Polytope of Type {20,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,12,4}*1920c
if this polytope has a name.
Group : SmallGroup(1920,238871)
Rank : 4
Schlafli Type : {20,12,4}
Number of vertices, edges, etc : 20, 120, 24, 4
Order of s0s1s2s3 : 60
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 : {10,12,4}*960c, {20,6,4}*960b
4-fold quotients : {10,6,4}*480b
5-fold quotients : {4,12,4}*384c
10-fold quotients : {2,12,4}*192c, {4,6,4}*192b
20-fold quotients : {2,6,4}*96c
40-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 17)( 6, 18)( 7, 19)( 8, 20)( 9, 13)( 10, 14)( 11, 15)( 12, 16)
( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)
( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)( 52, 56)
( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)
( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)(112,116)
(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)(132,136)
(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)(152,156)
(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)(172,176)
(185,197)(186,198)(187,199)(188,200)(189,193)(190,194)(191,195)(192,196)
(205,217)(206,218)(207,219)(208,220)(209,213)(210,214)(211,215)(212,216)
(225,237)(226,238)(227,239)(228,240)(229,233)(230,234)(231,235)(232,236)
(241,301)(242,302)(243,303)(244,304)(245,317)(246,318)(247,319)(248,320)
(249,313)(250,314)(251,315)(252,316)(253,309)(254,310)(255,311)(256,312)
(257,305)(258,306)(259,307)(260,308)(261,321)(262,322)(263,323)(264,324)
(265,337)(266,338)(267,339)(268,340)(269,333)(270,334)(271,335)(272,336)
(273,329)(274,330)(275,331)(276,332)(277,325)(278,326)(279,327)(280,328)
(281,341)(282,342)(283,343)(284,344)(285,357)(286,358)(287,359)(288,360)
(289,353)(290,354)(291,355)(292,356)(293,349)(294,350)(295,351)(296,352)
(297,345)(298,346)(299,347)(300,348)(361,421)(362,422)(363,423)(364,424)
(365,437)(366,438)(367,439)(368,440)(369,433)(370,434)(371,435)(372,436)
(373,429)(374,430)(375,431)(376,432)(377,425)(378,426)(379,427)(380,428)
(381,441)(382,442)(383,443)(384,444)(385,457)(386,458)(387,459)(388,460)
(389,453)(390,454)(391,455)(392,456)(393,449)(394,450)(395,451)(396,452)
(397,445)(398,446)(399,447)(400,448)(401,461)(402,462)(403,463)(404,464)
(405,477)(406,478)(407,479)(408,480)(409,473)(410,474)(411,475)(412,476)
(413,469)(414,470)(415,471)(416,472)(417,465)(418,466)(419,467)(420,468);;
s1 := ( 1,245)( 2,246)( 3,248)( 4,247)( 5,241)( 6,242)( 7,244)( 8,243)
( 9,257)( 10,258)( 11,260)( 12,259)( 13,253)( 14,254)( 15,256)( 16,255)
( 17,249)( 18,250)( 19,252)( 20,251)( 21,285)( 22,286)( 23,288)( 24,287)
( 25,281)( 26,282)( 27,284)( 28,283)( 29,297)( 30,298)( 31,300)( 32,299)
( 33,293)( 34,294)( 35,296)( 36,295)( 37,289)( 38,290)( 39,292)( 40,291)
( 41,265)( 42,266)( 43,268)( 44,267)( 45,261)( 46,262)( 47,264)( 48,263)
( 49,277)( 50,278)( 51,280)( 52,279)( 53,273)( 54,274)( 55,276)( 56,275)
( 57,269)( 58,270)( 59,272)( 60,271)( 61,305)( 62,306)( 63,308)( 64,307)
( 65,301)( 66,302)( 67,304)( 68,303)( 69,317)( 70,318)( 71,320)( 72,319)
( 73,313)( 74,314)( 75,316)( 76,315)( 77,309)( 78,310)( 79,312)( 80,311)
( 81,345)( 82,346)( 83,348)( 84,347)( 85,341)( 86,342)( 87,344)( 88,343)
( 89,357)( 90,358)( 91,360)( 92,359)( 93,353)( 94,354)( 95,356)( 96,355)
( 97,349)( 98,350)( 99,352)(100,351)(101,325)(102,326)(103,328)(104,327)
(105,321)(106,322)(107,324)(108,323)(109,337)(110,338)(111,340)(112,339)
