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Polytope of Type {40,6,3}

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