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Polytope of Type {3,12,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12,20}*1920
if this polytope has a name.
Group : SmallGroup(1920,238596)
Rank : 4
Schlafli Type : {3,12,20}
Number of vertices, edges, etc : 4, 24, 160, 20
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 : {3,6,20}*960, {3,12,10}*960
   4-fold quotients : {3,6,10}*480
   5-fold quotients : {3,12,4}*384
   10-fold quotients : {3,6,4}*192, {3,12,2}*192
   20-fold quotients : {3,6,2}*96
   40-fold quotients : {3,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  3,  4)(  5,  7)(  6,  8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)
( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 41, 81)
( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)( 49, 89)
( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 97)
( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)( 65,105)
( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)( 73,113)
( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)(123,124)
(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)(142,144)
(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(161,201)(162,202)
(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)
(171,212)(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)(178,218)
(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)(186,226)
(187,228)(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)
(195,236)(196,235)(197,239)(198,240)(199,237)(200,238)(241,242)(245,248)
(246,247)(249,250)(253,256)(254,255)(257,258)(261,264)(262,263)(265,266)
(269,272)(270,271)(273,274)(277,280)(278,279)(281,322)(282,321)(283,323)
(284,324)(285,328)(286,327)(287,326)(288,325)(289,330)(290,329)(291,331)
(292,332)(293,336)(294,335)(295,334)(296,333)(297,338)(298,337)(299,339)
(300,340)(301,344)(302,343)(303,342)(304,341)(305,346)(306,345)(307,347)
(308,348)(309,352)(310,351)(311,350)(312,349)(313,354)(314,353)(315,355)
(316,356)(317,360)(318,359)(319,358)(320,357)(361,362)(365,368)(366,367)
(369,370)(373,376)(374,375)(377,378)(381,384)(382,383)(385,386)(389,392)
(390,391)(393,394)(397,400)(398,399)(401,442)(402,441)(403,443)(404,444)
(405,448)(406,447)(407,446)(408,445)(409,450)(410,449)(411,451)(412,452)
(413,456)(414,455)(415,454)(416,453)(417,458)(418,457)(419,459)(420,460)
(421,464)(422,463)(423,462)(424,461)(425,466)(426,465)(427,467)(428,468)
(429,472)(430,471)(431,470)(432,469)(433,474)(434,473)(435,475)(436,476)
(437,480)(438,479)(439,478)(440,477);;
s1 := (  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);;
s2 := (  1,243)(  2,244)(  3,241)(  4,242)(  5,246)(  6,245)(  7,247)(  8,248)
(  9,275)( 10,276)( 11,273)( 12,274)( 13,278)( 14,277)( 15,279)( 16,280)
( 17,267)( 18,268)( 19,265)( 20,266)( 21,270)( 22,269)( 23,271)( 24,272)
( 25,259)( 26,260)( 27,257)( 28,258)( 29,262)( 30,261)( 31,263)( 32,264)
( 33,251)( 34,252)( 35,249)( 36,250)( 37,254)( 38,253)( 39,255)( 40,256)
( 41,323)( 42,324)( 43,321)( 44,322)( 45,326)( 46,325)( 47,327)( 48,328)
( 49,355)( 50,356)( 51,353)( 52,354)( 53,358)( 54,357)( 55,359)( 56,360)
( 57,347)( 58,348)( 59,345)( 60,346)( 61,350)( 62,349)( 63,351)( 64,352)
( 65,339)( 66,340)( 67,337)( 68,338)( 69,342)( 70,341)( 71,343)( 72,344)
( 73,331)( 74,332)( 75,329)( 76,330)( 77,334)( 78,333)( 79,335)( 80,336)
( 81,283)( 82,284)( 83,281)( 84,282)( 85,286)( 86,285)( 87,287)( 88,288)
( 89,315)( 90,316)( 91,313)( 92,314)( 93,318)( 94,317)( 95,319)( 96,320)
( 97,307)( 98,308)( 99,305)(100,306)(101,310)(102,309)(103,311)(104,312)
(105,299)(106,300)(107,297)(108,298)(109,302)(110,301)(111,303)(112,304)
(113,291)(114,292)(115,289)(116,290)(117,294)(118,293)(119,295)(120,296)
(121,363)(122,364)(123,361)(124,362)(125,366)(126,365)(127,367)(128,368)
(129,395)(130,396)(131,393)(132,394)(133,398)(134,397)(135,399)(136,400)
(137,387)(138,388)(139,385)(140,386)(141,390)(142,389)(143,391)(144,392)
(145,379)(146,380)(147,377)(148,378)(149,382)(150,381)(151,383)(152,384)
(153,371)(154,372)(155,369)(156,370)(157,374)(158,373)(159,375)(160,376)
(161,443)(162,444)(163,441)(164,442)(165,446)(166,445)(167,447)(168,448)
(169,475)(170,476)(171,473)(172,474)(173,478)(174,477)(175,479)(176,480)
(177,467)(178,468)(179,465)(180,466)(181,470)(182,469)(183,471)(184,472)
(185,459)(186,460)(187,457)(188,458)(189,462)(190,461)(191,463)(192,464)