(113,333)(114,334)(115,336)(116,335)(117,329)(118,330)(119,332)(120,331)
(121,365)(122,366)(123,368)(124,367)(125,361)(126,362)(127,364)(128,363)
(129,377)(130,378)(131,380)(132,379)(133,373)(134,374)(135,376)(136,375)
(137,369)(138,370)(139,372)(140,371)(141,405)(142,406)(143,408)(144,407)
(145,401)(146,402)(147,404)(148,403)(149,417)(150,418)(151,420)(152,419)
(153,413)(154,414)(155,416)(156,415)(157,409)(158,410)(159,412)(160,411)
(161,385)(162,386)(163,388)(164,387)(165,381)(166,382)(167,384)(168,383)
(169,397)(170,398)(171,400)(172,399)(173,393)(174,394)(175,396)(176,395)
(177,389)(178,390)(179,392)(180,391)(181,425)(182,426)(183,428)(184,427)
(185,421)(186,422)(187,424)(188,423)(189,437)(190,438)(191,440)(192,439)
(193,433)(194,434)(195,436)(196,435)(197,429)(198,430)(199,432)(200,431)
(201,465)(202,466)(203,468)(204,467)(205,461)(206,462)(207,464)(208,463)
(209,477)(210,478)(211,480)(212,479)(213,473)(214,474)(215,476)(216,475)
(217,469)(218,470)(219,472)(220,471)(221,445)(222,446)(223,448)(224,447)
(225,441)(226,442)(227,444)(228,443)(229,457)(230,458)(231,460)(232,459)
(233,453)(234,454)(235,456)(236,455)(237,449)(238,450)(239,452)(240,451);;
s2 := ( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 25)( 6, 28)( 7, 27)( 8, 26)
( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)( 54, 56)
( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)( 67, 87)
( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)( 75, 95)
( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)(110,112)
(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)(126,148)
(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)(134,156)
(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)(166,168)
(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)(185,205)
(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)(193,213)
(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)(222,224)
(226,228)(230,232)(234,236)(238,240)(241,381)(242,384)(243,383)(244,382)
(245,385)(246,388)(247,387)(248,386)(249,389)(250,392)(251,391)(252,390)
(253,393)(254,396)(255,395)(256,394)(257,397)(258,400)(259,399)(260,398)
(261,361)(262,364)(263,363)(264,362)(265,365)(266,368)(267,367)(268,366)
(269,369)(270,372)(271,371)(272,370)(273,373)(274,376)(275,375)(276,374)
(277,377)(278,380)(279,379)(280,378)(281,401)(282,404)(283,403)(284,402)
(285,405)(286,408)(287,407)(288,406)(289,409)(290,412)(291,411)(292,410)
(293,413)(294,416)(295,415)(296,414)(297,417)(298,420)(299,419)(300,418)
(301,441)(302,444)(303,443)(304,442)(305,445)(306,448)(307,447)(308,446)
(309,449)(310,452)(311,451)(312,450)(313,453)(314,456)(315,455)(316,454)
(317,457)(318,460)(319,459)(320,458)(321,421)(322,424)(323,423)(324,422)
(325,425)(326,428)(327,427)(328,426)(329,429)(330,432)(331,431)(332,430)
(333,433)(334,436)(335,435)(336,434)(337,437)(338,440)(339,439)(340,438)
(341,461)(342,464)(343,463)(344,462)(345,465)(346,468)(347,467)(348,466)
(349,469)(350,472)(351,471)(352,470)(353,473)(354,476)(355,475)(356,474)
(357,477)(358,480)(359,479)(360,478);;
s3 := ( 1,122)( 2,121)( 3,124)( 4,123)( 5,126)( 6,125)( 7,128)( 8,127)
( 9,130)( 10,129)( 11,132)( 12,131)( 13,134)( 14,133)( 15,136)( 16,135)
( 17,138)( 18,137)( 19,140)( 20,139)( 21,142)( 22,141)( 23,144)( 24,143)
( 25,146)( 26,145)( 27,148)( 28,147)( 29,150)( 30,149)( 31,152)( 32,151)
( 33,154)( 34,153)( 35,156)( 36,155)( 37,158)( 38,157)( 39,160)( 40,159)
