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