Polytope of Type {4,6,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,20}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240142)
Rank : 4
Schlafli Type : {4,6,20}
Number of vertices, edges, etc : 8, 24, 120, 20
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 : {4,6,20}*960b, {4,6,10}*960e
4-fold quotients : {2,6,20}*480a, {4,6,10}*480b
5-fold quotients : {4,6,4}*384b
8-fold quotients : {2,6,10}*240
10-fold quotients : {4,6,4}*192c, {4,6,2}*192
12-fold quotients : {2,2,20}*160
20-fold quotients : {2,6,4}*96a, {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
60-fold quotients : {2,2,4}*32
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 := ( 1,243)( 2,244)( 3,241)( 4,242)( 5,247)( 6,248)( 7,245)( 8,246)
( 9,251)( 10,252)( 11,249)( 12,250)( 13,255)( 14,256)( 15,253)( 16,254)
( 17,259)( 18,260)( 19,257)( 20,258)( 21,263)( 22,264)( 23,261)( 24,262)
( 25,267)( 26,268)( 27,265)( 28,266)( 29,271)( 30,272)( 31,269)( 32,270)
( 33,275)( 34,276)( 35,273)( 36,274)( 37,279)( 38,280)( 39,277)( 40,278)
( 41,283)( 42,284)( 43,281)( 44,282)( 45,287)( 46,288)( 47,285)( 48,286)
( 49,291)( 50,292)( 51,289)( 52,290)( 53,295)( 54,296)( 55,293)( 56,294)
( 57,299)( 58,300)( 59,297)( 60,298)( 61,303)( 62,304)( 63,301)( 64,302)
( 65,307)( 66,308)( 67,305)( 68,306)( 69,311)( 70,312)( 71,309)( 72,310)
( 73,315)( 74,316)( 75,313)( 76,314)( 77,319)( 78,320)( 79,317)( 80,318)
( 81,323)( 82,324)( 83,321)( 84,322)( 85,327)( 86,328)( 87,325)( 88,326)
( 89,331)( 90,332)( 91,329)( 92,330)( 93,335)( 94,336)( 95,333)( 96,334)
( 97,339)( 98,340)( 99,337)(100,338)(101,343)(102,344)(103,341)(104,342)
(105,347)(106,348)(107,345)(108,346)(109,351)(110,352)(111,349)(112,350)
(113,355)(114,356)(115,353)(116,354)(117,359)(118,360)(119,357)(120,358)
(121,363)(122,364)(123,361)(124,362)(125,367)(126,368)(127,365)(128,366)
(129,371)(130,372)(131,369)(132,370)(133,375)(134,376)(135,373)(136,374)
(137,379)(138,380)(139,377)(140,378)(141,383)(142,384)(143,381)(144,382)
(145,387)(146,388)(147,385)(148,386)(149,391)(150,392)(151,389)(152,390)
(153,395)(154,396)(155,393)(156,394)(157,399)(158,400)(159,397)(160,398)
(161,403)(162,404)(163,401)(164,402)(165,407)(166,408)(167,405)(168,406)
(169,411)(170,412)(171,409)(172,410)(173,415)(174,416)(175,413)(176,414)
(177,419)(178,420)(179,417)(180,418)(181,423)(182,424)(183,421)(184,422)
(185,427)(186,428)(187,425)(188,426)(189,431)(190,432)(191,429)(192,430)
(193,435)(194,436)(195,433)(196,434)(197,439)(198,440)(199,437)(200,438)
(201,443)(202,444)(203,441)(204,442)(205,447)(206,448)(207,445)(208,446)
(209,451)(210,452)(211,449)(212,450)(213,455)(214,456)(215,453)(216,454)
(217,459)(218,460)(219,457)(220,458)(221,463)(222,464)(223,461)(224,462)
(225,467)(226,468)(227,465)(228,466)(229,471)(230,472)(231,469)(232,470)
(233,475)(234,476)(235,473)(236,474)(237,479)(238,480)(239,477)(240,478);;
s1 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)( 23, 44)
( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)( 31, 52)
( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)( 39, 60)
( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)( 82,102)
( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)( 90,110)
( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)( 98,118)
( 99,120)(100,119)(123,124)(127,128)(131,132)(135,136)(139,140)(141,161)
(142,162)(143,164)(144,163)(145,165)(146,166)(147,168)(148,167)(149,169)
(150,170)(151,172)(152,171)(153,173)(154,174)(155,176)(156,175)(157,177)
(158,178)(159,180)(160,179)(183,184)(187,188)(191,192)(195,196)(199,200)
(201,221)(202,222)(203,224)(204,223)(205,225)(206,226)(207,228)(208,227)
(209,229)(210,230)(211,232)(212,231)(213,233)(214,234)(215,236)(216,235)
(217,237)(218,238)(219,240)(220,239)(243,244)(247,248)(251,252)(255,256)
(259,260)(261,281)(262,282)(263,284)(264,283)(265,285)(266,286)(267,288)
(268,287)(269,289)(270,290)(271,292)(272,291)(273,293)(274,294)(275,296)
(276,295)(277,297)(278,298)(279,300)(280,299)(303,304)(307,308)(311,312)
(315,316)(319,320)(321,341)(322,342)(323,344)(324,343)(325,345)(326,346)
(327,348)(328,347)(329,349)(330,350)(331,352)(332,351)(333,353)(334,354)
(335,356)(336,355)(337,357)(338,358)(339,360)(340,359)(363,364)(367,368)
(371,372)(375,376)(379,380)(381,401)(382,402)(383,404)(384,403)(385,405)
(386,406)(387,408)(388,407)(389,409)(390,410)(391,412)(392,411)(393,413)
(394,414)(395,416)(396,415)(397,417)(398,418)(399,420)(400,419)(423,424)
(427,428)(431,432)(435,436)(439,440)(441,461)(442,462)(443,464)(444,463)
(445,465)(446,466)(447,468)(448,467)(449,469)(450,470)(451,472)(452,471)
(453,473)(454,474)(455,476)(456,475)(457,477)(458,478)(459,480)(460,479);;
s2 := ( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 37)( 6, 40)( 7, 39)( 8, 38)
( 9, 33)( 10, 36)( 11, 35)( 12, 34)( 13, 29)( 14, 32)( 15, 31)( 16, 30)
( 17, 25)( 18, 28)( 19, 27)( 20, 26)( 42, 44)( 45, 57)( 46, 60)( 47, 59)
( 48, 58)( 49, 53)( 50, 56)( 51, 55)( 52, 54)( 61, 81)( 62, 84)( 63, 83)
( 64, 82)( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69, 93)( 70, 96)( 71, 95)
( 72, 94)( 73, 89)( 74, 92)( 75, 91)( 76, 90)( 77, 85)( 78, 88)( 79, 87)
( 80, 86)(102,104)(105,117)(106,120)(107,119)(108,118)(109,113)(110,116)
(111,115)(112,114)(121,201)(122,204)(123,203)(124,202)(125,217)(126,220)
(127,219)(128,218)(129,213)(130,216)(131,215)(132,214)(133,209)(134,212)
(135,211)(136,210)(137,205)(138,208)(139,207)(140,206)(141,181)(142,184)
(143,183)(144,182)(145,197)(146,200)(147,199)(148,198)(149,193)(150,196)
(151,195)(152,194)(153,189)(154,192)(155,191)(156,190)(157,185)(158,188)
(159,187)(160,186)(161,221)(162,224)(163,223)(164,222)(165,237)(166,240)
(167,239)(168,238)(169,233)(170,236)(171,235)(172,234)(173,229)(174,232)
(175,231)(176,230)(177,225)(178,228)(179,227)(180,226)(241,261)(242,264)
(243,263)(244,262)(245,277)(246,280)(247,279)(248,278)(249,273)(250,276)
(251,275)(252,274)(253,269)(254,272)(255,271)(256,270)(257,265)(258,268)