( 41,162)( 42,161)( 43,164)( 44,163)( 45,166)( 46,165)( 47,168)( 48,167)
( 49,170)( 50,169)( 51,172)( 52,171)( 53,174)( 54,173)( 55,176)( 56,175)
( 57,178)( 58,177)( 59,180)( 60,179)( 61,182)( 62,181)( 63,184)( 64,183)
( 65,186)( 66,185)( 67,188)( 68,187)( 69,190)( 70,189)( 71,192)( 72,191)
( 73,194)( 74,193)( 75,196)( 76,195)( 77,198)( 78,197)( 79,200)( 80,199)
( 81,202)( 82,201)( 83,204)( 84,203)( 85,206)( 86,205)( 87,208)( 88,207)
( 89,210)( 90,209)( 91,212)( 92,211)( 93,214)( 94,213)( 95,216)( 96,215)
( 97,218)( 98,217)( 99,220)(100,219)(101,222)(102,221)(103,224)(104,223)
(105,226)(106,225)(107,228)(108,227)(109,230)(110,229)(111,232)(112,231)
(113,234)(114,233)(115,236)(116,235)(117,238)(118,237)(119,240)(120,239)
(241,362)(242,361)(243,364)(244,363)(245,366)(246,365)(247,368)(248,367)
(249,370)(250,369)(251,372)(252,371)(253,374)(254,373)(255,376)(256,375)
(257,378)(258,377)(259,380)(260,379)(261,382)(262,381)(263,384)(264,383)
(265,386)(266,385)(267,388)(268,387)(269,390)(270,389)(271,392)(272,391)
(273,394)(274,393)(275,396)(276,395)(277,398)(278,397)(279,400)(280,399)
(281,402)(282,401)(283,404)(284,403)(285,406)(286,405)(287,408)(288,407)
(289,410)(290,409)(291,412)(292,411)(293,414)(294,413)(295,416)(296,415)
(297,418)(298,417)(299,420)(300,419)(301,422)(302,421)(303,424)(304,423)
(305,426)(306,425)(307,428)(308,427)(309,430)(310,429)(311,432)(312,431)
(313,434)(314,433)(315,436)(316,435)(317,438)(318,437)(319,440)(320,439)
(321,442)(322,441)(323,444)(324,443)(325,446)(326,445)(327,448)(328,447)
(329,450)(330,449)(331,452)(332,451)(333,454)(334,453)(335,456)(336,455)
(337,458)(338,457)(339,460)(340,459)(341,462)(342,461)(343,464)(344,463)
(345,466)(346,465)(347,468)(348,467)(349,470)(350,469)(351,472)(352,471)
(353,474)(354,473)(355,476)(356,475)(357,478)(358,477)(359,480)(360,479);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!( 5, 17)( 6, 18)( 7, 19)( 8, 20)( 9, 13)( 10, 14)( 11, 15)
( 12, 16)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)
( 32, 36)( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)
( 52, 56)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)
( 72, 76)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)
(112,116)(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)
(132,136)(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)
(152,156)(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)
(172,176)(185,197)(186,198)(187,199)(188,200)(189,193)(190,194)(191,195)
(192,196)(205,217)(206,218)(207,219)(208,220)(209,213)(210,214)(211,215)
(212,216)(225,237)(226,238)(227,239)(228,240)(229,233)(230,234)(231,235)
(232,236)(241,301)(242,302)(243,303)(244,304)(245,317)(246,318)(247,319)
(248,320)(249,313)(250,314)(251,315)(252,316)(253,309)(254,310)(255,311)
(256,312)(257,305)(258,306)(259,307)(260,308)(261,321)(262,322)(263,323)
(264,324)(265,337)(266,338)(267,339)(268,340)(269,333)(270,334)(271,335)
(272,336)(273,329)(274,330)(275,331)(276,332)(277,325)(278,326)(279,327)
(280,328)(281,341)(282,342)(283,343)(284,344)(285,357)(286,358)(287,359)
(288,360)(289,353)(290,354)(291,355)(292,356)(293,349)(294,350)(295,351)
(296,352)(297,345)(298,346)(299,347)(300,348)(361,421)(362,422)(363,423)
(364,424)(365,437)(366,438)(367,439)(368,440)(369,433)(370,434)(371,435)
(372,436)(373,429)(374,430)(375,431)(376,432)(377,425)(378,426)(379,427)
