Polytope of Type {4,24,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24,10}*1920d
if this polytope has a name.
Group : SmallGroup(1920,238608)
Rank : 4
Schlafli Type : {4,24,10}
Number of vertices, edges, etc : 4, 48, 120, 10
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {4,12,10}*960b
4-fold quotients : {4,6,10}*480b
5-fold quotients : {4,24,2}*384d
10-fold quotients : {4,12,2}*192b
20-fold quotients : {4,6,2}*96c
40-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 63)( 2, 64)( 3, 61)( 4, 62)( 5, 67)( 6, 68)( 7, 65)( 8, 66)
( 9, 71)( 10, 72)( 11, 69)( 12, 70)( 13, 75)( 14, 76)( 15, 73)( 16, 74)
( 17, 79)( 18, 80)( 19, 77)( 20, 78)( 21, 83)( 22, 84)( 23, 81)( 24, 82)
( 25, 87)( 26, 88)( 27, 85)( 28, 86)( 29, 91)( 30, 92)( 31, 89)( 32, 90)
( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 99)( 38,100)( 39, 97)( 40, 98)
( 41,103)( 42,104)( 43,101)( 44,102)( 45,107)( 46,108)( 47,105)( 48,106)
( 49,111)( 50,112)( 51,109)( 52,110)( 53,115)( 54,116)( 55,113)( 56,114)
( 57,119)( 58,120)( 59,117)( 60,118)(121,183)(122,184)(123,181)(124,182)
(125,187)(126,188)(127,185)(128,186)(129,191)(130,192)(131,189)(132,190)
(133,195)(134,196)(135,193)(136,194)(137,199)(138,200)(139,197)(140,198)
(141,203)(142,204)(143,201)(144,202)(145,207)(146,208)(147,205)(148,206)
(149,211)(150,212)(151,209)(152,210)(153,215)(154,216)(155,213)(156,214)
(157,219)(158,220)(159,217)(160,218)(161,223)(162,224)(163,221)(164,222)
(165,227)(166,228)(167,225)(168,226)(169,231)(170,232)(171,229)(172,230)
(173,235)(174,236)(175,233)(176,234)(177,239)(178,240)(179,237)(180,238)
(241,303)(242,304)(243,301)(244,302)(245,307)(246,308)(247,305)(248,306)
(249,311)(250,312)(251,309)(252,310)(253,315)(254,316)(255,313)(256,314)
(257,319)(258,320)(259,317)(260,318)(261,323)(262,324)(263,321)(264,322)
(265,327)(266,328)(267,325)(268,326)(269,331)(270,332)(271,329)(272,330)
(273,335)(274,336)(275,333)(276,334)(277,339)(278,340)(279,337)(280,338)
(281,343)(282,344)(283,341)(284,342)(285,347)(286,348)(287,345)(288,346)
(289,351)(290,352)(291,349)(292,350)(293,355)(294,356)(295,353)(296,354)
(297,359)(298,360)(299,357)(300,358)(361,423)(362,424)(363,421)(364,422)
(365,427)(366,428)(367,425)(368,426)(369,431)(370,432)(371,429)(372,430)
(373,435)(374,436)(375,433)(376,434)(377,439)(378,440)(379,437)(380,438)
(381,443)(382,444)(383,441)(384,442)(385,447)(386,448)(387,445)(388,446)
(389,451)(390,452)(391,449)(392,450)(393,455)(394,456)(395,453)(396,454)
(397,459)(398,460)(399,457)(400,458)(401,463)(402,464)(403,461)(404,462)
(405,467)(406,468)(407,465)(408,466)(409,471)(410,472)(411,469)(412,470)
(413,475)(414,476)(415,473)(416,474)(417,479)(418,480)(419,477)(420,478);;
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 := ( 1,261)( 2,264)( 3,263)( 4,262)( 5,277)( 6,280)( 7,279)( 8,278)
( 9,273)( 10,276)( 11,275)( 12,274)( 13,269)( 14,272)( 15,271)( 16,270)
( 17,265)( 18,268)( 19,267)( 20,266)( 21,241)( 22,244)( 23,243)( 24,242)
( 25,257)( 26,260)( 27,259)( 28,258)( 29,253)( 30,256)( 31,255)( 32,254)
( 33,249)( 34,252)( 35,251)( 36,250)( 37,245)( 38,248)( 39,247)( 40,246)
( 41,281)( 42,284)( 43,283)( 44,282)( 45,297)( 46,300)( 47,299)( 48,298)
( 49,293)( 50,296)( 51,295)( 52,294)( 53,289)( 54,292)( 55,291)( 56,290)
( 57,285)( 58,288)( 59,287)( 60,286)( 61,321)( 62,324)( 63,323)( 64,322)
( 65,337)( 66,340)( 67,339)( 68,338)( 69,333)( 70,336)( 71,335)( 72,334)
( 73,329)( 74,332)( 75,331)( 76,330)( 77,325)( 78,328)( 79,327)( 80,326)
( 81,301)( 82,304)( 83,303)( 84,302)( 85,317)( 86,320)( 87,319)( 88,318)
( 89,313)( 90,316)( 91,315)( 92,314)( 93,309)( 94,312)( 95,311)( 96,310)
( 97,305)( 98,308)( 99,307)(100,306)(101,341)(102,344)(103,343)(104,342)
(105,357)(106,360)(107,359)(108,358)(109,353)(110,356)(111,355)(112,354)
(113,349)(114,352)(115,351)(116,350)(117,345)(118,348)(119,347)(120,346)
(121,441)(122,444)(123,443)(124,442)(125,457)(126,460)(127,459)(128,458)
(129,453)(130,456)(131,455)(132,454)(133,449)(134,452)(135,451)(136,450)
(137,445)(138,448)(139,447)(140,446)(141,421)(142,424)(143,423)(144,422)
(145,437)(146,440)(147,439)(148,438)(149,433)(150,436)(151,435)(152,434)
(153,429)(154,432)(155,431)(156,430)(157,425)(158,428)(159,427)(160,426)
(161,461)(162,464)(163,463)(164,462)(165,477)(166,480)(167,479)(168,478)
(169,473)(170,476)(171,475)(172,474)(173,469)(174,472)(175,471)(176,470)
(177,465)(178,468)(179,467)(180,466)(181,381)(182,384)(183,383)(184,382)
(185,397)(186,400)(187,399)(188,398)(189,393)(190,396)(191,395)(192,394)
(193,389)(194,392)(195,391)(196,390)(197,385)(198,388)(199,387)(200,386)
(201,361)(202,364)(203,363)(204,362)(205,377)(206,380)(207,379)(208,378)
(209,373)(210,376)(211,375)(212,374)(213,369)(214,372)(215,371)(216,370)
(217,365)(218,368)(219,367)(220,366)(221,401)(222,404)(223,403)(224,402)
(225,417)(226,420)(227,419)(228,418)(229,413)(230,416)(231,415)(232,414)
(233,409)(234,412)(235,411)(236,410)(237,405)(238,408)(239,407)(240,406);;
s3 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9, 17)( 10, 18)( 11, 19)( 12, 20)
( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 29, 37)( 30, 38)( 31, 39)( 32, 40)
( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)
( 61, 65)( 62, 66)( 63, 67)( 64, 68)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 97)( 90, 98)( 91, 99)( 92,100)
(101,105)(102,106)(103,107)(104,108)(109,117)(110,118)(111,119)(112,120)
(121,125)(122,126)(123,127)(124,128)(129,137)(130,138)(131,139)(132,140)
(141,145)(142,146)(143,147)(144,148)(149,157)(150,158)(151,159)(152,160)
(161,165)(162,166)(163,167)(164,168)(169,177)(170,178)(171,179)(172,180)
(181,185)(182,186)(183,187)(184,188)(189,197)(190,198)(191,199)(192,200)
(201,205)(202,206)(203,207)(204,208)(209,217)(210,218)(211,219)(212,220)
(221,225)(222,226)(223,227)(224,228)(229,237)(230,238)(231,239)(232,240)
(241,245)(242,246)(243,247)(244,248)(249,257)(250,258)(251,259)(252,260)
(261,265)(262,266)(263,267)(264,268)(269,277)(270,278)(271,279)(272,280)
(281,285)(282,286)(283,287)(284,288)(289,297)(290,298)(291,299)(292,300)
(301,305)(302,306)(303,307)(304,308)(309,317)(310,318)(311,319)(312,320)
(321,325)(322,326)(323,327)(324,328)(329,337)(330,338)(331,339)(332,340)
(341,345)(342,346)(343,347)(344,348)(349,357)(350,358)(351,359)(352,360)
(361,365)(362,366)(363,367)(364,368)(369,377)(370,378)(371,379)(372,380)
(381,385)(382,386)(383,387)(384,388)(389,397)(390,398)(391,399)(392,400)
(401,405)(402,406)(403,407)(404,408)(409,417)(410,418)(411,419)(412,420)
(421,425)(422,426)(423,427)(424,428)(429,437)(430,438)(431,439)(432,440)
(441,445)(442,446)(443,447)(444,448)(449,457)(450,458)(451,459)(452,460)
