Polytope of Type {4,3,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,4,10}*1920
Also Known As : {{4,3}3,{3,4},{4,10|2}}. if this polytope has another name.
Group : SmallGroup(1920,240408)
Rank : 5
Schlafli Type : {4,3,4,10}
Number of vertices, edges, etc : 4, 12, 12, 40, 10
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 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) :
4-fold quotients : {4,3,2,10}*480
5-fold quotients : {4,3,4,2}*384a
8-fold quotients : {4,3,2,5}*240
10-fold quotients : {4,3,4,2}*192
20-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)
(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)
(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)
(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)
(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)
(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)
(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)
(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)
(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)
(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)
(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)
(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)
(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)(440,448)
(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)(456,464)
(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)(472,480);;
s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)( 23, 24)
( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 39, 40)( 41, 45)( 42, 46)
( 43, 48)( 44, 47)( 51, 52)( 55, 56)( 57, 61)( 58, 62)( 59, 64)( 60, 63)
( 67, 68)( 71, 72)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 81,161)( 82,162)
( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)( 90,174)
( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,177)( 98,178)
( 99,180)(100,179)(101,181)(102,182)(103,184)(104,183)(105,189)(106,190)
(107,192)(108,191)(109,185)(110,186)(111,188)(112,187)(113,193)(114,194)
(115,196)(116,195)(117,197)(118,198)(119,200)(120,199)(121,205)(122,206)
(123,208)(124,207)(125,201)(126,202)(127,204)(128,203)(129,209)(130,210)
(131,212)(132,211)(133,213)(134,214)(135,216)(136,215)(137,221)(138,222)
(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,225)(146,226)
(147,228)(148,227)(149,229)(150,230)(151,232)(152,231)(153,237)(154,238)
(155,240)(156,239)(157,233)(158,234)(159,236)(160,235)(243,244)(247,248)
(249,253)(250,254)(251,256)(252,255)(259,260)(263,264)(265,269)(266,270)
(267,272)(268,271)(275,276)(279,280)(281,285)(282,286)(283,288)(284,287)
(291,292)(295,296)(297,301)(298,302)(299,304)(300,303)(307,308)(311,312)
(313,317)(314,318)(315,320)(316,319)(321,401)(322,402)(323,404)(324,403)
(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)(332,415)
(333,409)(334,410)(335,412)(336,411)(337,417)(338,418)(339,420)(340,419)
(341,421)(342,422)(343,424)(344,423)(345,429)(346,430)(347,432)(348,431)
(349,425)(350,426)(351,428)(352,427)(353,433)(354,434)(355,436)(356,435)
(357,437)(358,438)(359,440)(360,439)(361,445)(362,446)(363,448)(364,447)
(365,441)(366,442)(367,444)(368,443)(369,449)(370,450)(371,452)(372,451)
(373,453)(374,454)(375,456)(376,455)(377,461)(378,462)(379,464)(380,463)
(381,457)(382,458)(383,460)(384,459)(385,465)(386,466)(387,468)(388,467)
(389,469)(390,470)(391,472)(392,471)(393,477)(394,478)(395,480)(396,479)
(397,473)(398,474)(399,476)(400,475);;
s2 := ( 1, 81)( 2, 84)( 3, 83)( 4, 82)( 5, 93)( 6, 96)( 7, 95)( 8, 94)
( 9, 89)( 10, 92)( 11, 91)( 12, 90)( 13, 85)( 14, 88)( 15, 87)( 16, 86)
( 17, 97)( 18,100)( 19, 99)( 20, 98)( 21,109)( 22,112)( 23,111)( 24,110)
( 25,105)( 26,108)( 27,107)( 28,106)( 29,101)( 30,104)( 31,103)( 32,102)