(380,428)(381,441)(382,442)(383,443)(384,444)(385,457)(386,458)(387,459)
(388,460)(389,453)(390,454)(391,455)(392,456)(393,449)(394,450)(395,451)
(396,452)(397,445)(398,446)(399,447)(400,448)(401,461)(402,462)(403,463)
(404,464)(405,477)(406,478)(407,479)(408,480)(409,473)(410,474)(411,475)
(412,476)(413,469)(414,470)(415,471)(416,472)(417,465)(418,466)(419,467)
(420,468);
s1 := Sym(480)!( 1,245)( 2,246)( 3,248)( 4,247)( 5,241)( 6,242)( 7,244)
( 8,243)( 9,257)( 10,258)( 11,260)( 12,259)( 13,253)( 14,254)( 15,256)
( 16,255)( 17,249)( 18,250)( 19,252)( 20,251)( 21,285)( 22,286)( 23,288)
( 24,287)( 25,281)( 26,282)( 27,284)( 28,283)( 29,297)( 30,298)( 31,300)
( 32,299)( 33,293)( 34,294)( 35,296)( 36,295)( 37,289)( 38,290)( 39,292)
( 40,291)( 41,265)( 42,266)( 43,268)( 44,267)( 45,261)( 46,262)( 47,264)
( 48,263)( 49,277)( 50,278)( 51,280)( 52,279)( 53,273)( 54,274)( 55,276)
( 56,275)( 57,269)( 58,270)( 59,272)( 60,271)( 61,305)( 62,306)( 63,308)
( 64,307)( 65,301)( 66,302)( 67,304)( 68,303)( 69,317)( 70,318)( 71,320)
( 72,319)( 73,313)( 74,314)( 75,316)( 76,315)( 77,309)( 78,310)( 79,312)
( 80,311)( 81,345)( 82,346)( 83,348)( 84,347)( 85,341)( 86,342)( 87,344)
( 88,343)( 89,357)( 90,358)( 91,360)( 92,359)( 93,353)( 94,354)( 95,356)
( 96,355)( 97,349)( 98,350)( 99,352)(100,351)(101,325)(102,326)(103,328)
(104,327)(105,321)(106,322)(107,324)(108,323)(109,337)(110,338)(111,340)
(112,339)(113,333)(114,334)(115,336)(116,335)(117,329)(118,330)(119,332)
(120,331)(121,365)(122,366)(123,368)(124,367)(125,361)(126,362)(127,364)
(128,363)(129,377)(130,378)(131,380)(132,379)(133,373)(134,374)(135,376)
(136,375)(137,369)(138,370)(139,372)(140,371)(141,405)(142,406)(143,408)
(144,407)(145,401)(146,402)(147,404)(148,403)(149,417)(150,418)(151,420)
(152,419)(153,413)(154,414)(155,416)(156,415)(157,409)(158,410)(159,412)
(160,411)(161,385)(162,386)(163,388)(164,387)(165,381)(166,382)(167,384)
(168,383)(169,397)(170,398)(171,400)(172,399)(173,393)(174,394)(175,396)
(176,395)(177,389)(178,390)(179,392)(180,391)(181,425)(182,426)(183,428)
(184,427)(185,421)(186,422)(187,424)(188,423)(189,437)(190,438)(191,440)
(192,439)(193,433)(194,434)(195,436)(196,435)(197,429)(198,430)(199,432)
(200,431)(201,465)(202,466)(203,468)(204,467)(205,461)(206,462)(207,464)
(208,463)(209,477)(210,478)(211,480)(212,479)(213,473)(214,474)(215,476)
(216,475)(217,469)(218,470)(219,472)(220,471)(221,445)(222,446)(223,448)
(224,447)(225,441)(226,442)(227,444)(228,443)(229,457)(230,458)(231,460)
(232,459)(233,453)(234,454)(235,456)(236,455)(237,449)(238,450)(239,452)
(240,451);
s2 := Sym(480)!( 1, 21)( 2, 24)( 3, 23)( 4, 22)( 5, 25)( 6, 28)( 7, 27)
( 8, 26)( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)
( 54, 56)( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)
( 67, 87)( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)
( 75, 95)( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)
(110,112)(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)
(126,148)(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)
(134,156)(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)
(166,168)(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)
(185,205)(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)
(193,213)(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)
(222,224)(226,228)(230,232)(234,236)(238,240)(241,381)(242,384)(243,383)
(244,382)(245,385)(246,388)(247,387)(248,386)(249,389)(250,392)(251,391)