(461,465)(462,466)(463,467)(464,468)(469,477)(470,478)(471,479)(472,480);;
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*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 1, 63)( 2, 64)( 3, 61)( 4, 62)( 5, 67)( 6, 68)( 7, 65)
( 8, 66)( 9, 71)( 10, 72)( 11, 69)( 12, 70)( 13, 75)( 14, 76)( 15, 73)
( 16, 74)( 17, 79)( 18, 80)( 19, 77)( 20, 78)( 21, 83)( 22, 84)( 23, 81)
( 24, 82)( 25, 87)( 26, 88)( 27, 85)( 28, 86)( 29, 91)( 30, 92)( 31, 89)
( 32, 90)( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 99)( 38,100)( 39, 97)
( 40, 98)( 41,103)( 42,104)( 43,101)( 44,102)( 45,107)( 46,108)( 47,105)
( 48,106)( 49,111)( 50,112)( 51,109)( 52,110)( 53,115)( 54,116)( 55,113)
( 56,114)( 57,119)( 58,120)( 59,117)( 60,118)(121,183)(122,184)(123,181)
(124,182)(125,187)(126,188)(127,185)(128,186)(129,191)(130,192)(131,189)
(132,190)(133,195)(134,196)(135,193)(136,194)(137,199)(138,200)(139,197)
(140,198)(141,203)(142,204)(143,201)(144,202)(145,207)(146,208)(147,205)
(148,206)(149,211)(150,212)(151,209)(152,210)(153,215)(154,216)(155,213)
(156,214)(157,219)(158,220)(159,217)(160,218)(161,223)(162,224)(163,221)
(164,222)(165,227)(166,228)(167,225)(168,226)(169,231)(170,232)(171,229)
(172,230)(173,235)(174,236)(175,233)(176,234)(177,239)(178,240)(179,237)
(180,238)(241,303)(242,304)(243,301)(244,302)(245,307)(246,308)(247,305)
(248,306)(249,311)(250,312)(251,309)(252,310)(253,315)(254,316)(255,313)
(256,314)(257,319)(258,320)(259,317)(260,318)(261,323)(262,324)(263,321)
(264,322)(265,327)(266,328)(267,325)(268,326)(269,331)(270,332)(271,329)
(272,330)(273,335)(274,336)(275,333)(276,334)(277,339)(278,340)(279,337)
(280,338)(281,343)(282,344)(283,341)(284,342)(285,347)(286,348)(287,345)
(288,346)(289,351)(290,352)(291,349)(292,350)(293,355)(294,356)(295,353)
(296,354)(297,359)(298,360)(299,357)(300,358)(361,423)(362,424)(363,421)
(364,422)(365,427)(366,428)(367,425)(368,426)(369,431)(370,432)(371,429)
(372,430)(373,435)(374,436)(375,433)(376,434)(377,439)(378,440)(379,437)
(380,438)(381,443)(382,444)(383,441)(384,442)(385,447)(386,448)(387,445)
(388,446)(389,451)(390,452)(391,449)(392,450)(393,455)(394,456)(395,453)
(396,454)(397,459)(398,460)(399,457)(400,458)(401,463)(402,464)(403,461)
(404,462)(405,467)(406,468)(407,465)(408,466)(409,471)(410,472)(411,469)
(412,470)(413,475)(414,476)(415,473)(416,474)(417,479)(418,480)(419,477)
(420,478);
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)!( 1,261)( 2,264)( 3,263)( 4,262)( 5,277)( 6,280)( 7,279)
( 8,278)( 9,273)( 10,276)( 11,275)( 12,274)( 13,269)( 14,272)( 15,271)
( 16,270)( 17,265)( 18,268)( 19,267)( 20,266)( 21,241)( 22,244)( 23,243)
( 24,242)( 25,257)( 26,260)( 27,259)( 28,258)( 29,253)( 30,256)( 31,255)
( 32,254)( 33,249)( 34,252)( 35,251)( 36,250)( 37,245)( 38,248)( 39,247)
( 40,246)( 41,281)( 42,284)( 43,283)( 44,282)( 45,297)( 46,300)( 47,299)
( 48,298)( 49,293)( 50,296)( 51,295)( 52,294)( 53,289)( 54,292)( 55,291)
( 56,290)( 57,285)( 58,288)( 59,287)( 60,286)( 61,321)( 62,324)( 63,323)
( 64,322)( 65,337)( 66,340)( 67,339)( 68,338)( 69,333)( 70,336)( 71,335)
( 72,334)( 73,329)( 74,332)( 75,331)( 76,330)( 77,325)( 78,328)( 79,327)
( 80,326)( 81,301)( 82,304)( 83,303)( 84,302)( 85,317)( 86,320)( 87,319)
( 88,318)( 89,313)( 90,316)( 91,315)( 92,314)( 93,309)( 94,312)( 95,311)
( 96,310)( 97,305)( 98,308)( 99,307)(100,306)(101,341)(102,344)(103,343)
(104,342)(105,357)(106,360)(107,359)(108,358)(109,353)(110,356)(111,355)
(112,354)(113,349)(114,352)(115,351)(116,350)(117,345)(118,348)(119,347)
(120,346)(121,441)(122,444)(123,443)(124,442)(125,457)(126,460)(127,459)
(128,458)(129,453)(130,456)(131,455)(132,454)(133,449)(134,452)(135,451)
(136,450)(137,445)(138,448)(139,447)(140,446)(141,421)(142,424)(143,423)
(144,422)(145,437)(146,440)(147,439)(148,438)(149,433)(150,436)(151,435)
(152,434)(153,429)(154,432)(155,431)(156,430)(157,425)(158,428)(159,427)
(160,426)(161,461)(162,464)(163,463)(164,462)(165,477)(166,480)(167,479)
(168,478)(169,473)(170,476)(171,475)(172,474)(173,469)(174,472)(175,471)
(176,470)(177,465)(178,468)(179,467)(180,466)(181,381)(182,384)(183,383)
(184,382)(185,397)(186,400)(187,399)(188,398)(189,393)(190,396)(191,395)
(192,394)(193,389)(194,392)(195,391)(196,390)(197,385)(198,388)(199,387)
(200,386)(201,361)(202,364)(203,363)(204,362)(205,377)(206,380)(207,379)
(208,378)(209,373)(210,376)(211,375)(212,374)(213,369)(214,372)(215,371)
(216,370)(217,365)(218,368)(219,367)(220,366)(221,401)(222,404)(223,403)
(224,402)(225,417)(226,420)(227,419)(228,418)(229,413)(230,416)(231,415)
(232,414)(233,409)(234,412)(235,411)(236,410)(237,405)(238,408)(239,407)
(240,406);
s3 := Sym(480)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9, 17)( 10, 18)( 11, 19)
( 12, 20)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 29, 37)( 30, 38)( 31, 39)
( 32, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 57)( 50, 58)( 51, 59)
( 52, 60)( 61, 65)( 62, 66)( 63, 67)( 64, 68)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 97)( 90, 98)( 91, 99)
( 92,100)(101,105)(102,106)(103,107)(104,108)(109,117)(110,118)(111,119)
(112,120)(121,125)(122,126)(123,127)(124,128)(129,137)(130,138)(131,139)
(132,140)(141,145)(142,146)(143,147)(144,148)(149,157)(150,158)(151,159)
(152,160)(161,165)(162,166)(163,167)(164,168)(169,177)(170,178)(171,179)
(172,180)(181,185)(182,186)(183,187)(184,188)(189,197)(190,198)(191,199)
(192,200)(201,205)(202,206)(203,207)(204,208)(209,217)(210,218)(211,219)
(212,220)(221,225)(222,226)(223,227)(224,228)(229,237)(230,238)(231,239)
(232,240)(241,245)(242,246)(243,247)(244,248)(249,257)(250,258)(251,259)
(252,260)(261,265)(262,266)(263,267)(264,268)(269,277)(270,278)(271,279)
(272,280)(281,285)(282,286)(283,287)(284,288)(289,297)(290,298)(291,299)
(292,300)(301,305)(302,306)(303,307)(304,308)(309,317)(310,318)(311,319)
(312,320)(321,325)(322,326)(323,327)(324,328)(329,337)(330,338)(331,339)
(332,340)(341,345)(342,346)(343,347)(344,348)(349,357)(350,358)(351,359)
(352,360)(361,365)(362,366)(363,367)(364,368)(369,377)(370,378)(371,379)
(372,380)(381,385)(382,386)(383,387)(384,388)(389,397)(390,398)(391,399)
(392,400)(401,405)(402,406)(403,407)(404,408)(409,417)(410,418)(411,419)
(412,420)(421,425)(422,426)(423,427)(424,428)(429,437)(430,438)(431,439)
(432,440)(441,445)(442,446)(443,447)(444,448)(449,457)(450,458)(451,459)
(452,460)(461,465)(462,466)(463,467)(464,468)(469,477)(470,478)(471,479)
(472,480);
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*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0 >;
References : None.
to this polytope