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