(252,390)(253,393)(254,396)(255,395)(256,394)(257,397)(258,400)(259,399)
(260,398)(261,361)(262,364)(263,363)(264,362)(265,365)(266,368)(267,367)
(268,366)(269,369)(270,372)(271,371)(272,370)(273,373)(274,376)(275,375)
(276,374)(277,377)(278,380)(279,379)(280,378)(281,401)(282,404)(283,403)
(284,402)(285,405)(286,408)(287,407)(288,406)(289,409)(290,412)(291,411)
(292,410)(293,413)(294,416)(295,415)(296,414)(297,417)(298,420)(299,419)
(300,418)(301,441)(302,444)(303,443)(304,442)(305,445)(306,448)(307,447)
(308,446)(309,449)(310,452)(311,451)(312,450)(313,453)(314,456)(315,455)
(316,454)(317,457)(318,460)(319,459)(320,458)(321,421)(322,424)(323,423)
(324,422)(325,425)(326,428)(327,427)(328,426)(329,429)(330,432)(331,431)
(332,430)(333,433)(334,436)(335,435)(336,434)(337,437)(338,440)(339,439)
(340,438)(341,461)(342,464)(343,463)(344,462)(345,465)(346,468)(347,467)
(348,466)(349,469)(350,472)(351,471)(352,470)(353,473)(354,476)(355,475)
(356,474)(357,477)(358,480)(359,479)(360,478);
s3 := Sym(480)!( 1,122)( 2,121)( 3,124)( 4,123)( 5,126)( 6,125)( 7,128)
( 8,127)( 9,130)( 10,129)( 11,132)( 12,131)( 13,134)( 14,133)( 15,136)
( 16,135)( 17,138)( 18,137)( 19,140)( 20,139)( 21,142)( 22,141)( 23,144)
( 24,143)( 25,146)( 26,145)( 27,148)( 28,147)( 29,150)( 30,149)( 31,152)
( 32,151)( 33,154)( 34,153)( 35,156)( 36,155)( 37,158)( 38,157)( 39,160)
( 40,159)( 41,162)( 42,161)( 43,164)( 44,163)( 45,166)( 46,165)( 47,168)
( 48,167)( 49,170)( 50,169)( 51,172)( 52,171)( 53,174)( 54,173)( 55,176)
( 56,175)( 57,178)( 58,177)( 59,180)( 60,179)( 61,182)( 62,181)( 63,184)
( 64,183)( 65,186)( 66,185)( 67,188)( 68,187)( 69,190)( 70,189)( 71,192)
( 72,191)( 73,194)( 74,193)( 75,196)( 76,195)( 77,198)( 78,197)( 79,200)
( 80,199)( 81,202)( 82,201)( 83,204)( 84,203)( 85,206)( 86,205)( 87,208)
( 88,207)( 89,210)( 90,209)( 91,212)( 92,211)( 93,214)( 94,213)( 95,216)
( 96,215)( 97,218)( 98,217)( 99,220)(100,219)(101,222)(102,221)(103,224)
(104,223)(105,226)(106,225)(107,228)(108,227)(109,230)(110,229)(111,232)
(112,231)(113,234)(114,233)(115,236)(116,235)(117,238)(118,237)(119,240)
(120,239)(241,362)(242,361)(243,364)(244,363)(245,366)(246,365)(247,368)
(248,367)(249,370)(250,369)(251,372)(252,371)(253,374)(254,373)(255,376)
(256,375)(257,378)(258,377)(259,380)(260,379)(261,382)(262,381)(263,384)
(264,383)(265,386)(266,385)(267,388)(268,387)(269,390)(270,389)(271,392)
(272,391)(273,394)(274,393)(275,396)(276,395)(277,398)(278,397)(279,400)
(280,399)(281,402)(282,401)(283,404)(284,403)(285,406)(286,405)(287,408)
(288,407)(289,410)(290,409)(291,412)(292,411)(293,414)(294,413)(295,416)
(296,415)(297,418)(298,417)(299,420)(300,419)(301,422)(302,421)(303,424)
(304,423)(305,426)(306,425)(307,428)(308,427)(309,430)(310,429)(311,432)
(312,431)(313,434)(314,433)(315,436)(316,435)(317,438)(318,437)(319,440)
(320,439)(321,442)(322,441)(323,444)(324,443)(325,446)(326,445)(327,448)
(328,447)(329,450)(330,449)(331,452)(332,451)(333,454)(334,453)(335,456)
(336,455)(337,458)(338,457)(339,460)(340,459)(341,462)(342,461)(343,464)
(344,463)(345,466)(346,465)(347,468)(348,467)(349,470)(350,469)(351,472)
(352,471)(353,474)(354,473)(355,476)(356,475)(357,478)(358,477)(359,480)
(360,479);
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,
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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