( 33,113)( 34,116)( 35,115)( 36,114)( 37,125)( 38,128)( 39,127)( 40,126)
( 41,121)( 42,124)( 43,123)( 44,122)( 45,117)( 46,120)( 47,119)( 48,118)
( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)( 56,142)
( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)( 64,134)
( 65,145)( 66,148)( 67,147)( 68,146)( 69,157)( 70,160)( 71,159)( 72,158)
( 73,153)( 74,156)( 75,155)( 76,154)( 77,149)( 78,152)( 79,151)( 80,150)
(162,164)(165,173)(166,176)(167,175)(168,174)(170,172)(178,180)(181,189)
(182,192)(183,191)(184,190)(186,188)(194,196)(197,205)(198,208)(199,207)
(200,206)(202,204)(210,212)(213,221)(214,224)(215,223)(216,222)(218,220)
(226,228)(229,237)(230,240)(231,239)(232,238)(234,236)(241,321)(242,324)
(243,323)(244,322)(245,333)(246,336)(247,335)(248,334)(249,329)(250,332)
(251,331)(252,330)(253,325)(254,328)(255,327)(256,326)(257,337)(258,340)
(259,339)(260,338)(261,349)(262,352)(263,351)(264,350)(265,345)(266,348)
(267,347)(268,346)(269,341)(270,344)(271,343)(272,342)(273,353)(274,356)
(275,355)(276,354)(277,365)(278,368)(279,367)(280,366)(281,361)(282,364)
(283,363)(284,362)(285,357)(286,360)(287,359)(288,358)(289,369)(290,372)
(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)(298,380)
(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,385)(306,388)
(307,387)(308,386)(309,397)(310,400)(311,399)(312,398)(313,393)(314,396)
(315,395)(316,394)(317,389)(318,392)(319,391)(320,390)(402,404)(405,413)
(406,416)(407,415)(408,414)(410,412)(418,420)(421,429)(422,432)(423,431)
(424,430)(426,428)(434,436)(437,445)(438,448)(439,447)(440,446)(442,444)
(450,452)(453,461)(454,464)(455,463)(456,462)(458,460)(466,468)(469,477)
(470,480)(471,479)(472,478)(474,476);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 66)( 18, 65)( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 72)( 24, 71)
( 25, 74)( 26, 73)( 27, 76)( 28, 75)( 29, 78)( 30, 77)( 31, 80)( 32, 79)
( 33, 50)( 34, 49)( 35, 52)( 36, 51)( 37, 54)( 38, 53)( 39, 56)( 40, 55)
( 41, 58)( 42, 57)( 43, 60)( 44, 59)( 45, 62)( 46, 61)( 47, 64)( 48, 63)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97,146)( 98,145)( 99,148)(100,147)(101,150)(102,149)(103,152)(104,151)
(105,154)(106,153)(107,156)(108,155)(109,158)(110,157)(111,160)(112,159)
(113,130)(114,129)(115,132)(116,131)(117,134)(118,133)(119,136)(120,135)
(121,138)(122,137)(123,140)(124,139)(125,142)(126,141)(127,144)(128,143)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,226)(178,225)(179,228)(180,227)(181,230)(182,229)(183,232)(184,231)
(185,234)(186,233)(187,236)(188,235)(189,238)(190,237)(191,240)(192,239)
(193,210)(194,209)(195,212)(196,211)(197,214)(198,213)(199,216)(200,215)
(201,218)(202,217)(203,220)(204,219)(205,222)(206,221)(207,224)(208,223)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,306)(258,305)(259,308)(260,307)(261,310)(262,309)(263,312)(264,311)
(265,314)(266,313)(267,316)(268,315)(269,318)(270,317)(271,320)(272,319)
(273,290)(274,289)(275,292)(276,291)(277,294)(278,293)(279,296)(280,295)
(281,298)(282,297)(283,300)(284,299)(285,302)(286,301)(287,304)(288,303)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,386)(338,385)(339,388)(340,387)(341,390)(342,389)(343,392)(344,391)
(345,394)(346,393)(347,396)(348,395)(349,398)(350,397)(351,400)(352,399)
(353,370)(354,369)(355,372)(356,371)(357,374)(358,373)(359,376)(360,375)
(361,378)(362,377)(363,380)(364,379)(365,382)(366,381)(367,384)(368,383)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,466)(418,465)(419,468)(420,467)(421,470)(422,469)(423,472)(424,471)
(425,474)(426,473)(427,476)(428,475)(429,478)(430,477)(431,480)(432,479)
(433,450)(434,449)(435,452)(436,451)(437,454)(438,453)(439,456)(440,455)
(441,458)(442,457)(443,460)(444,459)(445,462)(446,461)(447,464)(448,463);;
