Polytope of Type {8,4,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,15}*1920
if this polytope has a name.
Group : SmallGroup(1920,239556)
Rank : 4
Schlafli Type : {8,4,15}
Number of vertices, edges, etc : 8, 32, 60, 30
Order of s0s1s2s3 : 120
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 : {4,4,15}*960b
4-fold quotients : {8,2,15}*480, {2,4,15}*480
5-fold quotients : {8,4,3}*384
8-fold quotients : {4,2,15}*240, {2,4,15}*240
10-fold quotients : {4,4,3}*192b
12-fold quotients : {8,2,5}*160
16-fold quotients : {2,2,15}*120
20-fold quotients : {8,2,3}*96, {2,4,3}*96
24-fold quotients : {4,2,5}*80
40-fold quotients : {4,2,3}*48, {2,4,3}*48
48-fold quotients : {2,2,5}*40
80-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (121,181)(122,182)(123,183)(124,184)(125,185)(126,186)(127,187)(128,188)
(129,189)(130,190)(131,191)(132,192)(133,193)(134,194)(135,195)(136,196)
(137,197)(138,198)(139,199)(140,200)(141,201)(142,202)(143,203)(144,204)
(145,205)(146,206)(147,207)(148,208)(149,209)(150,210)(151,211)(152,212)
(153,213)(154,214)(155,215)(156,216)(157,217)(158,218)(159,219)(160,220)
(161,221)(162,222)(163,223)(164,224)(165,225)(166,226)(167,227)(168,228)
(169,229)(170,230)(171,231)(172,232)(173,233)(174,234)(175,235)(176,236)
(177,237)(178,238)(179,239)(180,240)(241,361)(242,362)(243,363)(244,364)
(245,365)(246,366)(247,367)(248,368)(249,369)(250,370)(251,371)(252,372)
(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)(260,380)
(261,381)(262,382)(263,383)(264,384)(265,385)(266,386)(267,387)(268,388)
(269,389)(270,390)(271,391)(272,392)(273,393)(274,394)(275,395)(276,396)
(277,397)(278,398)(279,399)(280,400)(281,401)(282,402)(283,403)(284,404)
(285,405)(286,406)(287,407)(288,408)(289,409)(290,410)(291,411)(292,412)
(293,413)(294,414)(295,415)(296,416)(297,417)(298,418)(299,419)(300,420)
(301,421)(302,422)(303,423)(304,424)(305,425)(306,426)(307,427)(308,428)
(309,429)(310,430)(311,431)(312,432)(313,433)(314,434)(315,435)(316,436)
(317,437)(318,438)(319,439)(320,440)(321,441)(322,442)(323,443)(324,444)
(325,445)(326,446)(327,447)(328,448)(329,449)(330,450)(331,451)(332,452)
(333,453)(334,454)(335,455)(336,456)(337,457)(338,458)(339,459)(340,460)
(341,461)(342,462)(343,463)(344,464)(345,465)(346,466)(347,467)(348,468)
(349,469)(350,470)(351,471)(352,472)(353,473)(354,474)(355,475)(356,476)
(357,477)(358,478)(359,479)(360,480);;
s1 := ( 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)
(121,423)(122,424)(123,421)(124,422)(125,427)(126,428)(127,425)(128,426)
(129,431)(130,432)(131,429)(132,430)(133,435)(134,436)(135,433)(136,434)
(137,439)(138,440)(139,437)(140,438)(141,443)(142,444)(143,441)(144,442)
(145,447)(146,448)(147,445)(148,446)(149,451)(150,452)(151,449)(152,450)
(153,455)(154,456)(155,453)(156,454)(157,459)(158,460)(159,457)(160,458)
(161,463)(162,464)(163,461)(164,462)(165,467)(166,468)(167,465)(168,466)
(169,471)(170,472)(171,469)(172,470)(173,475)(174,476)(175,473)(176,474)
(177,479)(178,480)(179,477)(180,478)(181,363)(182,364)(183,361)(184,362)
(185,367)(186,368)(187,365)(188,366)(189,371)(190,372)(191,369)(192,370)
(193,375)(194,376)(195,373)(196,374)(197,379)(198,380)(199,377)(200,378)
(201,383)(202,384)(203,381)(204,382)(205,387)(206,388)(207,385)(208,386)
(209,391)(210,392)(211,389)(212,390)(213,395)(214,396)(215,393)(216,394)
(217,399)(218,400)(219,397)(220,398)(221,403)(222,404)(223,401)(224,402)
(225,407)(226,408)(227,405)(228,406)(229,411)(230,412)(231,409)(232,410)
(233,415)(234,416)(235,413)(236,414)(237,419)(238,420)(239,417)(240,418);;
s2 := ( 3, 4)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)( 11, 16)
( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)
( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)
( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)
( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)
( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)
( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)
( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)(129,133)
(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)(145,177)
(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)(153,169)
(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(183,184)
(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)
(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)
(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)
(217,225)(218,226)(219,228)(220,227)(243,244)(245,257)(246,258)(247,260)
(248,259)(249,253)(250,254)(251,256)(252,255)(261,281)(262,282)(263,284)
(264,283)(265,297)(266,298)(267,300)(268,299)(269,293)(270,294)(271,296)
(272,295)(273,289)(274,290)(275,292)(276,291)(277,285)(278,286)(279,288)
(280,287)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)
