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