s4 := ( 1,257)( 2,258)( 3,259)( 4,260)( 5,261)( 6,262)( 7,263)( 8,264)
( 9,265)( 10,266)( 11,267)( 12,268)( 13,269)( 14,270)( 15,271)( 16,272)
( 17,241)( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)
( 25,249)( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 31,255)( 32,256)
( 33,305)( 34,306)( 35,307)( 36,308)( 37,309)( 38,310)( 39,311)( 40,312)
( 41,313)( 42,314)( 43,315)( 44,316)( 45,317)( 46,318)( 47,319)( 48,320)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,273)( 66,274)( 67,275)( 68,276)( 69,277)( 70,278)( 71,279)( 72,280)
( 73,281)( 74,282)( 75,283)( 76,284)( 77,285)( 78,286)( 79,287)( 80,288)
( 81,337)( 82,338)( 83,339)( 84,340)( 85,341)( 86,342)( 87,343)( 88,344)
( 89,345)( 90,346)( 91,347)( 92,348)( 93,349)( 94,350)( 95,351)( 96,352)
( 97,321)( 98,322)( 99,323)(100,324)(101,325)(102,326)(103,327)(104,328)
(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)(112,336)
(113,385)(114,386)(115,387)(116,388)(117,389)(118,390)(119,391)(120,392)
(121,393)(122,394)(123,395)(124,396)(125,397)(126,398)(127,399)(128,400)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,353)(146,354)(147,355)(148,356)(149,357)(150,358)(151,359)(152,360)
(153,361)(154,362)(155,363)(156,364)(157,365)(158,366)(159,367)(160,368)
(161,417)(162,418)(163,419)(164,420)(165,421)(166,422)(167,423)(168,424)
(169,425)(170,426)(171,427)(172,428)(173,429)(174,430)(175,431)(176,432)
(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)(184,408)
(185,409)(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)(192,416)
(193,465)(194,466)(195,467)(196,468)(197,469)(198,470)(199,471)(200,472)
(201,473)(202,474)(203,475)(204,476)(205,477)(206,478)(207,479)(208,480)
(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)
(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)
(225,433)(226,434)(227,435)(228,436)(229,437)(230,438)(231,439)(232,440)
(233,441)(234,442)(235,443)(236,444)(237,445)(238,446)(239,447)(240,448);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)
( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)
(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)
(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)
(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)
(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)
(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)
(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)
(312,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)
(328,336)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)
(344,352)(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)
(360,368)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)
(376,384)(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)
(392,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)
(408,416)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)
(424,432)(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)
(440,448)(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)
(456,464)(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)
(472,480);
s1 := Sym(480)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)
( 23, 24)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 39, 40)( 41, 45)
( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 55, 56)( 57, 61)( 58, 62)( 59, 64)
( 60, 63)( 67, 68)( 71, 72)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 81,161)
( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)
( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,177)
( 98,178)( 99,180)(100,179)(101,181)(102,182)(103,184)(104,183)(105,189)
(106,190)(107,192)(108,191)(109,185)(110,186)(111,188)(112,187)(113,193)
(114,194)(115,196)(116,195)(117,197)(118,198)(119,200)(120,199)(121,205)
