Polytope of Type {4,6,40}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,40}*1920b
if this polytope has a name.
Group : SmallGroup(1920,238620)
Rank : 4
Schlafli Type : {4,6,40}
Number of vertices, edges, etc : 4, 12, 120, 40
Order of s0s1s2s3 : 120
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}*960b
4-fold quotients : {4,6,10}*480b
5-fold quotients : {4,6,8}*384b
10-fold quotients : {4,6,4}*192c
20-fold quotients : {4,6,2}*96c
40-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)
(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432)
(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)(446,448)
(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)(462,464)
(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)(478,480);;
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)(241,381)(242,384)
(243,383)(244,382)(245,397)(246,400)(247,399)(248,398)(249,393)(250,396)
(251,395)(252,394)(253,389)(254,392)(255,391)(256,390)(257,385)(258,388)
(259,387)(260,386)(261,361)(262,364)(263,363)(264,362)(265,377)(266,380)
(267,379)(268,378)(269,373)(270,376)(271,375)(272,374)(273,369)(274,372)
(275,371)(276,370)(277,365)(278,368)(279,367)(280,366)(281,401)(282,404)
(283,403)(284,402)(285,417)(286,420)(287,419)(288,418)(289,413)(290,416)
(291,415)(292,414)(293,409)(294,412)(295,411)(296,410)(297,405)(298,408)
(299,407)(300,406)(301,441)(302,444)(303,443)(304,442)(305,457)(306,460)
(307,459)(308,458)(309,453)(310,456)(311,455)(312,454)(313,449)(314,452)
(315,451)(316,450)(317,445)(318,448)(319,447)(320,446)(321,421)(322,424)
(323,423)(324,422)(325,437)(326,440)(327,439)(328,438)(329,433)(330,436)
(331,435)(332,434)(333,429)(334,432)(335,431)(336,430)(337,425)(338,428)
(339,427)(340,426)(341,461)(342,464)(343,463)(344,462)(345,477)(346,480)
(347,479)(348,478)(349,473)(350,476)(351,475)(352,474)(353,469)(354,472)
(355,471)(356,470)(357,465)(358,468)(359,467)(360,466);;
s3 := ( 1,245)( 2,246)( 3,247)( 4,248)( 5,241)( 6,242)( 7,243)( 8,244)
( 9,257)( 10,258)( 11,259)( 12,260)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,249)( 18,250)( 19,251)( 20,252)( 21,265)( 22,266)( 23,267)( 24,268)
( 25,261)( 26,262)( 27,263)( 28,264)( 29,277)( 30,278)( 31,279)( 32,280)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,269)( 38,270)( 39,271)( 40,272)
( 41,285)( 42,286)( 43,287)( 44,288)( 45,281)( 46,282)( 47,283)( 48,284)
( 49,297)( 50,298)( 51,299)( 52,300)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,289)( 58,290)( 59,291)( 60,292)( 61,305)( 62,306)( 63,307)( 64,308)
( 65,301)( 66,302)( 67,303)( 68,304)( 69,317)( 70,318)( 71,319)( 72,320)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,309)( 78,310)( 79,311)( 80,312)
( 81,325)( 82,326)( 83,327)( 84,328)( 85,321)( 86,322)( 87,323)( 88,324)
( 89,337)( 90,338)( 91,339)( 92,340)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,329)( 98,330)( 99,331)(100,332)(101,345)(102,346)(103,347)(104,348)
(105,341)(106,342)(107,343)(108,344)(109,357)(110,358)(111,359)(112,360)
(113,353)(114,354)(115,355)(116,356)(117,349)(118,350)(119,351)(120,352)
(121,425)(122,426)(123,427)(124,428)(125,421)(126,422)(127,423)(128,424)
(129,437)(130,438)(131,439)(132,440)(133,433)(134,434)(135,435)(136,436)
(137,429)(138,430)(139,431)(140,432)(141,445)(142,446)(143,447)(144,448)
(145,441)(146,442)(147,443)(148,444)(149,457)(150,458)(151,459)(152,460)
(153,453)(154,454)(155,455)(156,456)(157,449)(158,450)(159,451)(160,452)
(161,465)(162,466)(163,467)(164,468)(165,461)(166,462)(167,463)(168,464)
(169,477)(170,478)(171,479)(172,480)(173,473)(174,474)(175,475)(176,476)
(177,469)(178,470)(179,471)(180,472)(181,365)(182,366)(183,367)(184,368)
(185,361)(186,362)(187,363)(188,364)(189,377)(190,378)(191,379)(192,380)
(193,373)(194,374)(195,375)(196,376)(197,369)(198,370)(199,371)(200,372)
(201,385)(202,386)(203,387)(204,388)(205,381)(206,382)(207,383)(208,384)
(209,397)(210,398)(211,399)(212,400)(213,393)(214,394)(215,395)(216,396)
(217,389)(218,390)(219,391)(220,392)(221,405)(222,406)(223,407)(224,408)
(225,401)(226,402)(227,403)(228,404)(229,417)(230,418)(231,419)(232,420)
