Polytope of Type {8,6,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,10}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240195)
Rank : 4
Schlafli Type : {8,6,10}
Number of vertices, edges, etc : 16, 48, 60, 10
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 : {4,6,10}*960e
4-fold quotients : {4,6,10}*480b
5-fold quotients : {8,6,2}*384b
8-fold quotients : {2,6,10}*240
10-fold quotients : {8,3,2}*192, {4,6,2}*192
20-fold quotients : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
24-fold quotients : {2,2,10}*80
40-fold quotients : {4,3,2}*48, {2,6,2}*48
48-fold quotients : {2,2,5}*40
80-fold quotients : {2,3,2}*24
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,125)( 2,126)( 3,128)( 4,127)( 5,122)( 6,121)( 7,123)( 8,124)
( 9,133)( 10,134)( 11,136)( 12,135)( 13,130)( 14,129)( 15,131)( 16,132)
( 17,141)( 18,142)( 19,144)( 20,143)( 21,138)( 22,137)( 23,139)( 24,140)
( 25,149)( 26,150)( 27,152)( 28,151)( 29,146)( 30,145)( 31,147)( 32,148)
( 33,157)( 34,158)( 35,160)( 36,159)( 37,154)( 38,153)( 39,155)( 40,156)
( 41,165)( 42,166)( 43,168)( 44,167)( 45,162)( 46,161)( 47,163)( 48,164)
( 49,173)( 50,174)( 51,176)( 52,175)( 53,170)( 54,169)( 55,171)( 56,172)
( 57,181)( 58,182)( 59,184)( 60,183)( 61,178)( 62,177)( 63,179)( 64,180)
( 65,189)( 66,190)( 67,192)( 68,191)( 69,186)( 70,185)( 71,187)( 72,188)
( 73,197)( 74,198)( 75,200)( 76,199)( 77,194)( 78,193)( 79,195)( 80,196)
( 81,205)( 82,206)( 83,208)( 84,207)( 85,202)( 86,201)( 87,203)( 88,204)
( 89,213)( 90,214)( 91,216)( 92,215)( 93,210)( 94,209)( 95,211)( 96,212)
( 97,221)( 98,222)( 99,224)(100,223)(101,218)(102,217)(103,219)(104,220)
(105,229)(106,230)(107,232)(108,231)(109,226)(110,225)(111,227)(112,228)
(113,237)(114,238)(115,240)(116,239)(117,234)(118,233)(119,235)(120,236)
(241,365)(242,366)(243,368)(244,367)(245,362)(246,361)(247,363)(248,364)
(249,373)(250,374)(251,376)(252,375)(253,370)(254,369)(255,371)(256,372)
(257,381)(258,382)(259,384)(260,383)(261,378)(262,377)(263,379)(264,380)
(265,389)(266,390)(267,392)(268,391)(269,386)(270,385)(271,387)(272,388)
(273,397)(274,398)(275,400)(276,399)(277,394)(278,393)(279,395)(280,396)
(281,405)(282,406)(283,408)(284,407)(285,402)(286,401)(287,403)(288,404)
(289,413)(290,414)(291,416)(292,415)(293,410)(294,409)(295,411)(296,412)
(297,421)(298,422)(299,424)(300,423)(301,418)(302,417)(303,419)(304,420)
(305,429)(306,430)(307,432)(308,431)(309,426)(310,425)(311,427)(312,428)
(313,437)(314,438)(315,440)(316,439)(317,434)(318,433)(319,435)(320,436)
(321,445)(322,446)(323,448)(324,447)(325,442)(326,441)(327,443)(328,444)
(329,453)(330,454)(331,456)(332,455)(333,450)(334,449)(335,451)(336,452)
(337,461)(338,462)(339,464)(340,463)(341,458)(342,457)(343,459)(344,460)
(345,469)(346,470)(347,472)(348,471)(349,466)(350,465)(351,467)(352,468)
(353,477)(354,478)(355,480)(356,479)(357,474)(358,473)(359,475)(360,476);;
s1 := ( 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)(121,122)
(125,128)(126,127)(129,130)(133,136)(134,135)(137,138)(141,144)(142,143)
(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)(161,202)(162,201)
