Polytope of Type {4,6,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,20}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240408)
Rank : 4
Schlafli Type : {4,6,20}
Number of vertices, edges, etc : 8, 24, 120, 20
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
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) :
2-fold quotients : {4,6,20}*960c
4-fold quotients : {2,6,20}*480b
5-fold quotients : {4,6,4}*384e
10-fold quotients : {4,3,4}*192b, {4,6,4}*192e, {4,6,4}*192g
20-fold quotients : {2,6,4}*96b, {4,3,4}*96
40-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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)
( 17,265)( 18,266)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)( 24,272)
( 25,257)( 26,258)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)( 32,264)
( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)
( 41,273)( 42,274)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)( 48,280)
( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)
( 57,289)( 58,290)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)( 64,296)
( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)
( 73,305)( 74,306)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)( 80,312)
( 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)
( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)
(105,337)(106,338)(107,339)(108,340)(109,341)(110,342)(111,343)(112,344)
(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)
(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)(128,360)
(129,377)(130,378)(131,379)(132,380)(133,381)(134,382)(135,383)(136,384)
(137,369)(138,370)(139,371)(140,372)(141,373)(142,374)(143,375)(144,376)
(145,393)(146,394)(147,395)(148,396)(149,397)(150,398)(151,399)(152,400)
(153,385)(154,386)(155,387)(156,388)(157,389)(158,390)(159,391)(160,392)
(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)
(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)
(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)(192,424)
(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)
(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)(208,440)
(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)
(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)
(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)(232,480)
(233,465)(234,466)(235,467)(236,468)(237,469)(238,470)(239,471)(240,472);;
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)
( 17,145)( 18,148)( 19,147)( 20,146)( 21,157)( 22,160)( 23,159)( 24,158)
( 25,153)( 26,156)( 27,155)( 28,154)( 29,149)( 30,152)( 31,151)( 32,150)
( 33,129)( 34,132)( 35,131)( 36,130)( 37,141)( 38,144)( 39,143)( 40,142)
( 41,137)( 42,140)( 43,139)( 44,138)( 45,133)( 46,136)( 47,135)( 48,134)
( 49,113)( 50,116)( 51,115)( 52,114)( 53,125)( 54,128)( 55,127)( 56,126)
( 57,121)( 58,124)( 59,123)( 60,122)( 61,117)( 62,120)( 63,119)( 64,118)
( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69,109)( 70,112)( 71,111)( 72,110)
( 73,105)( 74,108)( 75,107)( 76,106)( 77,101)( 78,104)( 79,103)( 80,102)
(162,164)(165,173)(166,176)(167,175)(168,174)(170,172)(177,225)(178,228)
(179,227)(180,226)(181,237)(182,240)(183,239)(184,238)(185,233)(186,236)
(187,235)(188,234)(189,229)(190,232)(191,231)(192,230)(193,209)(194,212)
(195,211)(196,210)(197,221)(198,224)(199,223)(200,222)(201,217)(202,220)
(203,219)(204,218)(205,213)(206,216)(207,215)(208,214)(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)(257,385)(258,388)
(259,387)(260,386)(261,397)(262,400)(263,399)(264,398)(265,393)(266,396)
(267,395)(268,394)(269,389)(270,392)(271,391)(272,390)(273,369)(274,372)
(275,371)(276,370)(277,381)(278,384)(279,383)(280,382)(281,377)(282,380)
(283,379)(284,378)(285,373)(286,376)(287,375)(288,374)(289,353)(290,356)
(291,355)(292,354)(293,365)(294,368)(295,367)(296,366)(297,361)(298,364)
(299,363)(300,362)(301,357)(302,360)(303,359)(304,358)(305,337)(306,340)
(307,339)(308,338)(309,349)(310,352)(311,351)(312,350)(313,345)(314,348)
(315,347)(316,346)(317,341)(318,344)(319,343)(320,342)(402,404)(405,413)
(406,416)(407,415)(408,414)(410,412)(417,465)(418,468)(419,467)(420,466)
(421,477)(422,480)(423,479)(424,478)(425,473)(426,476)(427,475)(428,474)