(233,413)(234,414)(235,415)(236,416)(237,409)(238,410)(239,411)(240,412);;
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*s0*s1*s2*s0*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*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, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)
(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)
(430,432)(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)
(446,448)(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)
(462,464)(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)
(478,480);
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)(241,381)
(242,384)(243,383)(244,382)(245,397)(246,400)(247,399)(248,398)(249,393)
(250,396)(251,395)(252,394)(253,389)(254,392)(255,391)(256,390)(257,385)
(258,388)(259,387)(260,386)(261,361)(262,364)(263,363)(264,362)(265,377)
(266,380)(267,379)(268,378)(269,373)(270,376)(271,375)(272,374)(273,369)
(274,372)(275,371)(276,370)(277,365)(278,368)(279,367)(280,366)(281,401)
(282,404)(283,403)(284,402)(285,417)(286,420)(287,419)(288,418)(289,413)
(290,416)(291,415)(292,414)(293,409)(294,412)(295,411)(296,410)(297,405)
(298,408)(299,407)(300,406)(301,441)(302,444)(303,443)(304,442)(305,457)
(306,460)(307,459)(308,458)(309,453)(310,456)(311,455)(312,454)(313,449)
(314,452)(315,451)(316,450)(317,445)(318,448)(319,447)(320,446)(321,421)
(322,424)(323,423)(324,422)(325,437)(326,440)(327,439)(328,438)(329,433)
(330,436)(331,435)(332,434)(333,429)(334,432)(335,431)(336,430)(337,425)
(338,428)(339,427)(340,426)(341,461)(342,464)(343,463)(344,462)(345,477)
(346,480)(347,479)(348,478)(349,473)(350,476)(351,475)(352,474)(353,469)
(354,472)(355,471)(356,470)(357,465)(358,468)(359,467)(360,466);
s3 := Sym(480)!( 1,245)( 2,246)( 3,247)( 4,248)( 5,241)( 6,242)( 7,243)
( 8,244)( 9,257)( 10,258)( 11,259)( 12,260)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,249)( 18,250)( 19,251)( 20,252)( 21,265)( 22,266)( 23,267)
( 24,268)( 25,261)( 26,262)( 27,263)( 28,264)( 29,277)( 30,278)( 31,279)
( 32,280)( 33,273)( 34,274)( 35,275)( 36,276)( 37,269)( 38,270)( 39,271)
( 40,272)( 41,285)( 42,286)( 43,287)( 44,288)( 45,281)( 46,282)( 47,283)
( 48,284)( 49,297)( 50,298)( 51,299)( 52,300)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,289)( 58,290)( 59,291)( 60,292)( 61,305)( 62,306)( 63,307)
( 64,308)( 65,301)( 66,302)( 67,303)( 68,304)( 69,317)( 70,318)( 71,319)
( 72,320)( 73,313)( 74,314)( 75,315)( 76,316)( 77,309)( 78,310)( 79,311)
( 80,312)( 81,325)( 82,326)( 83,327)( 84,328)( 85,321)( 86,322)( 87,323)
( 88,324)( 89,337)( 90,338)( 91,339)( 92,340)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,329)( 98,330)( 99,331)(100,332)(101,345)(102,346)(103,347)
(104,348)(105,341)(106,342)(107,343)(108,344)(109,357)(110,358)(111,359)
(112,360)(113,353)(114,354)(115,355)(116,356)(117,349)(118,350)(119,351)
(120,352)(121,425)(122,426)(123,427)(124,428)(125,421)(126,422)(127,423)
(128,424)(129,437)(130,438)(131,439)(132,440)(133,433)(134,434)(135,435)
(136,436)(137,429)(138,430)(139,431)(140,432)(141,445)(142,446)(143,447)
(144,448)(145,441)(146,442)(147,443)(148,444)(149,457)(150,458)(151,459)
(152,460)(153,453)(154,454)(155,455)(156,456)(157,449)(158,450)(159,451)
(160,452)(161,465)(162,466)(163,467)(164,468)(165,461)(166,462)(167,463)
(168,464)(169,477)(170,478)(171,479)(172,480)(173,473)(174,474)(175,475)
(176,476)(177,469)(178,470)(179,471)(180,472)(181,365)(182,366)(183,367)
(184,368)(185,361)(186,362)(187,363)(188,364)(189,377)(190,378)(191,379)
(192,380)(193,373)(194,374)(195,375)(196,376)(197,369)(198,370)(199,371)
(200,372)(201,385)(202,386)(203,387)(204,388)(205,381)(206,382)(207,383)
(208,384)(209,397)(210,398)(211,399)(212,400)(213,393)(214,394)(215,395)
(216,396)(217,389)(218,390)(219,391)(220,392)(221,405)(222,406)(223,407)
(224,408)(225,401)(226,402)(227,403)(228,404)(229,417)(230,418)(231,419)
(232,420)(233,413)(234,414)(235,415)(236,416)(237,409)(238,410)(239,411)
(240,412);
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*s0*s1*s2*s0*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*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