Polytope of Type {40,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,4,3}*1920
Also Known As : {{40,4|2},{4,3}}. if this polytope has another name.
Group : SmallGroup(1920,238620)
Rank : 4
Schlafli Type : {40,4,3}
Number of vertices, edges, etc : 40, 160, 12, 6
Order of s0s1s2s3 : 120
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
4-fold quotients : {40,2,3}*480, {10,4,3}*480
5-fold quotients : {8,4,3}*384
8-fold quotients : {20,2,3}*240
10-fold quotients : {4,4,3}*192b
16-fold quotients : {10,2,3}*120
20-fold quotients : {8,2,3}*96, {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 := ( 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)
(121,181)(122,182)(123,183)(124,184)(125,197)(126,198)(127,199)(128,200)
(129,193)(130,194)(131,195)(132,196)(133,189)(134,190)(135,191)(136,192)
(137,185)(138,186)(139,187)(140,188)(141,201)(142,202)(143,203)(144,204)
(145,217)(146,218)(147,219)(148,220)(149,213)(150,214)(151,215)(152,216)
(153,209)(154,210)(155,211)(156,212)(157,205)(158,206)(159,207)(160,208)
(161,221)(162,222)(163,223)(164,224)(165,237)(166,238)(167,239)(168,240)
(169,233)(170,234)(171,235)(172,236)(173,229)(174,230)(175,231)(176,232)
(177,225)(178,226)(179,227)(180,228)(241,361)(242,362)(243,363)(244,364)
(245,377)(246,378)(247,379)(248,380)(249,373)(250,374)(251,375)(252,376)
(253,369)(254,370)(255,371)(256,372)(257,365)(258,366)(259,367)(260,368)
(261,381)(262,382)(263,383)(264,384)(265,397)(266,398)(267,399)(268,400)
(269,393)(270,394)(271,395)(272,396)(273,389)(274,390)(275,391)(276,392)
(277,385)(278,386)(279,387)(280,388)(281,401)(282,402)(283,403)(284,404)
(285,417)(286,418)(287,419)(288,420)(289,413)(290,414)(291,415)(292,416)
(293,409)(294,410)(295,411)(296,412)(297,405)(298,406)(299,407)(300,408)
(301,421)(302,422)(303,423)(304,424)(305,437)(306,438)(307,439)(308,440)
(309,433)(310,434)(311,435)(312,436)(313,429)(314,430)(315,431)(316,432)
(317,425)(318,426)(319,427)(320,428)(321,441)(322,442)(323,443)(324,444)
(325,457)(326,458)(327,459)(328,460)(329,453)(330,454)(331,455)(332,456)
(333,449)(334,450)(335,451)(336,452)(337,445)(338,446)(339,447)(340,448)
(341,461)(342,462)(343,463)(344,464)(345,477)(346,478)(347,479)(348,480)
(349,473)(350,474)(351,475)(352,476)(353,469)(354,470)(355,471)(356,472)
(357,465)(358,466)(359,467)(360,468);;
s1 := ( 1,247)( 2,248)( 3,245)( 4,246)( 5,243)( 6,244)( 7,241)( 8,242)
( 9,259)( 10,260)( 11,257)( 12,258)( 13,255)( 14,256)( 15,253)( 16,254)
( 17,251)( 18,252)( 19,249)( 20,250)( 21,267)( 22,268)( 23,265)( 24,266)
( 25,263)( 26,264)( 27,261)( 28,262)( 29,279)( 30,280)( 31,277)( 32,278)
( 33,275)( 34,276)( 35,273)( 36,274)( 37,271)( 38,272)( 39,269)( 40,270)
( 41,287)( 42,288)( 43,285)( 44,286)( 45,283)( 46,284)( 47,281)( 48,282)
( 49,299)( 50,300)( 51,297)( 52,298)( 53,295)( 54,296)( 55,293)( 56,294)
( 57,291)( 58,292)( 59,289)( 60,290)( 61,307)( 62,308)( 63,305)( 64,306)
( 65,303)( 66,304)( 67,301)( 68,302)( 69,319)( 70,320)( 71,317)( 72,318)
( 73,315)( 74,316)( 75,313)( 76,314)( 77,311)( 78,312)( 79,309)( 80,310)