(429,469)(430,472)(431,471)(432,470)(433,449)(434,452)(435,451)(436,450)
(437,461)(438,464)(439,463)(440,462)(441,457)(442,460)(443,459)(444,458)
(445,453)(446,456)(447,455)(448,454);;
s3 := ( 1, 18)( 2, 17)( 3, 20)( 4, 19)( 5, 22)( 6, 21)( 7, 24)( 8, 23)
( 9, 26)( 10, 25)( 11, 28)( 12, 27)( 13, 30)( 14, 29)( 15, 32)( 16, 31)
( 33, 66)( 34, 65)( 35, 68)( 36, 67)( 37, 70)( 38, 69)( 39, 72)( 40, 71)
( 41, 74)( 42, 73)( 43, 76)( 44, 75)( 45, 78)( 46, 77)( 47, 80)( 48, 79)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 81, 98)( 82, 97)( 83,100)( 84, 99)( 85,102)( 86,101)( 87,104)( 88,103)
( 89,106)( 90,105)( 91,108)( 92,107)( 93,110)( 94,109)( 95,112)( 96,111)
(113,146)(114,145)(115,148)(116,147)(117,150)(118,149)(119,152)(120,151)
(121,154)(122,153)(123,156)(124,155)(125,158)(126,157)(127,160)(128,159)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(161,178)(162,177)(163,180)(164,179)(165,182)(166,181)(167,184)(168,183)
(169,186)(170,185)(171,188)(172,187)(173,190)(174,189)(175,192)(176,191)
(193,226)(194,225)(195,228)(196,227)(197,230)(198,229)(199,232)(200,231)
(201,234)(202,233)(203,236)(204,235)(205,238)(206,237)(207,240)(208,239)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(241,258)(242,257)(243,260)(244,259)(245,262)(246,261)(247,264)(248,263)
(249,266)(250,265)(251,268)(252,267)(253,270)(254,269)(255,272)(256,271)
(273,306)(274,305)(275,308)(276,307)(277,310)(278,309)(279,312)(280,311)
(281,314)(282,313)(283,316)(284,315)(285,318)(286,317)(287,320)(288,319)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(321,338)(322,337)(323,340)(324,339)(325,342)(326,341)(327,344)(328,343)
(329,346)(330,345)(331,348)(332,347)(333,350)(334,349)(335,352)(336,351)
(353,386)(354,385)(355,388)(356,387)(357,390)(358,389)(359,392)(360,391)
(361,394)(362,393)(363,396)(364,395)(365,398)(366,397)(367,400)(368,399)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(401,418)(402,417)(403,420)(404,419)(405,422)(406,421)(407,424)(408,423)
(409,426)(410,425)(411,428)(412,427)(413,430)(414,429)(415,432)(416,431)
(433,466)(434,465)(435,468)(436,467)(437,470)(438,469)(439,472)(440,471)
(441,474)(442,473)(443,476)(444,475)(445,478)(446,477)(447,480)(448,479)
(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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)( 17,265)( 18,266)( 19,267)( 20,268)( 21,269)( 22,270)( 23,271)
( 24,272)( 25,257)( 26,258)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)
( 32,264)( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)
( 40,288)( 41,273)( 42,274)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)
( 48,280)( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)
( 56,304)( 57,289)( 58,290)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)
( 64,296)( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)
( 72,320)( 73,305)( 74,306)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)
( 80,312)( 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)( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)
(104,352)(105,337)(106,338)(107,339)(108,340)(109,341)(110,342)(111,343)
(112,344)(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)
(120,368)(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)
(128,360)(129,377)(130,378)(131,379)(132,380)(133,381)(134,382)(135,383)
(136,384)(137,369)(138,370)(139,371)(140,372)(141,373)(142,374)(143,375)
(144,376)(145,393)(146,394)(147,395)(148,396)(149,397)(150,398)(151,399)
(152,400)(153,385)(154,386)(155,387)(156,388)(157,389)(158,390)(159,391)
(160,392)(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)(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)
(184,432)(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)
(192,424)(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)
(200,448)(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)
(208,440)(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)
(216,464)(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)
(224,456)(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)
(232,480)(233,465)(234,466)(235,467)(236,468)(237,469)(238,470)(239,471)
(240,472);
