Polytope of Type {3,8,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,8,20}*1920
if this polytope has a name.
Group : SmallGroup(1920,238596)
Rank : 4
Schlafli Type : {3,8,20}
Number of vertices, edges, etc : 6, 24, 160, 20
Order of s0s1s2s3 : 60
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 : {3,4,20}*960, {3,8,10}*960
4-fold quotients : {3,4,10}*480
5-fold quotients : {3,8,4}*384
8-fold quotients : {3,2,20}*240
10-fold quotients : {3,4,4}*192b, {3,8,2}*192
16-fold quotients : {3,2,10}*120
20-fold quotients : {3,4,2}*96
32-fold quotients : {3,2,5}*60
40-fold quotients : {3,2,4}*48, {3,4,2}*48
80-fold quotients : {3,2,2}*24
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)( 3,242)( 4,241)( 5,247)( 6,248)( 7,246)( 8,245)
( 9,275)( 10,276)( 11,274)( 12,273)( 13,279)( 14,280)( 15,278)( 16,277)
( 17,267)( 18,268)( 19,266)( 20,265)( 21,271)( 22,272)( 23,270)( 24,269)
( 25,259)( 26,260)( 27,258)( 28,257)( 29,263)( 30,264)( 31,262)( 32,261)
( 33,251)( 34,252)( 35,250)( 36,249)( 37,255)( 38,256)( 39,254)( 40,253)
( 41,283)( 42,284)( 43,282)( 44,281)( 45,287)( 46,288)( 47,286)( 48,285)
( 49,315)( 50,316)( 51,314)( 52,313)( 53,319)( 54,320)( 55,318)( 56,317)
( 57,307)( 58,308)( 59,306)( 60,305)( 61,311)( 62,312)( 63,310)( 64,309)
( 65,299)( 66,300)( 67,298)( 68,297)( 69,303)( 70,304)( 71,302)( 72,301)
( 73,291)( 74,292)( 75,290)( 76,289)( 77,295)( 78,296)( 79,294)( 80,293)
( 81,323)( 82,324)( 83,322)( 84,321)( 85,327)( 86,328)( 87,326)( 88,325)
( 89,355)( 90,356)( 91,354)( 92,353)( 93,359)( 94,360)( 95,358)( 96,357)
( 97,347)( 98,348)( 99,346)(100,345)(101,351)(102,352)(103,350)(104,349)
(105,339)(106,340)(107,338)(108,337)(109,343)(110,344)(111,342)(112,341)
(113,331)(114,332)(115,330)(116,329)(117,335)(118,336)(119,334)(120,333)
(121,363)(122,364)(123,362)(124,361)(125,367)(126,368)(127,366)(128,365)
(129,395)(130,396)(131,394)(132,393)(133,399)(134,400)(135,398)(136,397)
(137,387)(138,388)(139,386)(140,385)(141,391)(142,392)(143,390)(144,389)
(145,379)(146,380)(147,378)(148,377)(149,383)(150,384)(151,382)(152,381)
(153,371)(154,372)(155,370)(156,369)(157,375)(158,376)(159,374)(160,373)
(161,403)(162,404)(163,402)(164,401)(165,407)(166,408)(167,406)(168,405)
(169,435)(170,436)(171,434)(172,433)(173,439)(174,440)(175,438)(176,437)
(177,427)(178,428)(179,426)(180,425)(181,431)(182,432)(183,430)(184,429)
(185,419)(186,420)(187,418)(188,417)(189,423)(190,424)(191,422)(192,421)
(193,411)(194,412)(195,410)(196,409)(197,415)(198,416)(199,414)(200,413)
(201,443)(202,444)(203,442)(204,441)(205,447)(206,448)(207,446)(208,445)
(209,475)(210,476)(211,474)(212,473)(213,479)(214,480)(215,478)(216,477)
(217,467)(218,468)(219,466)(220,465)(221,471)(222,472)(223,470)(224,469)
(225,459)(226,460)(227,458)(228,457)(229,463)(230,464)(231,462)(232,461)
(233,451)(234,452)(235,450)(236,449)(237,455)(238,456)(239,454)(240,453);;
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*s0*s1*s2*s0*s1*s2*s1*s2*s0*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)( 3,242)( 4,241)( 5,247)( 6,248)( 7,246)
( 8,245)( 9,275)( 10,276)( 11,274)( 12,273)( 13,279)( 14,280)( 15,278)
( 16,277)( 17,267)( 18,268)( 19,266)( 20,265)( 21,271)( 22,272)( 23,270)
( 24,269)( 25,259)( 26,260)( 27,258)( 28,257)( 29,263)( 30,264)( 31,262)
( 32,261)( 33,251)( 34,252)( 35,250)( 36,249)( 37,255)( 38,256)( 39,254)
( 40,253)( 41,283)( 42,284)( 43,282)( 44,281)( 45,287)( 46,288)( 47,286)
( 48,285)( 49,315)( 50,316)( 51,314)( 52,313)( 53,319)( 54,320)( 55,318)
( 56,317)( 57,307)( 58,308)( 59,306)( 60,305)( 61,311)( 62,312)( 63,310)
( 64,309)( 65,299)( 66,300)( 67,298)( 68,297)( 69,303)( 70,304)( 71,302)
( 72,301)( 73,291)( 74,292)( 75,290)( 76,289)( 77,295)( 78,296)( 79,294)
( 80,293)( 81,323)( 82,324)( 83,322)( 84,321)( 85,327)( 86,328)( 87,326)
( 88,325)( 89,355)( 90,356)( 91,354)( 92,353)( 93,359)( 94,360)( 95,358)
( 96,357)( 97,347)( 98,348)( 99,346)(100,345)(101,351)(102,352)(103,350)
(104,349)(105,339)(106,340)(107,338)(108,337)(109,343)(110,344)(111,342)
(112,341)(113,331)(114,332)(115,330)(116,329)(117,335)(118,336)(119,334)
(120,333)(121,363)(122,364)(123,362)(124,361)(125,367)(126,368)(127,366)
(128,365)(129,395)(130,396)(131,394)(132,393)(133,399)(134,400)(135,398)
(136,397)(137,387)(138,388)(139,386)(140,385)(141,391)(142,392)(143,390)
(144,389)(145,379)(146,380)(147,378)(148,377)(149,383)(150,384)(151,382)
(152,381)(153,371)(154,372)(155,370)(156,369)(157,375)(158,376)(159,374)
(160,373)(161,403)(162,404)(163,402)(164,401)(165,407)(166,408)(167,406)
(168,405)(169,435)(170,436)(171,434)(172,433)(173,439)(174,440)(175,438)
(176,437)(177,427)(178,428)(179,426)(180,425)(181,431)(182,432)(183,430)
(184,429)(185,419)(186,420)(187,418)(188,417)(189,423)(190,424)(191,422)
(192,421)(193,411)(194,412)(195,410)(196,409)(197,415)(198,416)(199,414)
(200,413)(201,443)(202,444)(203,442)(204,441)(205,447)(206,448)(207,446)
(208,445)(209,475)(210,476)(211,474)(212,473)(213,479)(214,480)(215,478)
(216,477)(217,467)(218,468)(219,466)(220,465)(221,471)(222,472)(223,470)
(224,469)(225,459)(226,460)(227,458)(228,457)(229,463)(230,464)(231,462)
(232,461)(233,451)(234,452)(235,450)(236,449)(237,455)(238,456)(239,454)
(240,453);
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*s0*s1*s2*s0*s1*s2*s1*s2*s0*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