(311,316)(312,315)(321,341)(322,342)(323,344)(324,343)(325,357)(326,358)
(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)
(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(363,364)(365,377)
(366,378)(367,380)(368,379)(369,373)(370,374)(371,376)(372,375)(381,401)
(382,402)(383,404)(384,403)(385,417)(386,418)(387,420)(388,419)(389,413)
(390,414)(391,416)(392,415)(393,409)(394,410)(395,412)(396,411)(397,405)
(398,406)(399,408)(400,407)(423,424)(425,437)(426,438)(427,440)(428,439)
(429,433)(430,434)(431,436)(432,435)(441,461)(442,462)(443,464)(444,463)
(445,477)(446,478)(447,480)(448,479)(449,473)(450,474)(451,476)(452,475)
(453,469)(454,470)(455,472)(456,471)(457,465)(458,466)(459,468)(460,467);;
s3 := ( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 21)( 6, 24)( 7, 23)( 8, 22)
( 9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)
( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)
( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)
( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)
( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)
(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)(126,144)
(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)(134,156)
(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)(162,168)
(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)(181,205)
(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)(189,217)
(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)(197,209)
(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)(229,237)
(230,240)(231,239)(232,238)(234,236)(241,265)(242,268)(243,267)(244,266)
(245,261)(246,264)(247,263)(248,262)(249,277)(250,280)(251,279)(252,278)
(253,273)(254,276)(255,275)(256,274)(257,269)(258,272)(259,271)(260,270)
(281,285)(282,288)(283,287)(284,286)(289,297)(290,300)(291,299)(292,298)
(294,296)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)(307,323)
(308,322)(309,337)(310,340)(311,339)(312,338)(313,333)(314,336)(315,335)
(316,334)(317,329)(318,332)(319,331)(320,330)(341,345)(342,348)(343,347)
(344,346)(349,357)(350,360)(351,359)(352,358)(354,356)(361,385)(362,388)
(363,387)(364,386)(365,381)(366,384)(367,383)(368,382)(369,397)(370,400)
(371,399)(372,398)(373,393)(374,396)(375,395)(376,394)(377,389)(378,392)
(379,391)(380,390)(401,405)(402,408)(403,407)(404,406)(409,417)(410,420)
(411,419)(412,418)(414,416)(421,445)(422,448)(423,447)(424,446)(425,441)
(426,444)(427,443)(428,442)(429,457)(430,460)(431,459)(432,458)(433,453)
(434,456)(435,455)(436,454)(437,449)(438,452)(439,451)(440,450)(461,465)
(462,468)(463,467)(464,466)(469,477)(470,480)(471,479)(472,478)(474,476);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!(121,181)(122,182)(123,183)(124,184)(125,185)(126,186)(127,187)
(128,188)(129,189)(130,190)(131,191)(132,192)(133,193)(134,194)(135,195)
(136,196)(137,197)(138,198)(139,199)(140,200)(141,201)(142,202)(143,203)
(144,204)(145,205)(146,206)(147,207)(148,208)(149,209)(150,210)(151,211)
(152,212)(153,213)(154,214)(155,215)(156,216)(157,217)(158,218)(159,219)
(160,220)(161,221)(162,222)(163,223)(164,224)(165,225)(166,226)(167,227)
(168,228)(169,229)(170,230)(171,231)(172,232)(173,233)(174,234)(175,235)
(176,236)(177,237)(178,238)(179,239)(180,240)(241,361)(242,362)(243,363)
(244,364)(245,365)(246,366)(247,367)(248,368)(249,369)(250,370)(251,371)
(252,372)(253,373)(254,374)(255,375)(256,376)(257,377)(258,378)(259,379)
(260,380)(261,381)(262,382)(263,383)(264,384)(265,385)(266,386)(267,387)
(268,388)(269,389)(270,390)(271,391)(272,392)(273,393)(274,394)(275,395)
(276,396)(277,397)(278,398)(279,399)(280,400)(281,401)(282,402)(283,403)
(284,404)(285,405)(286,406)(287,407)(288,408)(289,409)(290,410)(291,411)
(292,412)(293,413)(294,414)(295,415)(296,416)(297,417)(298,418)(299,419)
(300,420)(301,421)(302,422)(303,423)(304,424)(305,425)(306,426)(307,427)
(308,428)(309,429)(310,430)(311,431)(312,432)(313,433)(314,434)(315,435)
(316,436)(317,437)(318,438)(319,439)(320,440)(321,441)(322,442)(323,443)
(324,444)(325,445)(326,446)(327,447)(328,448)(329,449)(330,450)(331,451)
(332,452)(333,453)(334,454)(335,455)(336,456)(337,457)(338,458)(339,459)
(340,460)(341,461)(342,462)(343,463)(344,464)(345,465)(346,466)(347,467)
(348,468)(349,469)(350,470)(351,471)(352,472)(353,473)(354,474)(355,475)
(356,476)(357,477)(358,478)(359,479)(360,480);
s1 := 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)(121,423)(122,424)(123,421)(124,422)(125,427)(126,428)(127,425)
(128,426)(129,431)(130,432)(131,429)(132,430)(133,435)(134,436)(135,433)
(136,434)(137,439)(138,440)(139,437)(140,438)(141,443)(142,444)(143,441)
(144,442)(145,447)(146,448)(147,445)(148,446)(149,451)(150,452)(151,449)