(163,203)(164,204)(165,208)(166,207)(167,206)(168,205)(169,210)(170,209)
(171,211)(172,212)(173,216)(174,215)(175,214)(176,213)(177,218)(178,217)
(179,219)(180,220)(181,224)(182,223)(183,222)(184,221)(185,226)(186,225)
(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,234)(194,233)
(195,235)(196,236)(197,240)(198,239)(199,238)(200,237)(243,244)(245,247)
(246,248)(251,252)(253,255)(254,256)(259,260)(261,263)(262,264)(267,268)
(269,271)(270,272)(275,276)(277,279)(278,280)(281,321)(282,322)(283,324)
(284,323)(285,327)(286,328)(287,325)(288,326)(289,329)(290,330)(291,332)
(292,331)(293,335)(294,336)(295,333)(296,334)(297,337)(298,338)(299,340)
(300,339)(301,343)(302,344)(303,341)(304,342)(305,345)(306,346)(307,348)
(308,347)(309,351)(310,352)(311,349)(312,350)(313,353)(314,354)(315,356)
(316,355)(317,359)(318,360)(319,357)(320,358)(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);;
s2 := ( 1, 41)( 2, 42)( 3, 47)( 4, 48)( 5, 46)( 6, 45)( 7, 43)( 8, 44)
( 9, 73)( 10, 74)( 11, 79)( 12, 80)( 13, 78)( 14, 77)( 15, 75)( 16, 76)
( 17, 65)( 18, 66)( 19, 71)( 20, 72)( 21, 70)( 22, 69)( 23, 67)( 24, 68)
( 25, 57)( 26, 58)( 27, 63)( 28, 64)( 29, 62)( 30, 61)( 31, 59)( 32, 60)
( 33, 49)( 34, 50)( 35, 55)( 36, 56)( 37, 54)( 38, 53)( 39, 51)( 40, 52)
( 83, 87)( 84, 88)( 85, 86)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)
( 94,117)( 95,115)( 96,116)( 97,105)( 98,106)( 99,111)(100,112)(101,110)
(102,109)(103,107)(104,108)(121,162)(122,161)(123,168)(124,167)(125,165)
(126,166)(127,164)(128,163)(129,194)(130,193)(131,200)(132,199)(133,197)
(134,198)(135,196)(136,195)(137,186)(138,185)(139,192)(140,191)(141,189)
(142,190)(143,188)(144,187)(145,178)(146,177)(147,184)(148,183)(149,181)
(150,182)(151,180)(152,179)(153,170)(154,169)(155,176)(156,175)(157,173)
(158,174)(159,172)(160,171)(201,202)(203,208)(204,207)(209,234)(210,233)
(211,240)(212,239)(213,237)(214,238)(215,236)(216,235)(217,226)(218,225)
(219,232)(220,231)(221,229)(222,230)(223,228)(224,227)(241,281)(242,282)
(243,287)(244,288)(245,286)(246,285)(247,283)(248,284)(249,313)(250,314)
(251,319)(252,320)(253,318)(254,317)(255,315)(256,316)(257,305)(258,306)
(259,311)(260,312)(261,310)(262,309)(263,307)(264,308)(265,297)(266,298)
(267,303)(268,304)(269,302)(270,301)(271,299)(272,300)(273,289)(274,290)
(275,295)(276,296)(277,294)(278,293)(279,291)(280,292)(323,327)(324,328)
(325,326)(329,353)(330,354)(331,359)(332,360)(333,358)(334,357)(335,355)
(336,356)(337,345)(338,346)(339,351)(340,352)(341,350)(342,349)(343,347)
(344,348)(361,402)(362,401)(363,408)(364,407)(365,405)(366,406)(367,404)
(368,403)(369,434)(370,433)(371,440)(372,439)(373,437)(374,438)(375,436)
(376,435)(377,426)(378,425)(379,432)(380,431)(381,429)(382,430)(383,428)
(384,427)(385,418)(386,417)(387,424)(388,423)(389,421)(390,422)(391,420)
(392,419)(393,410)(394,409)(395,416)(396,415)(397,413)(398,414)(399,412)
(400,411)(441,442)(443,448)(444,447)(449,474)(450,473)(451,480)(452,479)
(453,477)(454,478)(455,476)(456,475)(457,466)(458,465)(459,472)(460,471)
(461,469)(462,470)(463,468)(464,467);;
s3 := ( 1,249)( 2,250)( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)( 8,256)
( 9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)( 16,248)
( 17,273)( 18,274)( 19,275)( 20,276)( 21,277)( 22,278)( 23,279)( 24,280)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)( 40,264)
( 41,289)( 42,290)( 43,291)( 44,292)( 45,293)( 46,294)( 47,295)( 48,296)
( 49,281)( 50,282)( 51,283)( 52,284)( 53,285)( 54,286)( 55,287)( 56,288)
( 57,313)( 58,314)( 59,315)( 60,316)( 61,317)( 62,318)( 63,319)( 64,320)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)( 80,304)
( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)
( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)( 96,328)
( 97,353)( 98,354)( 99,355)(100,356)(101,357)(102,358)(103,359)(104,360)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)
(121,369)(122,370)(123,371)(124,372)(125,373)(126,374)(127,375)(128,376)
(129,361)(130,362)(131,363)(132,364)(133,365)(134,366)(135,367)(136,368)
(137,393)(138,394)(139,395)(140,396)(141,397)(142,398)(143,399)(144,400)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)(160,384)
(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)
(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)
(177,433)(178,434)(179,435)(180,436)(181,437)(182,438)(183,439)(184,440)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)(200,424)
(201,449)(202,450)(203,451)(204,452)(205,453)(206,454)(207,455)(208,456)
(209,441)(210,442)(211,443)(212,444)(213,445)(214,446)(215,447)(216,448)
(217,473)(218,474)(219,475)(220,476)(221,477)(222,478)(223,479)(224,480)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,457)(234,458)(235,459)(236,460)(237,461)(238,462)(239,463)(240,464);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 1,125)( 2,126)( 3,128)( 4,127)( 5,122)( 6,121)( 7,123)
( 8,124)( 9,133)( 10,134)( 11,136)( 12,135)( 13,130)( 14,129)( 15,131)
( 16,132)( 17,141)( 18,142)( 19,144)( 20,143)( 21,138)( 22,137)( 23,139)
( 24,140)( 25,149)( 26,150)( 27,152)( 28,151)( 29,146)( 30,145)( 31,147)
( 32,148)( 33,157)( 34,158)( 35,160)( 36,159)( 37,154)( 38,153)( 39,155)
( 40,156)( 41,165)( 42,166)( 43,168)( 44,167)( 45,162)( 46,161)( 47,163)
( 48,164)( 49,173)( 50,174)( 51,176)( 52,175)( 53,170)( 54,169)( 55,171)
( 56,172)( 57,181)( 58,182)( 59,184)( 60,183)( 61,178)( 62,177)( 63,179)
( 64,180)( 65,189)( 66,190)( 67,192)( 68,191)( 69,186)( 70,185)( 71,187)
( 72,188)( 73,197)( 74,198)( 75,200)( 76,199)( 77,194)( 78,193)( 79,195)
( 80,196)( 81,205)( 82,206)( 83,208)( 84,207)( 85,202)( 86,201)( 87,203)
( 88,204)( 89,213)( 90,214)( 91,216)( 92,215)( 93,210)( 94,209)( 95,211)
( 96,212)( 97,221)( 98,222)( 99,224)(100,223)(101,218)(102,217)(103,219)
(104,220)(105,229)(106,230)(107,232)(108,231)(109,226)(110,225)(111,227)
(112,228)(113,237)(114,238)(115,240)(116,239)(117,234)(118,233)(119,235)
(120,236)(241,365)(242,366)(243,368)(244,367)(245,362)(246,361)(247,363)
(248,364)(249,373)(250,374)(251,376)(252,375)(253,370)(254,369)(255,371)
(256,372)(257,381)(258,382)(259,384)(260,383)(261,378)(262,377)(263,379)
(264,380)(265,389)(266,390)(267,392)(268,391)(269,386)(270,385)(271,387)
(272,388)(273,397)(274,398)(275,400)(276,399)(277,394)(278,393)(279,395)
(280,396)(281,405)(282,406)(283,408)(284,407)(285,402)(286,401)(287,403)
(288,404)(289,413)(290,414)(291,416)(292,415)(293,410)(294,409)(295,411)
(296,412)(297,421)(298,422)(299,424)(300,423)(301,418)(302,417)(303,419)
(304,420)(305,429)(306,430)(307,432)(308,431)(309,426)(310,425)(311,427)
(312,428)(313,437)(314,438)(315,440)(316,439)(317,434)(318,433)(319,435)
(320,436)(321,445)(322,446)(323,448)(324,447)(325,442)(326,441)(327,443)
(328,444)(329,453)(330,454)(331,456)(332,455)(333,450)(334,449)(335,451)
(336,452)(337,461)(338,462)(339,464)(340,463)(341,458)(342,457)(343,459)
(344,460)(345,469)(346,470)(347,472)(348,471)(349,466)(350,465)(351,467)
(352,468)(353,477)(354,478)(355,480)(356,479)(357,474)(358,473)(359,475)
(360,476);
s1 := 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)
(121,122)(125,128)(126,127)(129,130)(133,136)(134,135)(137,138)(141,144)
(142,143)(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)(161,202)
(162,201)(163,203)(164,204)(165,208)(166,207)(167,206)(168,205)(169,210)
(170,209)(171,211)(172,212)(173,216)(174,215)(175,214)(176,213)(177,218)
(178,217)(179,219)(180,220)(181,224)(182,223)(183,222)(184,221)(185,226)
(186,225)(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,234)
(194,233)(195,235)(196,236)(197,240)(198,239)(199,238)(200,237)(243,244)
(245,247)(246,248)(251,252)(253,255)(254,256)(259,260)(261,263)(262,264)
(267,268)(269,271)(270,272)(275,276)(277,279)(278,280)(281,321)(282,322)
(283,324)(284,323)(285,327)(286,328)(287,325)(288,326)(289,329)(290,330)
(291,332)(292,331)(293,335)(294,336)(295,333)(296,334)(297,337)(298,338)
(299,340)(300,339)(301,343)(302,344)(303,341)(304,342)(305,345)(306,346)
(307,348)(308,347)(309,351)(310,352)(311,349)(312,350)(313,353)(314,354)
(315,356)(316,355)(317,359)(318,360)(319,357)(320,358)(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);
s2 := Sym(480)!( 1, 41)( 2, 42)( 3, 47)( 4, 48)( 5, 46)( 6, 45)( 7, 43)
( 8, 44)( 9, 73)( 10, 74)( 11, 79)( 12, 80)( 13, 78)( 14, 77)( 15, 75)
( 16, 76)( 17, 65)( 18, 66)( 19, 71)( 20, 72)( 21, 70)( 22, 69)( 23, 67)
( 24, 68)( 25, 57)( 26, 58)( 27, 63)( 28, 64)( 29, 62)( 30, 61)( 31, 59)
( 32, 60)( 33, 49)( 34, 50)( 35, 55)( 36, 56)( 37, 54)( 38, 53)( 39, 51)
( 40, 52)( 83, 87)( 84, 88)( 85, 86)( 89,113)( 90,114)( 91,119)( 92,120)
( 93,118)( 94,117)( 95,115)( 96,116)( 97,105)( 98,106)( 99,111)(100,112)
(101,110)(102,109)(103,107)(104,108)(121,162)(122,161)(123,168)(124,167)
(125,165)(126,166)(127,164)(128,163)(129,194)(130,193)(131,200)(132,199)
(133,197)(134,198)(135,196)(136,195)(137,186)(138,185)(139,192)(140,191)
(141,189)(142,190)(143,188)(144,187)(145,178)(146,177)(147,184)(148,183)
(149,181)(150,182)(151,180)(152,179)(153,170)(154,169)(155,176)(156,175)
(157,173)(158,174)(159,172)(160,171)(201,202)(203,208)(204,207)(209,234)
(210,233)(211,240)(212,239)(213,237)(214,238)(215,236)(216,235)(217,226)
(218,225)(219,232)(220,231)(221,229)(222,230)(223,228)(224,227)(241,281)
(242,282)(243,287)(244,288)(245,286)(246,285)(247,283)(248,284)(249,313)
(250,314)(251,319)(252,320)(253,318)(254,317)(255,315)(256,316)(257,305)
(258,306)(259,311)(260,312)(261,310)(262,309)(263,307)(264,308)(265,297)
(266,298)(267,303)(268,304)(269,302)(270,301)(271,299)(272,300)(273,289)
(274,290)(275,295)(276,296)(277,294)(278,293)(279,291)(280,292)(323,327)
(324,328)(325,326)(329,353)(330,354)(331,359)(332,360)(333,358)(334,357)
(335,355)(336,356)(337,345)(338,346)(339,351)(340,352)(341,350)(342,349)
(343,347)(344,348)(361,402)(362,401)(363,408)(364,407)(365,405)(366,406)
(367,404)(368,403)(369,434)(370,433)(371,440)(372,439)(373,437)(374,438)
(375,436)(376,435)(377,426)(378,425)(379,432)(380,431)(381,429)(382,430)
(383,428)(384,427)(385,418)(386,417)(387,424)(388,423)(389,421)(390,422)
(391,420)(392,419)(393,410)(394,409)(395,416)(396,415)(397,413)(398,414)
(399,412)(400,411)(441,442)(443,448)(444,447)(449,474)(450,473)(451,480)
(452,479)(453,477)(454,478)(455,476)(456,475)(457,466)(458,465)(459,472)
(460,471)(461,469)(462,470)(463,468)(464,467);
s3 := Sym(480)!( 1,249)( 2,250)( 3,251)( 4,252)( 5,253)( 6,254)( 7,255)
( 8,256)( 9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)
( 16,248)( 17,273)( 18,274)( 19,275)( 20,276)( 21,277)( 22,278)( 23,279)
( 24,280)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,257)( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)
( 40,264)( 41,289)( 42,290)( 43,291)( 44,292)( 45,293)( 46,294)( 47,295)
( 48,296)( 49,281)( 50,282)( 51,283)( 52,284)( 53,285)( 54,286)( 55,287)
( 56,288)( 57,313)( 58,314)( 59,315)( 60,316)( 61,317)( 62,318)( 63,319)
( 64,320)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,297)( 74,298)( 75,299)( 76,300)( 77,301)( 78,302)( 79,303)
( 80,304)( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)
( 88,336)( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)
( 96,328)( 97,353)( 98,354)( 99,355)(100,356)(101,357)(102,358)(103,359)
(104,360)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)
(120,344)(121,369)(122,370)(123,371)(124,372)(125,373)(126,374)(127,375)
(128,376)(129,361)(130,362)(131,363)(132,364)(133,365)(134,366)(135,367)
(136,368)(137,393)(138,394)(139,395)(140,396)(141,397)(142,398)(143,399)
(144,400)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,377)(154,378)(155,379)(156,380)(157,381)(158,382)(159,383)
(160,384)(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)
(168,416)(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)
(176,408)(177,433)(178,434)(179,435)(180,436)(181,437)(182,438)(183,439)
(184,440)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,417)(194,418)(195,419)(196,420)(197,421)(198,422)(199,423)
(200,424)(201,449)(202,450)(203,451)(204,452)(205,453)(206,454)(207,455)
(208,456)(209,441)(210,442)(211,443)(212,444)(213,445)(214,446)(215,447)
(216,448)(217,473)(218,474)(219,475)(220,476)(221,477)(222,478)(223,479)
(224,480)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,457)(234,458)(235,459)(236,460)(237,461)(238,462)(239,463)
(240,464);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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 >;
References : None.
to this polytope