(122,206)(123,208)(124,207)(125,201)(126,202)(127,204)(128,203)(129,209)
(130,210)(131,212)(132,211)(133,213)(134,214)(135,216)(136,215)(137,221)
(138,222)(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,225)
(146,226)(147,228)(148,227)(149,229)(150,230)(151,232)(152,231)(153,237)
(154,238)(155,240)(156,239)(157,233)(158,234)(159,236)(160,235)(243,244)
(247,248)(249,253)(250,254)(251,256)(252,255)(259,260)(263,264)(265,269)
(266,270)(267,272)(268,271)(275,276)(279,280)(281,285)(282,286)(283,288)
(284,287)(291,292)(295,296)(297,301)(298,302)(299,304)(300,303)(307,308)
(311,312)(313,317)(314,318)(315,320)(316,319)(321,401)(322,402)(323,404)
(324,403)(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)
(332,415)(333,409)(334,410)(335,412)(336,411)(337,417)(338,418)(339,420)
(340,419)(341,421)(342,422)(343,424)(344,423)(345,429)(346,430)(347,432)
(348,431)(349,425)(350,426)(351,428)(352,427)(353,433)(354,434)(355,436)
(356,435)(357,437)(358,438)(359,440)(360,439)(361,445)(362,446)(363,448)
(364,447)(365,441)(366,442)(367,444)(368,443)(369,449)(370,450)(371,452)
(372,451)(373,453)(374,454)(375,456)(376,455)(377,461)(378,462)(379,464)
(380,463)(381,457)(382,458)(383,460)(384,459)(385,465)(386,466)(387,468)
(388,467)(389,469)(390,470)(391,472)(392,471)(393,477)(394,478)(395,480)
(396,479)(397,473)(398,474)(399,476)(400,475);
s2 := Sym(480)!( 1, 81)( 2, 84)( 3, 83)( 4, 82)( 5, 93)( 6, 96)( 7, 95)
( 8, 94)( 9, 89)( 10, 92)( 11, 91)( 12, 90)( 13, 85)( 14, 88)( 15, 87)
( 16, 86)( 17, 97)( 18,100)( 19, 99)( 20, 98)( 21,109)( 22,112)( 23,111)
( 24,110)( 25,105)( 26,108)( 27,107)( 28,106)( 29,101)( 30,104)( 31,103)
( 32,102)( 33,113)( 34,116)( 35,115)( 36,114)( 37,125)( 38,128)( 39,127)
( 40,126)( 41,121)( 42,124)( 43,123)( 44,122)( 45,117)( 46,120)( 47,119)
( 48,118)( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)
( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)
( 64,134)( 65,145)( 66,148)( 67,147)( 68,146)( 69,157)( 70,160)( 71,159)
( 72,158)( 73,153)( 74,156)( 75,155)( 76,154)( 77,149)( 78,152)( 79,151)
( 80,150)(162,164)(165,173)(166,176)(167,175)(168,174)(170,172)(178,180)
(181,189)(182,192)(183,191)(184,190)(186,188)(194,196)(197,205)(198,208)
(199,207)(200,206)(202,204)(210,212)(213,221)(214,224)(215,223)(216,222)
(218,220)(226,228)(229,237)(230,240)(231,239)(232,238)(234,236)(241,321)
(242,324)(243,323)(244,322)(245,333)(246,336)(247,335)(248,334)(249,329)
(250,332)(251,331)(252,330)(253,325)(254,328)(255,327)(256,326)(257,337)
(258,340)(259,339)(260,338)(261,349)(262,352)(263,351)(264,350)(265,345)
(266,348)(267,347)(268,346)(269,341)(270,344)(271,343)(272,342)(273,353)
(274,356)(275,355)(276,354)(277,365)(278,368)(279,367)(280,366)(281,361)
(282,364)(283,363)(284,362)(285,357)(286,360)(287,359)(288,358)(289,369)
(290,372)(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)
(298,380)(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,385)
(306,388)(307,387)(308,386)(309,397)(310,400)(311,399)(312,398)(313,393)
(314,396)(315,395)(316,394)(317,389)(318,392)(319,391)(320,390)(402,404)
(405,413)(406,416)(407,415)(408,414)(410,412)(418,420)(421,429)(422,432)
(423,431)(424,430)(426,428)(434,436)(437,445)(438,448)(439,447)(440,446)
(442,444)(450,452)(453,461)(454,464)(455,463)(456,462)(458,460)(466,468)
(469,477)(470,480)(471,479)(472,478)(474,476);
s3 := Sym(480)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 66)( 18, 65)( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 72)
( 24, 71)( 25, 74)( 26, 73)( 27, 76)( 28, 75)( 29, 78)( 30, 77)( 31, 80)
( 32, 79)( 33, 50)( 34, 49)( 35, 52)( 36, 51)( 37, 54)( 38, 53)( 39, 56)
( 40, 55)( 41, 58)( 42, 57)( 43, 60)( 44, 59)( 45, 62)( 46, 61)( 47, 64)