(152,450)(153,455)(154,456)(155,453)(156,454)(157,459)(158,460)(159,457)
(160,458)(161,463)(162,464)(163,461)(164,462)(165,467)(166,468)(167,465)
(168,466)(169,471)(170,472)(171,469)(172,470)(173,475)(174,476)(175,473)
(176,474)(177,479)(178,480)(179,477)(180,478)(181,363)(182,364)(183,361)
(184,362)(185,367)(186,368)(187,365)(188,366)(189,371)(190,372)(191,369)
(192,370)(193,375)(194,376)(195,373)(196,374)(197,379)(198,380)(199,377)
(200,378)(201,383)(202,384)(203,381)(204,382)(205,387)(206,388)(207,385)
(208,386)(209,391)(210,392)(211,389)(212,390)(213,395)(214,396)(215,393)
(216,394)(217,399)(218,400)(219,397)(220,398)(221,403)(222,404)(223,401)
(224,402)(225,407)(226,408)(227,405)(228,406)(229,411)(230,412)(231,409)
(232,410)(233,415)(234,416)(235,413)(236,414)(237,419)(238,420)(239,417)
(240,418);
s2 := Sym(480)!( 3, 4)( 5, 17)( 6, 18)( 7, 20)( 8, 19)( 9, 13)( 10, 14)
( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)
( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)
( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)
( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)
( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)
( 98,106)( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)
(129,133)(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)
(145,177)(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)
(153,169)(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)
(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)
(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)
(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)
(216,231)(217,225)(218,226)(219,228)(220,227)(243,244)(245,257)(246,258)
(247,260)(248,259)(249,253)(250,254)(251,256)(252,255)(261,281)(262,282)
(263,284)(264,283)(265,297)(266,298)(267,300)(268,299)(269,293)(270,294)
(271,296)(272,295)(273,289)(274,290)(275,292)(276,291)(277,285)(278,286)
(279,288)(280,287)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)
(310,314)(311,316)(312,315)(321,341)(322,342)(323,344)(324,343)(325,357)
(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)
(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347)(363,364)
(365,377)(366,378)(367,380)(368,379)(369,373)(370,374)(371,376)(372,375)
(381,401)(382,402)(383,404)(384,403)(385,417)(386,418)(387,420)(388,419)
(389,413)(390,414)(391,416)(392,415)(393,409)(394,410)(395,412)(396,411)
(397,405)(398,406)(399,408)(400,407)(423,424)(425,437)(426,438)(427,440)
(428,439)(429,433)(430,434)(431,436)(432,435)(441,461)(442,462)(443,464)
(444,463)(445,477)(446,478)(447,480)(448,479)(449,473)(450,474)(451,476)
(452,475)(453,469)(454,470)(455,472)(456,471)(457,465)(458,466)(459,468)
(460,467);
s3 := Sym(480)!( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 21)( 6, 24)( 7, 23)
( 8, 22)( 9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)
( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)
( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)
( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)
( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)
(111,119)(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)
(126,144)(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)
(134,156)(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)
(162,168)(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)
(181,205)(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)
(189,217)(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)
(197,209)(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)
(229,237)(230,240)(231,239)(232,238)(234,236)(241,265)(242,268)(243,267)
(244,266)(245,261)(246,264)(247,263)(248,262)(249,277)(250,280)(251,279)
(252,278)(253,273)(254,276)(255,275)(256,274)(257,269)(258,272)(259,271)
(260,270)(281,285)(282,288)(283,287)(284,286)(289,297)(290,300)(291,299)
(292,298)(294,296)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)
(307,323)(308,322)(309,337)(310,340)(311,339)(312,338)(313,333)(314,336)
(315,335)(316,334)(317,329)(318,332)(319,331)(320,330)(341,345)(342,348)
(343,347)(344,346)(349,357)(350,360)(351,359)(352,358)(354,356)(361,385)
(362,388)(363,387)(364,386)(365,381)(366,384)(367,383)(368,382)(369,397)
(370,400)(371,399)(372,398)(373,393)(374,396)(375,395)(376,394)(377,389)
(378,392)(379,391)(380,390)(401,405)(402,408)(403,407)(404,406)(409,417)
(410,420)(411,419)(412,418)(414,416)(421,445)(422,448)(423,447)(424,446)
(425,441)(426,444)(427,443)(428,442)(429,457)(430,460)(431,459)(432,458)
(433,453)(434,456)(435,455)(436,454)(437,449)(438,452)(439,451)(440,450)
(461,465)(462,468)(463,467)(464,466)(469,477)(470,480)(471,479)(472,478)
(474,476);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 >;
References : None.
to this polytope