(259,267)(260,266)(282,284)(285,297)(286,300)(287,299)(288,298)(289,293)
(290,296)(291,295)(292,294)(301,321)(302,324)(303,323)(304,322)(305,337)
(306,340)(307,339)(308,338)(309,333)(310,336)(311,335)(312,334)(313,329)
(314,332)(315,331)(316,330)(317,325)(318,328)(319,327)(320,326)(342,344)
(345,357)(346,360)(347,359)(348,358)(349,353)(350,356)(351,355)(352,354)
(361,441)(362,444)(363,443)(364,442)(365,457)(366,460)(367,459)(368,458)
(369,453)(370,456)(371,455)(372,454)(373,449)(374,452)(375,451)(376,450)
(377,445)(378,448)(379,447)(380,446)(381,421)(382,424)(383,423)(384,422)
(385,437)(386,440)(387,439)(388,438)(389,433)(390,436)(391,435)(392,434)
(393,429)(394,432)(395,431)(396,430)(397,425)(398,428)(399,427)(400,426)
(401,461)(402,464)(403,463)(404,462)(405,477)(406,480)(407,479)(408,478)
(409,473)(410,476)(411,475)(412,474)(413,469)(414,472)(415,471)(416,470)
(417,465)(418,468)(419,467)(420,466);;
s3 := ( 1,125)( 2,126)( 3,127)( 4,128)( 5,121)( 6,122)( 7,123)( 8,124)
( 9,137)( 10,138)( 11,139)( 12,140)( 13,133)( 14,134)( 15,135)( 16,136)
( 17,129)( 18,130)( 19,131)( 20,132)( 21,145)( 22,146)( 23,147)( 24,148)
( 25,141)( 26,142)( 27,143)( 28,144)( 29,157)( 30,158)( 31,159)( 32,160)
( 33,153)( 34,154)( 35,155)( 36,156)( 37,149)( 38,150)( 39,151)( 40,152)
( 41,165)( 42,166)( 43,167)( 44,168)( 45,161)( 46,162)( 47,163)( 48,164)
( 49,177)( 50,178)( 51,179)( 52,180)( 53,173)( 54,174)( 55,175)( 56,176)
( 57,169)( 58,170)( 59,171)( 60,172)( 61,185)( 62,186)( 63,187)( 64,188)
( 65,181)( 66,182)( 67,183)( 68,184)( 69,197)( 70,198)( 71,199)( 72,200)
( 73,193)( 74,194)( 75,195)( 76,196)( 77,189)( 78,190)( 79,191)( 80,192)
( 81,205)( 82,206)( 83,207)( 84,208)( 85,201)( 86,202)( 87,203)( 88,204)
( 89,217)( 90,218)( 91,219)( 92,220)( 93,213)( 94,214)( 95,215)( 96,216)
( 97,209)( 98,210)( 99,211)(100,212)(101,225)(102,226)(103,227)(104,228)
(105,221)(106,222)(107,223)(108,224)(109,237)(110,238)(111,239)(112,240)
(113,233)(114,234)(115,235)(116,236)(117,229)(118,230)(119,231)(120,232)
(241,365)(242,366)(243,367)(244,368)(245,361)(246,362)(247,363)(248,364)
(249,377)(250,378)(251,379)(252,380)(253,373)(254,374)(255,375)(256,376)
(257,369)(258,370)(259,371)(260,372)(261,385)(262,386)(263,387)(264,388)
(265,381)(266,382)(267,383)(268,384)(269,397)(270,398)(271,399)(272,400)
(273,393)(274,394)(275,395)(276,396)(277,389)(278,390)(279,391)(280,392)
(281,405)(282,406)(283,407)(284,408)(285,401)(286,402)(287,403)(288,404)
(289,417)(290,418)(291,419)(292,420)(293,413)(294,414)(295,415)(296,416)
(297,409)(298,410)(299,411)(300,412)(301,425)(302,426)(303,427)(304,428)
(305,421)(306,422)(307,423)(308,424)(309,437)(310,438)(311,439)(312,440)
(313,433)(314,434)(315,435)(316,436)(317,429)(318,430)(319,431)(320,432)
(321,445)(322,446)(323,447)(324,448)(325,441)(326,442)(327,443)(328,444)
(329,457)(330,458)(331,459)(332,460)(333,453)(334,454)(335,455)(336,456)
(337,449)(338,450)(339,451)(340,452)(341,465)(342,466)(343,467)(344,468)