( 48, 63)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97,146)( 98,145)( 99,148)(100,147)(101,150)(102,149)(103,152)
(104,151)(105,154)(106,153)(107,156)(108,155)(109,158)(110,157)(111,160)
(112,159)(113,130)(114,129)(115,132)(116,131)(117,134)(118,133)(119,136)
(120,135)(121,138)(122,137)(123,140)(124,139)(125,142)(126,141)(127,144)
(128,143)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,226)(178,225)(179,228)(180,227)(181,230)(182,229)(183,232)
(184,231)(185,234)(186,233)(187,236)(188,235)(189,238)(190,237)(191,240)
(192,239)(193,210)(194,209)(195,212)(196,211)(197,214)(198,213)(199,216)
(200,215)(201,218)(202,217)(203,220)(204,219)(205,222)(206,221)(207,224)
(208,223)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,306)(258,305)(259,308)(260,307)(261,310)(262,309)(263,312)
(264,311)(265,314)(266,313)(267,316)(268,315)(269,318)(270,317)(271,320)
(272,319)(273,290)(274,289)(275,292)(276,291)(277,294)(278,293)(279,296)
(280,295)(281,298)(282,297)(283,300)(284,299)(285,302)(286,301)(287,304)
(288,303)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,386)(338,385)(339,388)(340,387)(341,390)(342,389)(343,392)
(344,391)(345,394)(346,393)(347,396)(348,395)(349,398)(350,397)(351,400)
(352,399)(353,370)(354,369)(355,372)(356,371)(357,374)(358,373)(359,376)
(360,375)(361,378)(362,377)(363,380)(364,379)(365,382)(366,381)(367,384)
(368,383)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,466)(418,465)(419,468)(420,467)(421,470)(422,469)(423,472)
(424,471)(425,474)(426,473)(427,476)(428,475)(429,478)(430,477)(431,480)
(432,479)(433,450)(434,449)(435,452)(436,451)(437,454)(438,453)(439,456)
(440,455)(441,458)(442,457)(443,460)(444,459)(445,462)(446,461)(447,464)
(448,463);
s4 := Sym(480)!( 1,257)( 2,258)( 3,259)( 4,260)( 5,261)( 6,262)( 7,263)
( 8,264)( 9,265)( 10,266)( 11,267)( 12,268)( 13,269)( 14,270)( 15,271)
( 16,272)( 17,241)( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)
( 24,248)( 25,249)( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 31,255)
( 32,256)( 33,305)( 34,306)( 35,307)( 36,308)( 37,309)( 38,310)( 39,311)
( 40,312)( 41,313)( 42,314)( 43,315)( 44,316)( 45,317)( 46,318)( 47,319)
( 48,320)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,273)( 66,274)( 67,275)( 68,276)( 69,277)( 70,278)( 71,279)
( 72,280)( 73,281)( 74,282)( 75,283)( 76,284)( 77,285)( 78,286)( 79,287)
( 80,288)( 81,337)( 82,338)( 83,339)( 84,340)( 85,341)( 86,342)( 87,343)
( 88,344)( 89,345)( 90,346)( 91,347)( 92,348)( 93,349)( 94,350)( 95,351)
( 96,352)( 97,321)( 98,322)( 99,323)(100,324)(101,325)(102,326)(103,327)
(104,328)(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)
(112,336)(113,385)(114,386)(115,387)(116,388)(117,389)(118,390)(119,391)
(120,392)(121,393)(122,394)(123,395)(124,396)(125,397)(126,398)(127,399)
(128,400)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,353)(146,354)(147,355)(148,356)(149,357)(150,358)(151,359)
(152,360)(153,361)(154,362)(155,363)(156,364)(157,365)(158,366)(159,367)
(160,368)(161,417)(162,418)(163,419)(164,420)(165,421)(166,422)(167,423)
(168,424)(169,425)(170,426)(171,427)(172,428)(173,429)(174,430)(175,431)
(176,432)(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)
(184,408)(185,409)(186,410)(187,411)(188,412)(189,413)(190,414)(191,415)
(192,416)(193,465)(194,466)(195,467)(196,468)(197,469)(198,470)(199,471)
(200,472)(201,473)(202,474)(203,475)(204,476)(205,477)(206,478)(207,479)
(208,480)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)
(224,464)(225,433)(226,434)(227,435)(228,436)(229,437)(230,438)(231,439)
(232,440)(233,441)(234,442)(235,443)(236,444)(237,445)(238,446)(239,447)
(240,448);
poly := sub<Sym(480)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
References : None.
to this polytope