(193,451)(194,452)(195,449)(196,450)(197,454)(198,453)(199,455)(200,456)
(201,403)(202,404)(203,401)(204,402)(205,406)(206,405)(207,407)(208,408)
(209,435)(210,436)(211,433)(212,434)(213,438)(214,437)(215,439)(216,440)
(217,427)(218,428)(219,425)(220,426)(221,430)(222,429)(223,431)(224,432)
(225,419)(226,420)(227,417)(228,418)(229,422)(230,421)(231,423)(232,424)
(233,411)(234,412)(235,409)(236,410)(237,414)(238,413)(239,415)(240,416);;
s3 := (  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)
( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)( 24, 40)
( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)( 48, 56)
( 57, 73)( 58, 74)( 59, 75)( 60, 76)( 61, 77)( 62, 78)( 63, 79)( 64, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,113)( 98,114)( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)
(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)
(137,153)(138,154)(139,155)(140,156)(141,157)(142,158)(143,159)(144,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,193)(178,194)(179,195)(180,196)(181,197)(182,198)(183,199)(184,200)
(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)
(217,233)(218,234)(219,235)(220,236)(221,237)(222,238)(223,239)(224,240)
(241,369)(242,370)(243,371)(244,372)(245,373)(246,374)(247,375)(248,376)
(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)(256,368)
(257,393)(258,394)(259,395)(260,396)(261,397)(262,398)(263,399)(264,400)
(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)
(273,377)(274,378)(275,379)(276,380)(277,381)(278,382)(279,383)(280,384)
(281,409)(282,410)(283,411)(284,412)(285,413)(286,414)(287,415)(288,416)
(289,401)(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)(296,408)
(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)(304,440)
(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)
(313,417)(314,418)(315,419)(316,420)(317,421)(318,422)(319,423)(320,424)
(321,449)(322,450)(323,451)(324,452)(325,453)(326,454)(327,455)(328,456)
(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)(336,448)
(337,473)(338,474)(339,475)(340,476)(341,477)(342,478)(343,479)(344,480)
(345,465)(346,466)(347,467)(348,468)(349,469)(350,470)(351,471)(352,472)
(353,457)(354,458)(355,459)(356,460)(357,461)(358,462)(359,463)(360,464);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s1*s2*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*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(480)!(  3,  4)(  5,  7)(  6,  8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)
( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)
( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)
( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)
( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)
( 65,105)( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)
( 73,113)( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)
(123,124)(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)
(142,144)(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(161,201)
(162,202)(163,204)(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)
(170,210)(171,212)(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)
(178,218)(179,220)(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)
(186,226)(187,228)(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)
(194,234)(195,236)(196,235)(197,239)(198,240)(199,237)(200,238)(241,242)
(245,248)(246,247)(249,250)(253,256)(254,255)(257,258)(261,264)(262,263)
(265,266)(269,272)(270,271)(273,274)(277,280)(278,279)(281,322)(282,321)
(283,323)(284,324)(285,328)(286,327)(287,326)(288,325)(289,330)(290,329)
(291,331)(292,332)(293,336)(294,335)(295,334)(296,333)(297,338)(298,337)
(299,339)(300,340)(301,344)(302,343)(303,342)(304,341)(305,346)(306,345)
(307,347)(308,348)(309,352)(310,351)(311,350)(312,349)(313,354)(314,353)
(315,355)(316,356)(317,360)(318,359)(319,358)(320,357)(361,362)(365,368)
(366,367)(369,370)(373,376)(374,375)(377,378)(381,384)(382,383)(385,386)
(389,392)(390,391)(393,394)(397,400)(398,399)(401,442)(402,441)(403,443)
(404,444)(405,448)(406,447)(407,446)(408,445)(409,450)(410,449)(411,451)
(412,452)(413,456)(414,455)(415,454)(416,453)(417,458)(418,457)(419,459)
(420,460)(421,464)(422,463)(423,462)(424,461)(425,466)(426,465)(427,467)
(428,468)(429,472)(430,471)(431,470)(432,469)(433,474)(434,473)(435,475)
