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