(345,461)(346,462)(347,463)(348,464)(349,477)(350,478)(351,479)(352,480)
(353,473)(354,474)(355,475)(356,476)(357,469)(358,470)(359,471)(360,472);;
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,
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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)!( 1,243)( 2,244)( 3,241)( 4,242)( 5,247)( 6,248)( 7,245)
( 8,246)( 9,251)( 10,252)( 11,249)( 12,250)( 13,255)( 14,256)( 15,253)
( 16,254)( 17,259)( 18,260)( 19,257)( 20,258)( 21,263)( 22,264)( 23,261)
( 24,262)( 25,267)( 26,268)( 27,265)( 28,266)( 29,271)( 30,272)( 31,269)
( 32,270)( 33,275)( 34,276)( 35,273)( 36,274)( 37,279)( 38,280)( 39,277)
( 40,278)( 41,283)( 42,284)( 43,281)( 44,282)( 45,287)( 46,288)( 47,285)
( 48,286)( 49,291)( 50,292)( 51,289)( 52,290)( 53,295)( 54,296)( 55,293)
( 56,294)( 57,299)( 58,300)( 59,297)( 60,298)( 61,303)( 62,304)( 63,301)
( 64,302)( 65,307)( 66,308)( 67,305)( 68,306)( 69,311)( 70,312)( 71,309)
( 72,310)( 73,315)( 74,316)( 75,313)( 76,314)( 77,319)( 78,320)( 79,317)
( 80,318)( 81,323)( 82,324)( 83,321)( 84,322)( 85,327)( 86,328)( 87,325)
( 88,326)( 89,331)( 90,332)( 91,329)( 92,330)( 93,335)( 94,336)( 95,333)
( 96,334)( 97,339)( 98,340)( 99,337)(100,338)(101,343)(102,344)(103,341)
(104,342)(105,347)(106,348)(107,345)(108,346)(109,351)(110,352)(111,349)
(112,350)(113,355)(114,356)(115,353)(116,354)(117,359)(118,360)(119,357)
(120,358)(121,363)(122,364)(123,361)(124,362)(125,367)(126,368)(127,365)
(128,366)(129,371)(130,372)(131,369)(132,370)(133,375)(134,376)(135,373)
(136,374)(137,379)(138,380)(139,377)(140,378)(141,383)(142,384)(143,381)
(144,382)(145,387)(146,388)(147,385)(148,386)(149,391)(150,392)(151,389)
(152,390)(153,395)(154,396)(155,393)(156,394)(157,399)(158,400)(159,397)
(160,398)(161,403)(162,404)(163,401)(164,402)(165,407)(166,408)(167,405)
(168,406)(169,411)(170,412)(171,409)(172,410)(173,415)(174,416)(175,413)
(176,414)(177,419)(178,420)(179,417)(180,418)(181,423)(182,424)(183,421)
(184,422)(185,427)(186,428)(187,425)(188,426)(189,431)(190,432)(191,429)
(192,430)(193,435)(194,436)(195,433)(196,434)(197,439)(198,440)(199,437)
(200,438)(201,443)(202,444)(203,441)(204,442)(205,447)(206,448)(207,445)
(208,446)(209,451)(210,452)(211,449)(212,450)(213,455)(214,456)(215,453)
(216,454)(217,459)(218,460)(219,457)(220,458)(221,463)(222,464)(223,461)
(224,462)(225,467)(226,468)(227,465)(228,466)(229,471)(230,472)(231,469)
(232,470)(233,475)(234,476)(235,473)(236,474)(237,479)(238,480)(239,477)
(240,478);
s1 := Sym(480)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)
( 23, 44)( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)
( 31, 52)( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)
( 39, 60)( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)
( 82,102)( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)
( 90,110)( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)
( 98,118)( 99,120)(100,119)(123,124)(127,128)(131,132)(135,136)(139,140)