(436,476)(437,480)(438,479)(439,478)(440,477);
s1 := 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);
s2 := Sym(480)!(  1,243)(  2,244)(  3,241)(  4,242)(  5,246)(  6,245)(  7,247)
(  8,248)(  9,275)( 10,276)( 11,273)( 12,274)( 13,278)( 14,277)( 15,279)
( 16,280)( 17,267)( 18,268)( 19,265)( 20,266)( 21,270)( 22,269)( 23,271)
( 24,272)( 25,259)( 26,260)( 27,257)( 28,258)( 29,262)( 30,261)( 31,263)
( 32,264)( 33,251)( 34,252)( 35,249)( 36,250)( 37,254)( 38,253)( 39,255)
( 40,256)( 41,323)( 42,324)( 43,321)( 44,322)( 45,326)( 46,325)( 47,327)
( 48,328)( 49,355)( 50,356)( 51,353)( 52,354)( 53,358)( 54,357)( 55,359)
( 56,360)( 57,347)( 58,348)( 59,345)( 60,346)( 61,350)( 62,349)( 63,351)
( 64,352)( 65,339)( 66,340)( 67,337)( 68,338)( 69,342)( 70,341)( 71,343)
( 72,344)( 73,331)( 74,332)( 75,329)( 76,330)( 77,334)( 78,333)( 79,335)
( 80,336)( 81,283)( 82,284)( 83,281)( 84,282)( 85,286)( 86,285)( 87,287)
( 88,288)( 89,315)( 90,316)( 91,313)( 92,314)( 93,318)( 94,317)( 95,319)
( 96,320)( 97,307)( 98,308)( 99,305)(100,306)(101,310)(102,309)(103,311)
(104,312)(105,299)(106,300)(107,297)(108,298)(109,302)(110,301)(111,303)
(112,304)(113,291)(114,292)(115,289)(116,290)(117,294)(118,293)(119,295)
(120,296)(121,363)(122,364)(123,361)(124,362)(125,366)(126,365)(127,367)
(128,368)(129,395)(130,396)(131,393)(132,394)(133,398)(134,397)(135,399)
(136,400)(137,387)(138,388)(139,385)(140,386)(141,390)(142,389)(143,391)
(144,392)(145,379)(146,380)(147,377)(148,378)(149,382)(150,381)(151,383)
(152,384)(153,371)(154,372)(155,369)(156,370)(157,374)(158,373)(159,375)
(160,376)(161,443)(162,444)(163,441)(164,442)(165,446)(166,445)(167,447)
(168,448)(169,475)(170,476)(171,473)(172,474)(173,478)(174,477)(175,479)
(176,480)(177,467)(178,468)(179,465)(180,466)(181,470)(182,469)(183,471)
(184,472)(185,459)(186,460)(187,457)(188,458)(189,462)(190,461)(191,463)
(192,464)(193,451)(194,452)(195,449)(196,450)(197,454)(198,453)(199,455)
(200,456)(201,403)(202,404)(203,401)(204,402)(205,406)(206,405)(207,407)
(208,408)(209,435)(210,436)(211,433)(212,434)(213,438)(214,437)(215,439)
(216,440)(217,427)(218,428)(219,425)(220,426)(221,430)(222,429)(223,431)
(224,432)(225,419)(226,420)(227,417)(228,418)(229,422)(230,421)(231,423)
(232,424)(233,411)(234,412)(235,409)(236,410)(237,414)(238,413)(239,415)
(240,416);
s3 := Sym(480)!(  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)
(  8, 16)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)
( 24, 40)( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)
( 48, 56)( 57, 73)( 58, 74)( 59, 75)( 60, 76)( 61, 77)( 62, 78)( 63, 79)
( 64, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,113)( 98,114)( 99,115)(100,116)(101,117)(102,118)(103,119)
(104,120)(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)
(128,136)(137,153)(138,154)(139,155)(140,156)(141,157)(142,158)(143,159)
(144,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,193)(178,194)(179,195)(180,196)(181,197)(182,198)(183,199)
(184,200)(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)
(208,216)(217,233)(218,234)(219,235)(220,236)(221,237)(222,238)(223,239)
(224,240)(241,369)(242,370)(243,371)(244,372)(245,373)(246,374)(247,375)
(248,376)(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)
(256,368)(257,393)(258,394)(259,395)(260,396)(261,397)(262,398)(263,399)
(264,400)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)
(272,392)(273,377)(274,378)(275,379)(276,380)(277,381)(278,382)(279,383)
(280,384)(281,409)(282,410)(283,411)(284,412)(285,413)(286,414)(287,415)
(288,416)(289,401)(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)
(296,408)(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)
(304,440)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)
(312,432)(313,417)(314,418)(315,419)(316,420)(317,421)(318,422)(319,423)
(320,424)(321,449)(322,450)(323,451)(324,452)(325,453)(326,454)(327,455)
(328,456)(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)
(336,448)(337,473)(338,474)(339,475)(340,476)(341,477)(342,478)(343,479)
(344,480)(345,465)(346,466)(347,467)(348,468)(349,469)(350,470)(351,471)
(352,472)(353,457)(354,458)(355,459)(356,460)(357,461)(358,462)(359,463)
(360,464);
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s1*s2*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*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope