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