)(248,283)(249,290)(250,289)
(251,296)(252,295)(253,293)(254,294)(255,292)(256,291)(257,298)(258,297)
(259,304)(260,303)(261,301)(262,302)(263,300)(264,299)(265,306)(266,305)
(267,312)(268,311)(269,309)(270,310)(271,308)(272,307)(273,314)(274,313)
(275,320)(276,319)(277,317)(278,318)(279,316)(280,315)(321,322)(323,328)
(324,327)(329,330)(331,336)(332,335)(337,338)(339,344)(340,343)(345,346)
(347,352)(348,351)(353,354)(355,360)(356,359)(361,402)(362,401)(363,408)
(364,407)(365,405)(366,406)(367,404)(368,403)(369,410)(370,409)(371,416)
(372,415)(373,413)(374,414)(375,412)(376,411)(377,418)(378,417)(379,424)
(380,423)(381,421)(382,422)(383,420)(384,419)(385,426)(386,425)(387,432)
(388,431)(389,429)(390,430)(391,428)(392,427)(393,434)(394,433)(395,440)
(396,439)(397,437)(398,438)(399,436)(400,435)(441,442)(443,448)(444,447)
(449,450)(451,456)(452,455)(457,458)(459,464)(460,463)(465,466)(467,472)
(468,471)(473,474)(475,480)(476,479);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)
(248,368)(249,393)(250,394)(251,395)(252,396)(253,397)(254,398)(255,399)
(256,400)(257,385)(258,386)(259,387)(260,388)(261,389)(262,390)(263,391)
(264,392)(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)
(272,384)(273,369)(274,370)(275,371)(276,372)(277,373)(278,374)(279,375)
(280,376)(281,401)(282,402)(283,403)(284,404)(285,405)(286,406)(287,407)
(288,408)(289,433)(290,434)(291,435)(292,436)(293,437)(294,438)(295,439)
(296,440)(297,425)(298,426)(299,427)(300,428)(301,429)(302,430)(303,431)
(304,432)(305,417)(306,418)(307,419)(308,420)(309,421)(310,422)(311,423)
(312,424)(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)
(320,416)(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)
(328,448)(329,473)(330,474)(331,475)(332,476)(333,477)(334,478)(335,479)
(336,480)(337,465)(338,466)(339,467)(340,468)(341,469)(342,470)(343,471)
(344,472)(345,457)(346,458)(347,459)(348,460)(349,461)(350,462)(351,463)
(352,464)(353,449)(354,450)(355,451)(356,452)(357,453)(358,454)(359,455)
(360,456);
s1 := Sym(480)!( 1,253)( 2,254)( 3,256)( 4,255)( 5,250)( 6,249)( 7,251)
( 8,252)( 9,245)( 10,246)( 11,248)( 12,247)( 13,242)( 14,241)( 15,243)
( 16,244)( 17,277)( 18,278)( 19,280)( 20,279)( 21,274)( 22,273)( 23,275)
( 24,276)( 25,269)( 26,270)( 27,272)( 28,271)( 29,266)( 30,265)( 31,267)
( 32,268)( 33,261)( 34,262)( 35,264)( 36,263)( 37,258)( 38,257)( 39,259)
( 40,260)( 41,293)( 42,294)( 43,296)( 44,295)( 45,290)( 46,289)( 47,291)
( 48,292)( 49,285)( 50,286)( 51,288)( 52,287)( 53,282)( 54,281)( 55,283)
( 56,284)( 57,317)( 58,318)( 59,320)( 60,319)( 61,314)( 62,313)( 63,315)
( 64,316)( 65,309)( 66,310)( 67,312)( 68,311)( 69,306)( 70,305)( 71,307)
( 72,308)( 73,301)( 74,302)( 75,304)( 76,303)( 77,298)( 78,297)( 79,299)
( 80,300)( 81,333)( 82,334)( 83,336)( 84,335)( 85,330)( 86,329)( 87,331)
( 88,332)( 89,325)( 90,326)( 91,328)( 92,327)( 93,322)( 94,321)( 95,323)
( 96,324)( 97,357)( 98,358)( 99,360)(100,359)(101,354)(102,353)(103,355)
(104,356)(105,349)(106,350)(107,352)(108,351)(109,346)(110,345)(111,347)
(112,348)(113,341)(114,342)(115,344)(116,343)(117,338)(118,337)(119,339)
(120,340)(121,373)(122,374)(123,376)(124,375)(125,370)(126,369)(127,371)
(128,372)(129,365)(130,366)(131,368)(132,367)(133,362)(134,361)(135,363)
(136,364)(137,397)(138,398)(139,400)(140,399)(141,394)(142,393)(143,395)
(144,396)(145,389)(146,390)(147,392)(148,391)(149,386)(150,385)(151,387)
(152,388)(153,381)(154,382)(155,384)(156,383)(157,378)(158,377)(159,379)
(160,380)(161,413)(162,414)(163,416)(164,415)(165,410)(166,409)(167,411)
(168,412)(169,405)(170,406)(171,408)(172,407)(173,402)(174,401)(175,403)
(176,404)(177,437)(178,438)(179,440)(180,439)(181,434)(182,433)(183,435)
(184,436)(185,429)(186,430)(187,432)(188,431)(189,426)(190,425)(191,427)
