Polytope of Type {4,15,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,15,4}*960a
if this polytope has a name.
Group : SmallGroup(960,11381)
Rank : 4
Schlafli Type : {4,15,4}
Number of vertices, edges, etc : 4, 60, 60, 8
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,15,4,2} of size 1920
Vertex Figure Of :
{2,4,15,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,15,4}*480
4-fold quotients : {4,15,2}*240
5-fold quotients : {4,3,4}*192a
10-fold quotients : {4,3,4}*96
20-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,15,8}*1920, {4,15,4}*1920c, {4,30,4}*1920c, {4,30,4}*1920f
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 := ( 1, 81)( 2, 84)( 3, 83)( 4, 82)( 5, 89)( 6, 92)( 7, 91)( 8, 90)
( 9, 85)( 10, 88)( 11, 87)( 12, 86)( 13, 93)( 14, 96)( 15, 95)( 16, 94)
( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)( 24,154)
( 25,149)( 26,152)( 27,151)( 28,150)( 29,157)( 30,160)( 31,159)( 32,158)
( 33,129)( 34,132)( 35,131)( 36,130)( 37,137)( 38,140)( 39,139)( 40,138)
( 41,133)( 42,136)( 43,135)( 44,134)( 45,141)( 46,144)( 47,143)( 48,142)
( 49,113)( 50,116)( 51,115)( 52,114)( 53,121)( 54,124)( 55,123)( 56,122)
( 57,117)( 58,120)( 59,119)( 60,118)( 61,125)( 62,128)( 63,127)( 64,126)
( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69,105)( 70,108)( 71,107)( 72,106)
( 73,101)( 74,104)( 75,103)( 76,102)( 77,109)( 78,112)( 79,111)( 80,110)
(162,164)(165,169)(166,172)(167,171)(168,170)(174,176)(177,225)(178,228)
(179,227)(180,226)(181,233)(182,236)(183,235)(184,234)(185,229)(186,232)
(187,231)(188,230)(189,237)(190,240)(191,239)(192,238)(193,209)(194,212)
(195,211)(196,210)(197,217)(198,220)(199,219)(200,218)(201,213)(202,216)
(203,215)(204,214)(205,221)(206,224)(207,223)(208,222)(241,321)(242,324)
(243,323)(244,322)(245,329)(246,332)(247,331)(248,330)(249,325)(250,328)
(251,327)(252,326)(253,333)(254,336)(255,335)(256,334)(257,385)(258,388)
(259,387)(260,386)(261,393)(262,396)(263,395)(264,394)(265,389)(266,392)
(267,391)(268,390)(269,397)(270,400)(271,399)(272,398)(273,369)(274,372)
(275,371)(276,370)(277,377)(278,380)(279,379)(280,378)(281,373)(282,376)
(283,375)(284,374)(285,381)(286,384)(287,383)(288,382)(289,353)(290,356)
(291,355)(292,354)(293,361)(294,364)(295,363)(296,362)(297,357)(298,360)
(299,359)(300,358)(301,365)(302,368)(303,367)(304,366)(305,337)(306,340)
(307,339)(308,338)(309,345)(310,348)(311,347)(312,346)(313,341)(314,344)
(315,343)(316,342)(317,349)(318,352)(319,351)(320,350)(402,404)(405,409)
(406,412)(407,411)(408,410)(414,416)(417,465)(418,468)(419,467)(420,466)
(421,473)(422,476)(423,475)(424,474)(425,469)(426,472)(427,471)(428,470)
(429,477)(430,480)(431,479)(432,478)(433,449)(434,452)(435,451)(436,450)
(437,457)(438,460)(439,459)(440,458)(441,453)(442,456)(443,455)(444,454)
