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