(141,161)(142,162)(143,164)(144,163)(145,165)(146,166)(147,168)(148,167)
(149,169)(150,170)(151,172)(152,171)(153,173)(154,174)(155,176)(156,175)
(157,177)(158,178)(159,180)(160,179)(183,184)(187,188)(191,192)(195,196)
(199,200)(201,221)(202,222)(203,224)(204,223)(205,225)(206,226)(207,228)
(208,227)(209,229)(210,230)(211,232)(212,231)(213,233)(214,234)(215,236)
(216,235)(217,237)(218,238)(219,240)(220,239)(243,244)(247,248)(251,252)
(255,256)(259,260)(261,281)(262,282)(263,284)(264,283)(265,285)(266,286)
(267,288)(268,287)(269,289)(270,290)(271,292)(272,291)(273,293)(274,294)
(275,296)(276,295)(277,297)(278,298)(279,300)(280,299)(303,304)(307,308)
(311,312)(315,316)(319,320)(321,341)(322,342)(323,344)(324,343)(325,345)
(326,346)(327,348)(328,347)(329,349)(330,350)(331,352)(332,351)(333,353)
(334,354)(335,356)(336,355)(337,357)(338,358)(339,360)(340,359)(363,364)
(367,368)(371,372)(375,376)(379,380)(381,401)(382,402)(383,404)(384,403)
(385,405)(386,406)(387,408)(388,407)(389,409)(390,410)(391,412)(392,411)
(393,413)(394,414)(395,416)(396,415)(397,417)(398,418)(399,420)(400,419)
(423,424)(427,428)(431,432)(435,436)(439,440)(441,461)(442,462)(443,464)
(444,463)(445,465)(446,466)(447,468)(448,467)(449,469)(450,470)(451,472)
(452,471)(453,473)(454,474)(455,476)(456,475)(457,477)(458,478)(459,480)
(460,479);
s2 := Sym(480)!( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 37)( 6, 40)( 7, 39)
( 8, 38)( 9, 33)( 10, 36)( 11, 35)( 12, 34)( 13, 29)( 14, 32)( 15, 31)
( 16, 30)( 17, 25)( 18, 28)( 19, 27)( 20, 26)( 42, 44)( 45, 57)( 46, 60)
( 47, 59)( 48, 58)( 49, 53)( 50, 56)( 51, 55)( 52, 54)( 61, 81)( 62, 84)
( 63, 83)( 64, 82)( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69, 93)( 70, 96)
( 71, 95)( 72, 94)( 73, 89)( 74, 92)( 75, 91)( 76, 90)( 77, 85)( 78, 88)
( 79, 87)( 80, 86)(102,104)(105,117)(106,120)(107,119)(108,118)(109,113)
(110,116)(111,115)(112,114)(121,201)(122,204)(123,203)(124,202)(125,217)
(126,220)(127,219)(128,218)(129,213)(130,216)(131,215)(132,214)(133,209)
(134,212)(135,211)(136,210)(137,205)(138,208)(139,207)(140,206)(141,181)
(142,184)(143,183)(144,182)(145,197)(146,200)(147,199)(148,198)(149,193)
(150,196)(151,195)(152,194)(153,189)(154,192)(155,191)(156,190)(157,185)
(158,188)(159,187)(160,186)(161,221)(162,224)(163,223)(164,222)(165,237)
(166,240)(167,239)(168,238)(169,233)(170,236)(171,235)(172,234)(173,229)
(174,232)(175,231)(176,230)(177,225)(178,228)(179,227)(180,226)(241,261)
(242,264)(243,263)(244,262)(245,277)(246,280)(247,279)(248,278)(249,273)
(250,276)(251,275)(252,274)(253,269)(254,272)(255,271)(256,270)(257,265)
(258,268)(259,267)(260,266)(282,284)(285,297)(286,300)(287,299)(288,298)
(289,293)(290,296)(291,295)(292,294)(301,321)(302,324)(303,323)(304,322)
(305,337)(306,340)(307,339)(308,338)(309,333)(310,336)(311,335)(312,334)
(313,329)(314,332)(315,331)(316,330)(317,325)(318,328)(319,327)(320,326)
(342,344)(345,357)(346,360)(347,359)(348,358)(349,353)(350,356)(351,355)