(192,428)(193,421)(194,422)(195,424)(196,423)(197,418)(198,417)(199,419)
(200,420)(201,453)(202,454)(203,456)(204,455)(205,450)(206,449)(207,451)
(208,452)(209,445)(210,446)(211,448)(212,447)(213,442)(214,441)(215,443)
(216,444)(217,477)(218,478)(219,480)(220,479)(221,474)(222,473)(223,475)
(224,476)(225,469)(226,470)(227,472)(228,471)(229,466)(230,465)(231,467)
(232,468)(233,461)(234,462)(235,464)(236,463)(237,458)(238,457)(239,459)
(240,460);
s2 := 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)
(123,124)(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)
(142,144)(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(161,201)
(162,202)(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)
(170,210)(171,212)(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)
(178,218)(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)
(186,226)(187,228)(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)
(194,234)(195,236)(196,235)(197,239)(198,240)(199,237)(200,238)(241,242)
(245,248)(246,247)(249,250)(253,256)(254,255)(257,258)(261,264)(262,263)
(265,266)(269,272)(270,271)(273,274)(277,280)(278,279)(281,322)(282,321)
(283,323)(284,324)(285,328)(286,327)(287,326)(288,325)(289,330)(290,329)
(291,331)(292,332)(293,336)(294,335)(295,334)(296,333)(297,338)(298,337)
(299,339)(300,340)(301,344)(302,343)(303,342)(304,341)(305,346)(306,345)
(307,347)(308,348)(309,352)(310,351)(311,350)(312,349)(313,354)(314,353)
(315,355)(316,356)(317,360)(318,359)(319,358)(320,357)(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);
s3 := Sym(480)!( 1, 41)( 2, 42)( 3, 47)( 4, 48)( 5, 46)( 6, 45)( 7, 43)
( 8, 44)( 9, 49)( 10, 50)( 11, 55)( 12, 56)( 13, 54)( 14, 53)( 15, 51)
( 16, 52)( 17, 57)( 18, 58)( 19, 63)( 20, 64)( 21, 62)( 22, 61)( 23, 59)
( 24, 60)( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)
( 32, 68)( 33, 73)( 34, 74)( 35, 79)( 36, 80)( 37, 78)( 38, 77)( 39, 75)
( 40, 76)( 83, 87)( 84, 88)( 85, 86)( 91, 95)( 92, 96)( 93, 94)( 99,103)
(100,104)(101,102)(107,111)(108,112)(109,110)(115,119)(116,120)(117,118)
(121,161)(122,162)(123,167)(124,168)(125,166)(126,165)(127,163)(128,164)
(129,169)(130,170)(131,175)(132,176)(133,174)(134,173)(135,171)(136,172)
(137,177)(138,178)(139,183)(140,184)(141,182)(142,181)(143,179)(144,180)
(145,185)(146,186)(147,191)(148,192)(149,190)(150,189)(151,187)(152,188)
(153,193)(154,194)(155,199)(156,200)(157,198)(158,197)(159,195)(160,196)
(203,207)(204,208)(205,206)(211,215)(212,216)(213,214)(219,223)(220,224)
(221,222)(227,231)(228,232)(229,230)(235,239)(236,240)(237,238)(241,282)
(242,281)(243,288)(244,287)(245,285)(246,286)(247,284)(248,283)(249,290)
(250,289)(251,296)(252,295)(253,293)(254,294)(255,292)(256,291)(257,298)
(258,297)(259,304)(260,303)(261,301)(262,302)(263,300)(264,299)(265,306)
(266,305)(267,312)(268,311)(269,309)(270,310)(271,308)(272,307)(273,314)
(274,313)(275,320)(276,319)(277,317)(278,318)(279,316)(280,315)(321,322)
(323,328)(324,327)(329,330)(331,336)(332,335)(337,338)(339,344)(340,343)
(345,346)(347,352)(348,351)(353,354)(355,360)(356,359)(361,402)(362,401)
(363,408)(364,407)(365,405)(366,406)(367,404)(368,403)(369,410)(370,409)
(371,416)(372,415)(373,413)(374,414)(375,412)(376,411)(377,418)(378,417)
(379,424)(380,423)(381,421)(382,422)(383,420)(384,419)(385,426)(386,425)
(387,432)(388,431)(389,429)(390,430)(391,428)(392,427)(393,434)(394,433)
(395,440)(396,439)(397,437)(398,438)(399,436)(400,435)(441,442)(443,448)
(444,447)(449,450)(451,456)(452,455)(457,458)(459,464)(460,463)(465,466)
(467,472)(468,471)(473,474)(475,480)(476,479);
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,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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