(445,461)(446,464)(447,463)(448,462);;
s2 := ( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 29)( 6, 30)( 7, 32)( 8, 31)
( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 21)( 14, 22)( 15, 24)( 16, 23)
( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)( 40, 79)
( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)( 48, 71)
( 51, 52)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 59, 60)( 81,177)( 82,178)
( 83,180)( 84,179)( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)( 90,186)
( 91,188)( 92,187)( 93,181)( 94,182)( 95,184)( 96,183)( 97,161)( 98,162)
( 99,164)(100,163)(101,173)(102,174)(103,176)(104,175)(105,169)(106,170)
(107,172)(108,171)(109,165)(110,166)(111,168)(112,167)(113,225)(114,226)
(115,228)(116,227)(117,237)(118,238)(119,240)(120,239)(121,233)(122,234)
(123,236)(124,235)(125,229)(126,230)(127,232)(128,231)(129,209)(130,210)
(131,212)(132,211)(133,221)(134,222)(135,224)(136,223)(137,217)(138,218)
(139,220)(140,219)(141,213)(142,214)(143,216)(144,215)(145,193)(146,194)
(147,196)(148,195)(149,205)(150,206)(151,208)(152,207)(153,201)(154,202)
(155,204)(156,203)(157,197)(158,198)(159,200)(160,199)(241,257)(242,258)
(243,260)(244,259)(245,269)(246,270)(247,272)(248,271)(249,265)(250,266)
(251,268)(252,267)(253,261)(254,262)(255,264)(256,263)(273,305)(274,306)
(275,308)(276,307)(277,317)(278,318)(279,320)(280,319)(281,313)(282,314)
(283,316)(284,315)(285,309)(286,310)(287,312)(288,311)(291,292)(293,301)
(294,302)(295,304)(296,303)(299,300)(321,417)(322,418)(323,420)(324,419)
(325,429)(326,430)(327,432)(328,431)(329,425)(330,426)(331,428)(332,427)
(333,421)(334,422)(335,424)(336,423)(337,401)(338,402)(339,404)(340,403)
(341,413)(342,414)(343,416)(344,415)(345,409)(346,410)(347,412)(348,411)
(349,405)(350,406)(351,408)(352,407)(353,465)(354,466)(355,468)(356,467)
(357,477)(358,478)(359,480)(360,479)(361,473)(362,474)(363,476)(364,475)
(365,469)(366,470)(367,472)(368,471)(369,449)(370,450)(371,452)(372,451)
(373,461)(374,462)(375,464)(376,463)(377,457)(378,458)(379,460)(380,459)
(381,453)(382,454)(383,456)(384,455)(385,433)(386,434)(387,436)(388,435)
(389,445)(390,446)(391,448)(392,447)(393,441)(394,442)(395,444)(396,443)
(397,437)(398,438)(399,440)(400,439);;
s3 := ( 1,243)( 2,244)( 3,241)( 4,242)( 5,247)( 6,248)( 7,245)( 8,246)
( 9,251)( 10,252)( 11,249)( 12,250)( 13,255)( 14,256)( 15,253)( 16,254)
( 17,259)( 18,260)( 19,257)( 20,258)( 21,263)( 22,264)( 23,261)( 24,262)
( 25,267)( 26,268)( 27,265)( 28,266)( 29,271)( 30,272)( 31,269)( 32,270)
( 33,275)( 34,276)( 35,273)( 36,274)( 37,279)( 38,280)( 39,277)( 40,278)
( 41,283)( 42,284)( 43,281)( 44,282)( 45,287)( 46,288)( 47,285)( 48,286)
( 49,291)( 50,292)( 51,289)( 52,290)( 53,295)( 54,296)( 55,293)( 56,294)
( 57,299)( 58,300)( 59,297)( 60,298)( 61,303)( 62,304)( 63,301)( 64,302)