( 81,327)( 82,328)( 83,325)( 84,326)( 85,323)( 86,324)( 87,321)( 88,322)
( 89,339)( 90,340)( 91,337)( 92,338)( 93,335)( 94,336)( 95,333)( 96,334)
( 97,331)( 98,332)( 99,329)(100,330)(101,347)(102,348)(103,345)(104,346)
(105,343)(106,344)(107,341)(108,342)(109,359)(110,360)(111,357)(112,358)
(113,355)(114,356)(115,353)(116,354)(117,351)(118,352)(119,349)(120,350)
(121,427)(122,428)(123,425)(124,426)(125,423)(126,424)(127,421)(128,422)
(129,439)(130,440)(131,437)(132,438)(133,435)(134,436)(135,433)(136,434)
(137,431)(138,432)(139,429)(140,430)(141,447)(142,448)(143,445)(144,446)
(145,443)(146,444)(147,441)(148,442)(149,459)(150,460)(151,457)(152,458)
(153,455)(154,456)(155,453)(156,454)(157,451)(158,452)(159,449)(160,450)
(161,467)(162,468)(163,465)(164,466)(165,463)(166,464)(167,461)(168,462)
(169,479)(170,480)(171,477)(172,478)(173,475)(174,476)(175,473)(176,474)
(177,471)(178,472)(179,469)(180,470)(181,367)(182,368)(183,365)(184,366)
(185,363)(186,364)(187,361)(188,362)(189,379)(190,380)(191,377)(192,378)
(193,375)(194,376)(195,373)(196,374)(197,371)(198,372)(199,369)(200,370)
(201,387)(202,388)(203,385)(204,386)(205,383)(206,384)(207,381)(208,382)
(209,399)(210,400)(211,397)(212,398)(213,395)(214,396)(215,393)(216,394)
(217,391)(218,392)(219,389)(220,390)(221,407)(222,408)(223,405)(224,406)
(225,403)(226,404)(227,401)(228,402)(229,419)(230,420)(231,417)(232,418)
(233,415)(234,416)(235,413)(236,414)(237,411)(238,412)(239,409)(240,410);;
s2 := ( 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)(123,124)(127,128)(131,132)(135,136)(139,140)(141,161)
(142,162)(143,164)(144,163)(145,165)(146,166)(147,168)(148,167)(149,169)
(150,170)(151,172)(152,171)(153,173)(154,174)(155,176)(156,175)(157,177)
(158,178)(159,180)(160,179)(183,184)(187,188)(191,192)(195,196)(199,200)
(201,221)(202,222)(203,224)(204,223)(205,225)(206,226)(207,228)(208,227)
(209,229)(210,230)(211,232)(212,231)(213,233)(214,234)(215,236)(216,235)
(217,237)(218,238)(219,240)(220,239)(243,244)(247,248)(251,252)(255,256)
(259,260)(261,281)(262,282)(263,284)(264,283)(265,285)(266,286)(267,288)
(268,287)(269,289)(270,290)(271,292)(272,291)(273,293)(274,294)(275,296)
(276,295)(277,297)(278,298)(279,300)(280,299)(303,304)(307,308)(311,312)
(315,316)(319,320)(321,341)(322,342)(323,344)(324,343)(325,345)(326,346)
(327,348)(328,347)(329,349)(330,350)(331,352)(332,351)(333,353)(334,354)
(335,356)(336,355)(337,357)(338,358)(339,360)(340,359)(363,364)(367,368)
(371,372)(375,376)(379,380)(381,401)(382,402)(383,404)(384,403)(385,405)
(386,406)(387,408)(388,407)(389,409)(390,410)(391,412)(392,411)(393,413)
(394,414)(395,416)(396,415)(397,417)(398,418)(399,420)(400,419)(423,424)
(427,428)(431,432)(435,436)(439,440)(441,461)(442,462)(443,464)(444,463)
(445,465)(446,466)(447,468)(448,467)(449,469)(450,470)(451,472)(452,471)
(453,473)(454,474)(455,476)(456,475)(457,477)(458,478)(459,480)(460,479);;
s3 := ( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 25)( 6, 28)( 7, 27)( 8, 26)
( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)( 54, 56)
( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)( 67, 87)
( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)( 75, 95)
( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)(110,112)
(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)(126,148)
(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)(134,156)
(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)(166,168)
(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)(185,205)
(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)(193,213)
(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)(222,224)
(226,228)(230,232)(234,236)(238,240)(241,261)(242,264)(243,263)(244,262)
(245,265)(246,268)(247,267)(248,266)(249,269)(250,272)(251,271)(252,270)
(253,273)(254,276)(255,275)(256,274)(257,277)(258,280)(259,279)(260,278)
(282,284)(286,288)(290,292)(294,296)(298,300)(301,321)(302,324)(303,323)
(304,322)(305,325)(306,328)(307,327)(308,326)(309,329)(310,332)(311,331)
(312,330)(313,333)(314,336)(315,335)(316,334)(317,337)(318,340)(319,339)
(320,338)(342,344)(346,348)(350,352)(354,356)(358,360)(361,381)(362,384)
(363,383)(364,382)(365,385)(366,388)(367,387)(368,386)(369,389)(370,392)
(371,391)(372,390)(373,393)(374,396)(375,395)(376,394)(377,397)(378,400)
(379,399)(380,398)(402,404)(406,408)(410,412)(414,416)(418,420)(421,441)
(422,444)(423,443)(424,442)(425,445)(426,448)(427,447)(428,446)(429,449)
(430,452)(431,451)(432,450)(433,453)(434,456)(435,455)(436,454)(437,457)
(438,460)(439,459)(440,458)(462,464)(466,468)(470,472)(474,476)(478,480);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, 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*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)!( 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)(121,181)(122,182)(123,183)(124,184)(125,197)(126,198)(127,199)
(128,200)(129,193)(130,194)(131,195)(132,196)(133,189)(134,190)(135,191)
(136,192)(137,185)(138,186)(139,187)(140,188)(141,201)(142,202)(143,203)
(144,204)(145,217)(146,218)(147,219)(148,220)(149,213)(150,214)(151,215)
(152,216)(153,209)(154,210)(155,211)(156,212)(157,205)(158,206)(159,207)
(160,208)(161,221)(162,222)(163,223)(164,224)(165,237)(166,238)(167,239)
(168,240)(169,233)(170,234)(171,235)(172,236)(173,229)(174,230)(175,231)
(176,232)(177,225)(178,226)(179,227)(180,228)(241,361)(242,362)(243,363)
(244,364)(245,377)(246,378)(247,379)(248,380)(249,373)(250,374)(251,375)
(252,376)(253,369)(254,370)(255,371)(256,372)(257,365)(258,366)(259,367)
(260,368)(261,381)(262,382)(263,383)(264,384)(265,397)(266,398)(267,399)
(268,400)(269,393)(270,394)(271,395)(272,396)(273,389)(274,390)(275,391)
(276,392)(277,385)(278,386)(279,387)(280,388)(281,401)(282,402)(283,403)
(284,404)(285,417)(286,418)(287,419)(288,420)(289,413)(290,414)(291,415)
(292,416)(293,409)(294,410)(295,411)(296,412)(297,405)(298,406)(299,407)
(300,408)(301,421)(302,422)(303,423)(304,424)(305,437)(306,438)(307,439)
(308,440)(309,433)(310,434)(311,435)(312,436)(313,429)(314,430)(315,431)
(316,432)(317,425)(318,426)(319,427)(320,428)(321,441)(322,442)(323,443)
(324,444)(325,457)(326,458)(327,459)(328,460)(329,453)(330,454)(331,455)
(332,456)(333,449)(334,450)(335,451)(336,452)(337,445)(338,446)(339,447)
(340,448)(341,461)(342,462)(343,463)(344,464)(345,477)(346,478)(347,479)
(348,480)(349,473)(350,474)(351,475)(352,476)(353,469)(354,470)(355,471)
(356,472)(357,465)(358,466)(359,467)(360,468);
s1 := Sym(480)!( 1,247)( 2,248)( 3,245)( 4,246)( 5,243)( 6,244)( 7,241)
( 8,242)( 9,259)( 10,260)( 11,257)( 12,258)( 13,255)( 14,256)( 15,253)
( 16,254)( 17,251)( 18,252)( 19,249)( 20,250)( 21,267)( 22,268)( 23,265)
( 24,266)( 25,263)( 26,264)( 27,261)( 28,262)( 29,279)( 30,280)( 31,277)
( 32,278)( 33,275)( 34,276)( 35,273)( 36,274)( 37,271)( 38,272)( 39,269)
( 40,270)( 41,287)( 42,288)( 43,285)( 44,286)( 45,283)( 46,284)( 47,281)
( 48,282)( 49,299)( 50,300)( 51,297)( 52,298)( 53,295)( 54,296)( 55,293)
( 56,294)( 57,291)( 58,292)( 59,289)( 60,290)( 61,307)( 62,308)( 63,305)
( 64,306)( 65,303)( 66,304)( 67,301)( 68,302)( 69,319)( 70,320)( 71,317)
( 72,318)( 73,315)( 74,316)( 75,313)( 76,314)( 77,311)( 78,312)( 79,309)
( 80,310)( 81,327)( 82,328)( 83,325)( 84,326)( 85,323)( 86,324)( 87,321)
( 88,322)( 89,339)( 90,340)( 91,337)( 92,338)( 93,335)( 94,336)( 95,333)
( 96,334)( 97,331)( 98,332)( 99,329)(100,330)(101,347)(102,348)(103,345)
(104,346)(105,343)(106,344)(107,341)(108,342)(109,359)(110,360)(111,357)
(112,358)(113,355)(114,356)(115,353)(116,354)(117,351)(118,352)(119,349)
(120,350)(121,427)(122,428)(123,425)(124,426)(125,423)(126,424)(127,421)
(128,422)(129,439)(130,440)(131,437)(132,438)(133,435)(134,436)(135,433)
(136,434)(137,431)(138,432)(139,429)(140,430)(141,447)(142,448)(143,445)
(144,446)(145,443)(146,444)(147,441)(148,442)(149,459)(150,460)(151,457)
(152,458)(153,455)(154,456)(155,453)(156,454)(157,451)(158,452)(159,449)
(160,450)(161,467)(162,468)(163,465)(164,466)(165,463)(166,464)(167,461)
(168,462)(169,479)(170,480)(171,477)(172,478)(173,475)(174,476)(175,473)
(176,474)(177,471)(178,472)(179,469)(180,470)(181,367)(182,368)(183,365)
(184,366)(185,363)(186,364)(187,361)(188,362)(189,379)(190,380)(191,377)
(192,378)(193,375)(194,376)(195,373)(196,374)(197,371)(198,372)(199,369)
(200,370)(201,387)(202,388)(203,385)(204,386)(205,383)(206,384)(207,381)
(208,382)(209,399)(210,400)(211,397)(212,398)(213,395)(214,396)(215,393)
(216,394)(217,391)(218,392)(219,389)(220,390)(221,407)(222,408)(223,405)
(224,406)(225,403)(226,404)(227,401)(228,402)(229,419)(230,420)(231,417)
(232,418)(233,415)(234,416)(235,413)(236,414)(237,411)(238,412)(239,409)
(240,410);
s2 := 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)(123,124)(127,128)(131,132)(135,136)(139,140)
(141,161)(142,162)(143,164)(144,163)(145,165)(146,166)(147,168)(148,167)
(149,169)(150,170)(151,172)(152,171)(153,173)(154,174)(155,176)(156,175)
(157,177)(158,178)(159,180)(160,179)(183,184)(187,188)(191,192)(195,196)
(199,200)(201,221)(202,222)(203,224)(204,223)(205,225)(206,226)(207,228)
(208,227)(209,229)(210,230)(211,232)(212,231)(213,233)(214,234)(215,236)
(216,235)(217,237)(218,238)(219,240)(220,239)(243,244)(247,248)(251,252)
(255,256)(259,260)(261,281)(262,282)(263,284)(264,283)(265,285)(266,286)
(267,288)(268,287)(269,289)(270,290)(271,292)(272,291)(273,293)(274,294)
(275,296)(276,295)(277,297)(278,298)(279,300)(280,299)(303,304)(307,308)
(311,312)(315,316)(319,320)(321,341)(322,342)(323,344)(324,343)(325,345)
(326,346)(327,348)(328,347)(329,349)(330,350)(331,352)(332,351)(333,353)
(334,354)(335,356)(336,355)(337,357)(338,358)(339,360)(340,359)(363,364)
(367,368)(371,372)(375,376)(379,380)(381,401)(382,402)(383,404)(384,403)
(385,405)(386,406)(387,408)(388,407)(389,409)(390,410)(391,412)(392,411)
(393,413)(394,414)(395,416)(396,415)(397,417)(398,418)(399,420)(400,419)
(423,424)(427,428)(431,432)(435,436)(439,440)(441,461)(442,462)(443,464)
(444,463)(445,465)(446,466)(447,468)(448,467)(449,469)(450,470)(451,472)
(452,471)(453,473)(454,474)(455,476)(456,475)(457,477)(458,478)(459,480)
(460,479);
s3 := Sym(480)!( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 25)( 6, 28)( 7, 27)
( 8, 26)( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)
( 54, 56)( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)
( 67, 87)( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)
( 75, 95)( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)
(110,112)(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)
(126,148)(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)
(134,156)(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)
(166,168)(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)
(185,205)(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)
(193,213)(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)
(222,224)(226,228)(230,232)(234,236)(238,240)(241,261)(242,264)(243,263)
(244,262)(245,265)(246,268)(247,267)(248,266)(249,269)(250,272)(251,271)
(252,270)(253,273)(254,276)(255,275)(256,274)(257,277)(258,280)(259,279)
(260,278)(282,284)(286,288)(290,292)(294,296)(298,300)(301,321)(302,324)
(303,323)(304,322)(305,325)(306,328)(307,327)(308,326)(309,329)(310,332)
(311,331)(312,330)(313,333)(314,336)(315,335)(316,334)(317,337)(318,340)
(319,339)(320,338)(342,344)(346,348)(350,352)(354,356)(358,360)(361,381)
(362,384)(363,383)(364,382)(365,385)(366,388)(367,387)(368,386)(369,389)
(370,392)(371,391)(372,390)(373,393)(374,396)(375,395)(376,394)(377,397)
(378,400)(379,399)(380,398)(402,404)(406,408)(410,412)(414,416)(418,420)
(421,441)(422,444)(423,443)(424,442)(425,445)(426,448)(427,447)(428,446)
(429,449)(430,452)(431,451)(432,450)(433,453)(434,456)(435,455)(436,454)
(437,457)(438,460)(439,459)(440,458)(462,464)(466,468)(470,472)(474,476)
(478,480);
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,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
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*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