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)( 17,145)( 18,148)( 19,147)( 20,146)( 21,157)( 22,160)( 23,159)
( 24,158)( 25,153)( 26,156)( 27,155)( 28,154)( 29,149)( 30,152)( 31,151)
( 32,150)( 33,129)( 34,132)( 35,131)( 36,130)( 37,141)( 38,144)( 39,143)
( 40,142)( 41,137)( 42,140)( 43,139)( 44,138)( 45,133)( 46,136)( 47,135)
( 48,134)( 49,113)( 50,116)( 51,115)( 52,114)( 53,125)( 54,128)( 55,127)
( 56,126)( 57,121)( 58,124)( 59,123)( 60,122)( 61,117)( 62,120)( 63,119)
( 64,118)( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69,109)( 70,112)( 71,111)
( 72,110)( 73,105)( 74,108)( 75,107)( 76,106)( 77,101)( 78,104)( 79,103)
( 80,102)(162,164)(165,173)(166,176)(167,175)(168,174)(170,172)(177,225)
(178,228)(179,227)(180,226)(181,237)(182,240)(183,239)(184,238)(185,233)
(186,236)(187,235)(188,234)(189,229)(190,232)(191,231)(192,230)(193,209)
(194,212)(195,211)(196,210)(197,221)(198,224)(199,223)(200,222)(201,217)
(202,220)(203,219)(204,218)(205,213)(206,216)(207,215)(208,214)(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)(257,385)
(258,388)(259,387)(260,386)(261,397)(262,400)(263,399)(264,398)(265,393)
(266,396)(267,395)(268,394)(269,389)(270,392)(271,391)(272,390)(273,369)
(274,372)(275,371)(276,370)(277,381)(278,384)(279,383)(280,382)(281,377)
(282,380)(283,379)(284,378)(285,373)(286,376)(287,375)(288,374)(289,353)
(290,356)(291,355)(292,354)(293,365)(294,368)(295,367)(296,366)(297,361)
(298,364)(299,363)(300,362)(301,357)(302,360)(303,359)(304,358)(305,337)
(306,340)(307,339)(308,338)(309,349)(310,352)(311,351)(312,350)(313,345)
(314,348)(315,347)(316,346)(317,341)(318,344)(319,343)(320,342)(402,404)
(405,413)(406,416)(407,415)(408,414)(410,412)(417,465)(418,468)(419,467)
(420,466)(421,477)(422,480)(423,479)(424,478)(425,473)(426,476)(427,475)
(428,474)(429,469)(430,472)(431,471)(432,470)(433,449)(434,452)(435,451)
(436,450)(437,461)(438,464)(439,463)(440,462)(441,457)(442,460)(443,459)
(444,458)(445,453)(446,456)(447,455)(448,454);
s3 := Sym(480)!( 1, 18)( 2, 17)( 3, 20)( 4, 19)( 5, 22)( 6, 21)( 7, 24)
( 8, 23)( 9, 26)( 10, 25)( 11, 28)( 12, 27)( 13, 30)( 14, 29)( 15, 32)
( 16, 31)( 33, 66)( 34, 65)( 35, 68)( 36, 67)( 37, 70)( 38, 69)( 39, 72)
( 40, 71)( 41, 74)( 42, 73)( 43, 76)( 44, 75)( 45, 78)( 46, 77)( 47, 80)
( 48, 79)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 81, 98)( 82, 97)( 83,100)( 84, 99)( 85,102)( 86,101)( 87,104)
( 88,103)( 89,106)( 90,105)( 91,108)( 92,107)( 93,110)( 94,109)( 95,112)
( 96,111)(113,146)(114,145)(115,148)(116,147)(117,150)(118,149)(119,152)
(120,151)(121,154)(122,153)(123,156)(124,155)(125,158)(126,157)(127,160)
(128,159)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(161,178)(162,177)(163,180)(164,179)(165,182)(166,181)(167,184)
(168,183)(169,186)(170,185)(171,188)(172,187)(173,190)(174,189)(175,192)
(176,191)(193,226)(194,225)(195,228)(196,227)(197,230)(198,229)(199,232)
(200,231)(201,234)(202,233)(203,236)(204,235)(205,238)(206,237)(207,240)
(208,239)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(241,258)(242,257)(243,260)(244,259)(245,262)(246,261)(247,264)
(248,263)(249,266)(250,265)(251,268)(252,267)(253,270)(254,269)(255,272)
(256,271)(273,306)(274,305)(275,308)(276,307)(277,310)(278,309)(279,312)
(280,311)(281,314)(282,313)(283,316)(284,315)(285,318)(286,317)(287,320)
(288,319)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(321,338)(322,337)(323,340)(324,339)(325,342)(326,341)(327,344)
(328,343)(329,346)(330,345)(331,348)(332,347)(333,350)(334,349)(335,352)
(336,351)(353,386)(354,385)(355,388)(356,387)(357,390)(358,389)(359,392)
(360,391)(361,394)(362,393)(363,396)(364,395)(365,398)(366,397)(367,400)
(368,399)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(401,418)(402,417)(403,420)(404,419)(405,422)(406,421)(407,424)
(408,423)(409,426)(410,425)(411,428)(412,427)(413,430)(414,429)(415,432)
(416,431)(433,466)(434,465)(435,468)(436,467)(437,470)(438,469)(439,472)
(440,471)(441,474)(442,473)(443,476)(444,475)(445,478)(446,477)(447,480)
(448,479)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)
(463,464);
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,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2 >;
References : None.
to this polytope