( 65,307)( 66,308)( 67,305)( 68,306)( 69,311)( 70,312)( 71,309)( 72,310)
( 73,315)( 74,316)( 75,313)( 76,314)( 77,319)( 78,320)( 79,317)( 80,318)
( 81,323)( 82,324)( 83,321)( 84,322)( 85,327)( 86,328)( 87,325)( 88,326)
( 89,331)( 90,332)( 91,329)( 92,330)( 93,335)( 94,336)( 95,333)( 96,334)
( 97,339)( 98,340)( 99,337)(100,338)(101,343)(102,344)(103,341)(104,342)
(105,347)(106,348)(107,345)(108,346)(109,351)(110,352)(111,349)(112,350)
(113,355)(114,356)(115,353)(116,354)(117,359)(118,360)(119,357)(120,358)
(121,363)(122,364)(123,361)(124,362)(125,367)(126,368)(127,365)(128,366)
(129,371)(130,372)(131,369)(132,370)(133,375)(134,376)(135,373)(136,374)
(137,379)(138,380)(139,377)(140,378)(141,383)(142,384)(143,381)(144,382)
(145,387)(146,388)(147,385)(148,386)(149,391)(150,392)(151,389)(152,390)
(153,395)(154,396)(155,393)(156,394)(157,399)(158,400)(159,397)(160,398)
(161,403)(162,404)(163,401)(164,402)(165,407)(166,408)(167,405)(168,406)
(169,411)(170,412)(171,409)(172,410)(173,415)(174,416)(175,413)(176,414)
(177,419)(178,420)(179,417)(180,418)(181,423)(182,424)(183,421)(184,422)
(185,427)(186,428)(187,425)(188,426)(189,431)(190,432)(191,429)(192,430)
(193,435)(194,436)(195,433)(196,434)(197,439)(198,440)(199,437)(200,438)
(201,443)(202,444)(203,441)(204,442)(205,447)(206,448)(207,445)(208,446)
(209,451)(210,452)(211,449)(212,450)(213,455)(214,456)(215,453)(216,454)
(217,459)(218,460)(219,457)(220,458)(221,463)(222,464)(223,461)(224,462)
(225,467)(226,468)(227,465)(228,466)(229,471)(230,472)(231,469)(232,470)
(233,475)(234,476)(235,473)(236,474)(237,479)(238,480)(239,477)(240,478);;
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*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)!( 1, 81)( 2, 84)( 3, 83)( 4, 82)( 5, 89)( 6, 92)( 7, 91)
( 8, 90)( 9, 85)( 10, 88)( 11, 87)( 12, 86)( 13, 93)( 14, 96)( 15, 95)
( 16, 94)( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)
( 24,154)( 25,149)( 26,152)( 27,151)( 28,150)( 29,157)( 30,160)( 31,159)
( 32,158)( 33,129)( 34,132)( 35,131)( 36,130)( 37,137)( 38,140)( 39,139)
( 40,138)( 41,133)( 42,136)( 43,135)( 44,134)( 45,141)( 46,144)( 47,143)
( 48,142)( 49,113)( 50,116)( 51,115)( 52,114)( 53,121)( 54,124)( 55,123)
( 56,122)( 57,117)( 58,120)( 59,119)( 60,118)( 61,125)( 62,128)( 63,127)
( 64,126)( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69,105)( 70,108)( 71,107)
( 72,106)( 73,101)( 74,104)( 75,103)( 76,102)( 77,109)( 78,112)( 79,111)
( 80,110)(162,164)(165,169)(166,172)(167,171)(168,170)(174,176)(177,225)
(178,228)(179,227)(180,226)(181,233)(182,236)(183,235)(184,234)(185,229)
(186,232)(187,231)(188,230)(189,237)(190,240)(191,239)(192,238)(193,209)
(194,212)(195,211)(196,210)(197,217)(198,220)(199,219)(200,218)(201,213)
(202,216)(203,215)(204,214)(205,221)(206,224)(207,223)(208,222)(241,321)
(242,324)(243,323)(244,322)(245,329)(246,332)(247,331)(248,330)(249,325)
(250,328)(251,327)(252,326)(253,333)(254,336)(255,335)(256,334)(257,385)
(258,388)(259,387)(260,386)(261,393)(262,396)(263,395)(264,394)(265,389)
(266,392)(267,391)(268,390)(269,397)(270,400)(271,399)(272,398)(273,369)
(274,372)(275,371)(276,370)(277,377)(278,380)(279,379)(280,378)(281,373)
(282,376)(283,375)(284,374)(285,381)(286,384)(287,383)(288,382)(289,353)
(290,356)(291,355)(292,354)(293,361)(294,364)(295,363)(296,362)(297,357)
(298,360)(299,359)(300,358)(301,365)(302,368)(303,367)(304,366)(305,337)
(306,340)(307,339)(308,338)(309,345)(310,348)(311,347)(312,346)(313,341)
(314,344)(315,343)(316,342)(317,349)(318,352)(319,351)(320,350)(402,404)
(405,409)(406,412)(407,411)(408,410)(414,416)(417,465)(418,468)(419,467)
(420,466)(421,473)(422,476)(423,475)(424,474)(425,469)(426,472)(427,471)
(428,470)(429,477)(430,480)(431,479)(432,478)(433,449)(434,452)(435,451)
(436,450)(437,457)(438,460)(439,459)(440,458)(441,453)(442,456)(443,455)
(444,454)(445,461)(446,464)(447,463)(448,462);
s2 := Sym(480)!( 1, 17)( 2, 18)( 3, 20)( 4, 19)( 5, 29)( 6, 30)( 7, 32)
( 8, 31)( 9, 25)( 10, 26)( 11, 28)( 12, 27)( 13, 21)( 14, 22)( 15, 24)
( 16, 23)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)
( 40, 79)( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)
( 48, 71)( 51, 52)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 59, 60)( 81,177)
( 82,178)( 83,180)( 84,179)( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)
( 90,186)( 91,188)( 92,187)( 93,181)( 94,182)( 95,184)( 96,183)( 97,161)
( 98,162)( 99,164)(100,163)(101,173)(102,174)(103,176)(104,175)(105,169)
(106,170)(107,172)(108,171)(109,165)(110,166)(111,168)(112,167)(113,225)
(114,226)(115,228)(116,227)(117,237)(118,238)(119,240)(120,239)(121,233)
(122,234)(123,236)(124,235)(125,229)(126,230)(127,232)(128,231)(129,209)
(130,210)(131,212)(132,211)(133,221)(134,222)(135,224)(136,223)(137,217)
(138,218)(139,220)(140,219)(141,213)(142,214)(143,216)(144,215)(145,193)
(146,194)(147,196)(148,195)(149,205)(150,206)(151,208)(152,207)(153,201)
(154,202)(155,204)(156,203)(157,197)(158,198)(159,200)(160,199)(241,257)
(242,258)(243,260)(244,259)(245,269)(246,270)(247,272)(248,271)(249,265)
(250,266)(251,268)(252,267)(253,261)(254,262)(255,264)(256,263)(273,305)
(274,306)(275,308)(276,307)(277,317)(278,318)(279,320)(280,319)(281,313)
(282,314)(283,316)(284,315)(285,309)(286,310)(287,312)(288,311)(291,292)
(293,301)(294,302)(295,304)(296,303)(299,300)(321,417)(322,418)(323,420)
(324,419)(325,429)(326,430)(327,432)(328,431)(329,425)(330,426)(331,428)
(332,427)(333,421)(334,422)(335,424)(336,423)(337,401)(338,402)(339,404)
(340,403)(341,413)(342,414)(343,416)(344,415)(345,409)(346,410)(347,412)