(352,354)(361,441)(362,444)(363,443)(364,442)(365,457)(366,460)(367,459)
(368,458)(369,453)(370,456)(371,455)(372,454)(373,449)(374,452)(375,451)
(376,450)(377,445)(378,448)(379,447)(380,446)(381,421)(382,424)(383,423)
(384,422)(385,437)(386,440)(387,439)(388,438)(389,433)(390,436)(391,435)
(392,434)(393,429)(394,432)(395,431)(396,430)(397,425)(398,428)(399,427)
(400,426)(401,461)(402,464)(403,463)(404,462)(405,477)(406,480)(407,479)
(408,478)(409,473)(410,476)(411,475)(412,474)(413,469)(414,472)(415,471)
(416,470)(417,465)(418,468)(419,467)(420,466);
s3 := Sym(480)!( 1,125)( 2,126)( 3,127)( 4,128)( 5,121)( 6,122)( 7,123)
( 8,124)( 9,137)( 10,138)( 11,139)( 12,140)( 13,133)( 14,134)( 15,135)
( 16,136)( 17,129)( 18,130)( 19,131)( 20,132)( 21,145)( 22,146)( 23,147)
( 24,148)( 25,141)( 26,142)( 27,143)( 28,144)( 29,157)( 30,158)( 31,159)
( 32,160)( 33,153)( 34,154)( 35,155)( 36,156)( 37,149)( 38,150)( 39,151)
( 40,152)( 41,165)( 42,166)( 43,167)( 44,168)( 45,161)( 46,162)( 47,163)
( 48,164)( 49,177)( 50,178)( 51,179)( 52,180)( 53,173)( 54,174)( 55,175)
( 56,176)( 57,169)( 58,170)( 59,171)( 60,172)( 61,185)( 62,186)( 63,187)
( 64,188)( 65,181)( 66,182)( 67,183)( 68,184)( 69,197)( 70,198)( 71,199)
( 72,200)( 73,193)( 74,194)( 75,195)( 76,196)( 77,189)( 78,190)( 79,191)
( 80,192)( 81,205)( 82,206)( 83,207)( 84,208)( 85,201)( 86,202)( 87,203)
( 88,204)( 89,217)( 90,218)( 91,219)( 92,220)( 93,213)( 94,214)( 95,215)
( 96,216)( 97,209)( 98,210)( 99,211)(100,212)(101,225)(102,226)(103,227)
(104,228)(105,221)(106,222)(107,223)(108,224)(109,237)(110,238)(111,239)
(112,240)(113,233)(114,234)(115,235)(116,236)(117,229)(118,230)(119,231)
(120,232)(241,365)(242,366)(243,367)(244,368)(245,361)(246,362)(247,363)
(248,364)(249,377)(250,378)(251,379)(252,380)(253,373)(254,374)(255,375)
(256,376)(257,369)(258,370)(259,371)(260,372)(261,385)(262,386)(263,387)
(264,388)(265,381)(266,382)(267,383)(268,384)(269,397)(270,398)(271,399)
(272,400)(273,393)(274,394)(275,395)(276,396)(277,389)(278,390)(279,391)
(280,392)(281,405)(282,406)(283,407)(284,408)(285,401)(286,402)(287,403)
(288,404)(289,417)(290,418)(291,419)(292,420)(293,413)(294,414)(295,415)
(296,416)(297,409)(298,410)(299,411)(300,412)(301,425)(302,426)(303,427)
(304,428)(305,421)(306,422)(307,423)(308,424)(309,437)(310,438)(311,439)
(312,440)(313,433)(314,434)(315,435)(316,436)(317,429)(318,430)(319,431)
(320,432)(321,445)(322,446)(323,447)(324,448)(325,441)(326,442)(327,443)
(328,444)(329,457)(330,458)(331,459)(332,460)(333,453)(334,454)(335,455)
(336,456)(337,449)(338,450)(339,451)(340,452)(341,465)(342,466)(343,467)
(344,468)(345,461)(346,462)(347,463)(348,464)(349,477)(350,478)(351,479)
(352,480)(353,473)(354,474)(355,475)(356,476)(357,469)(358,470)(359,471)
(360,472);
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, 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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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