(348,411)(349,405)(350,406)(351,408)(352,407)(353,465)(354,466)(355,468)
(356,467)(357,477)(358,478)(359,480)(360,479)(361,473)(362,474)(363,476)
(364,475)(365,469)(366,470)(367,472)(368,471)(369,449)(370,450)(371,452)
(372,451)(373,461)(374,462)(375,464)(376,463)(377,457)(378,458)(379,460)
(380,459)(381,453)(382,454)(383,456)(384,455)(385,433)(386,434)(387,436)
(388,435)(389,445)(390,446)(391,448)(392,447)(393,441)(394,442)(395,444)
(396,443)(397,437)(398,438)(399,440)(400,439);
s3 := Sym(480)!( 1,243)( 2,244)( 3,241)( 4,242)( 5,247)( 6,248)( 7,245)
( 8,246)( 9,251)( 10,252)( 11,249)( 12,250)( 13,255)( 14,256)( 15,253)
( 16,254)( 17,259)( 18,260)( 19,257)( 20,258)( 21,263)( 22,264)( 23,261)
( 24,262)( 25,267)( 26,268)( 27,265)( 28,266)( 29,271)( 30,272)( 31,269)
( 32,270)( 33,275)( 34,276)( 35,273)( 36,274)( 37,279)( 38,280)( 39,277)
( 40,278)( 41,283)( 42,284)( 43,281)( 44,282)( 45,287)( 46,288)( 47,285)
( 48,286)( 49,291)( 50,292)( 51,289)( 52,290)( 53,295)( 54,296)( 55,293)
( 56,294)( 57,299)( 58,300)( 59,297)( 60,298)( 61,303)( 62,304)( 63,301)
( 64,302)( 65,307)( 66,308)( 67,305)( 68,306)( 69,311)( 70,312)( 71,309)
( 72,310)( 73,315)( 74,316)( 75,313)( 76,314)( 77,319)( 78,320)( 79,317)
( 80,318)( 81,323)( 82,324)( 83,321)( 84,322)( 85,327)( 86,328)( 87,325)
( 88,326)( 89,331)( 90,332)( 91,329)( 92,330)( 93,335)( 94,336)( 95,333)
( 96,334)( 97,339)( 98,340)( 99,337)(100,338)(101,343)(102,344)(103,341)
(104,342)(105,347)(106,348)(107,345)(108,346)(109,351)(110,352)(111,349)
(112,350)(113,355)(114,356)(115,353)(116,354)(117,359)(118,360)(119,357)
(120,358)(121,363)(122,364)(123,361)(124,362)(125,367)(126,368)(127,365)
(128,366)(129,371)(130,372)(131,369)(132,370)(133,375)(134,376)(135,373)
(136,374)(137,379)(138,380)(139,377)(140,378)(141,383)(142,384)(143,381)
(144,382)(145,387)(146,388)(147,385)(148,386)(149,391)(150,392)(151,389)
(152,390)(153,395)(154,396)(155,393)(156,394)(157,399)(158,400)(159,397)
(160,398)(161,403)(162,404)(163,401)(164,402)(165,407)(166,408)(167,405)
(168,406)(169,411)(170,412)(171,409)(172,410)(173,415)(174,416)(175,413)
(176,414)(177,419)(178,420)(179,417)(180,418)(181,423)(182,424)(183,421)
(184,422)(185,427)(186,428)(187,425)(188,426)(189,431)(190,432)(191,429)
(192,430)(193,435)(194,436)(195,433)(196,434)(197,439)(198,440)(199,437)
(200,438)(201,443)(202,444)(203,441)(204,442)(205,447)(206,448)(207,445)
(208,446)(209,451)(210,452)(211,449)(212,450)(213,455)(214,456)(215,453)
(216,454)(217,459)(218,460)(219,457)(220,458)(221,463)(222,464)(223,461)
(224,462)(225,467)(226,468)(227,465)(228,466)(229,471)(230,472)(231,469)
(232,470)(233,475)(234,476)(235,473)(236,474)(237,479)(238,480)(239,477)
(240,478);
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*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope