Polytope of Type {6,40}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,40}*1920a
if this polytope has a name.
Group : SmallGroup(1920,238293)
Rank : 3
Schlafli Type : {6,40}
Number of vertices, edges, etc : 24, 480, 160
Order of s0s1s2 : 30
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {6,40}*960c
4-fold quotients : {6,20}*480c
5-fold quotients : {6,8}*384d
8-fold quotients : {6,20}*240b
10-fold quotients : {6,8}*192a
16-fold quotients : {6,10}*120
20-fold quotients : {6,4}*96
40-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
48-fold quotients : {2,10}*40
80-fold quotients : {3,4}*24, {6,2}*24
96-fold quotients : {2,5}*20
160-fold quotients : {3,2}*12
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)( 21, 22)
( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 37, 38)( 41, 45)( 42, 46)
( 43, 48)( 44, 47)( 51, 52)( 53, 54)( 57, 61)( 58, 62)( 59, 64)( 60, 63)
( 67, 68)( 69, 70)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 81,161)( 82,162)
( 83,164)( 84,163)( 85,166)( 86,165)( 87,167)( 88,168)( 89,173)( 90,174)
( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,177)( 98,178)
( 99,180)(100,179)(101,182)(102,181)(103,183)(104,184)(105,189)(106,190)
(107,192)(108,191)(109,185)(110,186)(111,188)(112,187)(113,193)(114,194)
(115,196)(116,195)(117,198)(118,197)(119,199)(120,200)(121,205)(122,206)
(123,208)(124,207)(125,201)(126,202)(127,204)(128,203)(129,209)(130,210)
(131,212)(132,211)(133,214)(134,213)(135,215)(136,216)(137,221)(138,222)
(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,225)(146,226)
(147,228)(148,227)(149,230)(150,229)(151,231)(152,232)(153,237)(154,238)
(155,240)(156,239)(157,233)(158,234)(159,236)(160,235)(243,244)(245,246)
(249,253)(250,254)(251,256)(252,255)(259,260)(261,262)(265,269)(266,270)
(267,272)(268,271)(275,276)(277,278)(281,285)(282,286)(283,288)(284,287)
(291,292)(293,294)(297,301)(298,302)(299,304)(300,303)(307,308)(309,310)
(313,317)(314,318)(315,320)(316,319)(321,401)(322,402)(323,404)(324,403)
(325,406)(326,405)(327,407)(328,408)(329,413)(330,414)(331,416)(332,415)
(333,409)(334,410)(335,412)(336,411)(337,417)(338,418)(339,420)(340,419)
(341,422)(342,421)(343,423)(344,424)(345,429)(346,430)(347,432)(348,431)
(349,425)(350,426)(351,428)(352,427)(353,433)(354,434)(355,436)(356,435)
(357,438)(358,437)(359,439)(360,440)(361,445)(362,446)(363,448)(364,447)
(365,441)(366,442)(367,444)(368,443)(369,449)(370,450)(371,452)(372,451)
(373,454)(374,453)(375,455)(376,456)(377,461)(378,462)(379,464)(380,463)
(381,457)(382,458)(383,460)(384,459)(385,465)(386,466)(387,468)(388,467)
(389,470)(390,469)(391,471)(392,472)(393,477)(394,478)(395,480)(396,479)
(397,473)(398,474)(399,476)(400,475);;
s1 := ( 1, 81)( 2, 84)( 3, 83)( 4, 82)( 5, 95)( 6, 94)( 7, 93)( 8, 96)
( 9, 91)( 10, 90)( 11, 89)( 12, 92)( 13, 87)( 14, 86)( 15, 85)( 16, 88)
( 17,145)( 18,148)( 19,147)( 20,146)( 21,159)( 22,158)( 23,157)( 24,160)
( 25,155)( 26,154)( 27,153)( 28,156)( 29,151)( 30,150)( 31,149)( 32,152)
( 33,129)( 34,132)( 35,131)( 36,130)( 37,143)( 38,142)( 39,141)( 40,144)
( 41,139)( 42,138)( 43,137)( 44,140)( 45,135)( 46,134)( 47,133)( 48,136)
( 49,113)( 50,116)( 51,115)( 52,114)( 53,127)( 54,126)( 55,125)( 56,128)
( 57,123)( 58,122)( 59,121)( 60,124)( 61,119)( 62,118)( 63,117)( 64,120)
( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69,111)( 70,110)( 71,109)( 72,112)
( 73,107)( 74,106)( 75,105)( 76,108)( 77,103)( 78,102)( 79,101)( 80,104)
(162,164)(165,175)(166,174)(167,173)(168,176)(169,171)(177,225)(178,228)
(179,227)(180,226)(181,239)(182,238)(183,237)(184,240)(185,235)(186,234)
(187,233)(188,236)(189,231)(190,230)(191,229)(192,232)(193,209)(194,212)
(195,211)(196,210)(197,223)(198,222)(199,221)(200,224)(201,219)(202,218)
(203,217)(204,220)(205,215)(206,214)(207,213)(208,216)(241,321)(242,324)
(243,323)(244,322)(245,335)(246,334)(247,333)(248,336)(249,331)(250,330)
(251,329)(252,332)(253,327)(254,326)(255,325)(256,328)(257,385)(258,388)
(259,387)(260,386)(261,399)(262,398)(263,397)(264,400)(265,395)(266,394)
(267,393)(268,396)(269,391)(270,390)(271,389)(272,392)(273,369)(274,372)
(275,371)(276,370)(277,383)(278,382)(279,381)(280,384)(281,379)(282,378)
(283,377)(284,380)(285,375)(286,374)(287,373)(288,376)(289,353)(290,356)
(291,355)(292,354)(293,367)(294,366)(295,365)(296,368)(297,363)(298,362)
(299,361)(300,364)(301,359)(302,358)(303,357)(304,360)(305,337)(306,340)
(307,339)(308,338)(309,351)(310,350)(311,349)(312,352)(313,347)(314,346)
(315,345)(316,348)(317,343)(318,342)(319,341)(320,344)(402,404)(405,415)
(406,414)(407,413)(408,416)(409,411)(417,465)(418,468)(419,467)(420,466)
(421,479)(422,478)(423,477)(424,480)(425,475)(426,474)(427,473)(428,476)
(429,471)(430,470)(431,469)(432,472)(433,449)(434,452)(435,451)(436,450)
(437,463)(438,462)(439,461)(440,464)(441,459)(442,458)(443,457)(444,460)
(445,455)(446,454)(447,453)(448,456);;
s2 := ( 1,263)( 2,264)( 3,261)( 4,262)( 5,259)( 6,260)( 7,257)( 8,258)
( 9,269)( 10,270)( 11,271)( 12,272)( 13,265)( 14,266)( 15,267)( 16,268)
( 17,247)( 18,248)( 19,245)( 20,246)( 21,243)( 22,244)( 23,241)( 24,242)
( 25,253)( 26,254)( 27,255)( 28,256)( 29,249)( 30,250)( 31,251)( 32,252)
( 33,311)( 34,312)( 35,309)( 36,310)( 37,307)( 38,308)( 39,305)( 40,306)
( 41,317)( 42,318)( 43,319)( 44,320)( 45,313)( 46,314)( 47,315)( 48,316)
( 49,295)( 50,296)( 51,293)( 52,294)( 53,291)( 54,292)( 55,289)( 56,290)
( 57,301)( 58,302)( 59,303)( 60,304)( 61,297)( 62,298)( 63,299)( 64,300)
( 65,279)( 66,280)( 67,277)( 68,278)( 69,275)( 70,276)( 71,273)( 72,274)
( 73,285)( 74,286)( 75,287)( 76,288)( 77,281)( 78,282)( 79,283)( 80,284)
( 81,343)( 82,344)( 83,341)( 84,342)( 85,339)( 86,340)( 87,337)( 88,338)
( 89,349)( 90,350)( 91,351)( 92,352)( 93,345)( 94,346)( 95,347)( 96,348)
( 97,327)( 98,328)( 99,325)(100,326)(101,323)(102,324)(103,321)(104,322)
(105,333)(106,334)(107,335)(108,336)(109,329)(110,330)(111,331)(112,332)
(113,391)(114,392)(115,389)(116,390)(117,387)(118,388)(119,385)(120,386)
(121,397)(122,398)(123,399)(124,400)(125,393)(126,394)(127,395)(128,396)
(129,375)(130,376)(131,373)(132,374)(133,371)(134,372)(135,369)(136,370)
(137,381)(138,382)(139,383)(140,384)(141,377)(142,378)(143,379)(144,380)
(145,359)(146,360)(147,357)(148,358)(149,355)(150,356)(151,353)(152,354)
(153,365)(154,366)(155,367)(156,368)(157,361)(158,362)(159,363)(160,364)
(161,423)(162,424)(163,421)(164,422)(165,419)(166,420)(167,417)(168,418)
(169,429)(170,430)(171,431)(172,432)(173,425)(174,426)(175,427)(176,428)
(177,407)(178,408)(179,405)(180,406)(181,403)(182,404)(183,401)(184,402)
(185,413)(186,414)(187,415)(188,416)(189,409)(190,410)(191,411)(192,412)
(193,471)(194,472)(195,469)(196,470)(197,467)(198,468)(199,465)(200,466)
(201,477)(202,478)(203,479)(204,480)(205,473)(206,474)(207,475)(208,476)
(209,455)(210,456)(211,453)(212,454)(213,451)(214,452)(215,449)(216,450)
(217,461)(218,462)(219,463)(220,464)(221,457)(222,458)(223,459)(224,460)
(225,439)(226,440)(227,437)(228,438)(229,435)(230,436)(231,433)(232,434)
(233,445)(234,446)(235,447)(236,448)(237,441)(238,442)(239,443)(240,444);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(480)!( 3, 4)( 5, 6)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)
( 21, 22)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 37, 38)( 41, 45)
( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 53, 54)( 57, 61)( 58, 62)( 59, 64)
( 60, 63)( 67, 68)( 69, 70)( 73, 77)( 74, 78)( 75, 80)( 76, 79)( 81,161)
( 82,162)( 83,164)( 84,163)( 85,166)( 86,165)( 87,167)( 88,168)( 89,173)
( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,177)
( 98,178)( 99,180)(100,179)(101,182)(102,181)(103,183)(104,184)(105,189)
(106,190)(107,192)(108,191)(109,185)(110,186)(111,188)(112,187)(113,193)
(114,194)(115,196)(116,195)(117,198)(118,197)(119,199)(120,200)(121,205)
(122,206)(123,208)(124,207)(125,201)(126,202)(127,204)(128,203)(129,209)
(130,210)(131,212)(132,211)(133,214)(134,213)(135,215)(136,216)(137,221)
(138,222)(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,225)
(146,226)(147,228)(148,227)(149,230)(150,229)(151,231)(152,232)(153,237)
(154,238)(155,240)(156,239)(157,233)(158,234)(159,236)(160,235)(243,244)
(245,246)(249,253)(250,254)(251,256)(252,255)(259,260)(261,262)(265,269)
(266,270)(267,272)(268,271)(275,276)(277,278)(281,285)(282,286)(283,288)
(284,287)(291,292)(293,294)(297,301)(298,302)(299,304)(300,303)(307,308)
(309,310)(313,317)(314,318)(315,320)(316,319)(321,401)(322,402)(323,404)
(324,403)(325,406)(326,405)(327,407)(328,408)(329,413)(330,414)(331,416)
(332,415)(333,409)(334,410)(335,412)(336,411)(337,417)(338,418)(339,420)
(340,419)(341,422)(342,421)(343,423)(344,424)(345,429)(346,430)(347,432)
(348,431)(349,425)(350,426)(351,428)(352,427)(353,433)(354,434)(355,436)
(356,435)(357,438)(358,437)(359,439)(360,440)(361,445)(362,446)(363,448)
(364,447)(365,441)(366,442)(367,444)(368,443)(369,449)(370,450)(371,452)
(372,451)(373,454)(374,453)(375,455)(376,456)(377,461)(378,462)(379,464)
(380,463)(381,457)(382,458)(383,460)(384,459)(385,465)(386,466)(387,468)
(388,467)(389,470)(390,469)(391,471)(392,472)(393,477)(394,478)(395,480)
(396,479)(397,473)(398,474)(399,476)(400,475);
s1 := Sym(480)!( 1, 81)( 2, 84)( 3, 83)( 4, 82)( 5, 95)( 6, 94)( 7, 93)
( 8, 96)( 9, 91)( 10, 90)( 11, 89)( 12, 92)( 13, 87)( 14, 86)( 15, 85)
( 16, 88)( 17,145)( 18,148)( 19,147)( 20,146)( 21,159)( 22,158)( 23,157)
( 24,160)( 25,155)( 26,154)( 27,153)( 28,156)( 29,151)( 30,150)( 31,149)
( 32,152)( 33,129)( 34,132)( 35,131)( 36,130)( 37,143)( 38,142)( 39,141)
( 40,144)( 41,139)( 42,138)( 43,137)( 44,140)( 45,135)( 46,134)( 47,133)
( 48,136)( 49,113)( 50,116)( 51,115)( 52,114)( 53,127)( 54,126)( 55,125)
( 56,128)( 57,123)( 58,122)( 59,121)( 60,124)( 61,119)( 62,118)( 63,117)
( 64,120)( 65, 97)( 66,100)( 67, 99)( 68, 98)( 69,111)( 70,110)( 71,109)
( 72,112)( 73,107)( 74,106)( 75,105)( 76,108)( 77,103)( 78,102)( 79,101)
( 80,104)(162,164)(165,175)(166,174)(167,173)(168,176)(169,171)(177,225)
(178,228)(179,227)(180,226)(181,239)(182,238)(183,237)(184,240)(185,235)
(186,234)(187,233)(188,236)(189,231)(190,230)(191,229)(192,232)(193,209)
(194,212)(195,211)(196,210)(197,223)(198,222)(199,221)(200,224)(201,219)
(202,218)(203,217)(204,220)(205,215)(206,214)(207,213)(208,216)(241,321)
(242,324)(243,323)(244,322)(245,335)(246,334)(247,333)(248,336)(249,331)
(250,330)(251,329)(252,332)(253,327)(254,326)(255,325)(256,328)(257,385)
(258,388)(259,387)(260,386)(261,399)(262,398)(263,397)(264,400)(265,395)
(266,394)(267,393)(268,396)(269,391)(270,390)(271,389)(272,392)(273,369)
(274,372)(275,371)(276,370)(277,383)(278,382)(279,381)(280,384)(281,379)
(282,378)(283,377)(284,380)(285,375)(286,374)(287,373)(288,376)(289,353)
(290,356)(291,355)(292,354)(293,367)(294,366)(295,365)(296,368)(297,363)
(298,362)(299,361)(300,364)(301,359)(302,358)(303,357)(304,360)(305,337)
(306,340)(307,339)(308,338)(309,351)(310,350)(311,349)(312,352)(313,347)
(314,346)(315,345)(316,348)(317,343)(318,342)(319,341)(320,344)(402,404)
(405,415)(406,414)(407,413)(408,416)(409,411)(417,465)(418,468)(419,467)
(420,466)(421,479)(422,478)(423,477)(424,480)(425,475)(426,474)(427,473)
(428,476)(429,471)(430,470)(431,469)(432,472)(433,449)(434,452)(435,451)
(436,450)(437,463)(438,462)(439,461)(440,464)(441,459)(442,458)(443,457)
(444,460)(445,455)(446,454)(447,453)(448,456);
s2 := Sym(480)!( 1,263)( 2,264)( 3,261)( 4,262)( 5,259)( 6,260)( 7,257)
( 8,258)( 9,269)( 10,270)( 11,271)( 12,272)( 13,265)( 14,266)( 15,267)
( 16,268)( 17,247)( 18,248)( 19,245)( 20,246)( 21,243)( 22,244)( 23,241)
( 24,242)( 25,253)( 26,254)( 27,255)( 28,256)( 29,249)( 30,250)( 31,251)
( 32,252)( 33,311)( 34,312)( 35,309)( 36,310)( 37,307)( 38,308)( 39,305)
( 40,306)( 41,317)( 42,318)( 43,319)( 44,320)( 45,313)( 46,314)( 47,315)
( 48,316)( 49,295)( 50,296)( 51,293)( 52,294)( 53,291)( 54,292)( 55,289)
( 56,290)( 57,301)( 58,302)( 59,303)( 60,304)( 61,297)( 62,298)( 63,299)
( 64,300)( 65,279)( 66,280)( 67,277)( 68,278)( 69,275)( 70,276)( 71,273)
( 72,274)( 73,285)( 74,286)( 75,287)( 76,288)( 77,281)( 78,282)( 79,283)
( 80,284)( 81,343)( 82,344)( 83,341)( 84,342)( 85,339)( 86,340)( 87,337)
( 88,338)( 89,349)( 90,350)( 91,351)( 92,352)( 93,345)( 94,346)( 95,347)
( 96,348)( 97,327)( 98,328)( 99,325)(100,326)(101,323)(102,324)(103,321)
(104,322)(105,333)(106,334)(107,335)(108,336)(109,329)(110,330)(111,331)
(112,332)(113,391)(114,392)(115,389)(116,390)(117,387)(118,388)(119,385)
(120,386)(121,397)(122,398)(123,399)(124,400)(125,393)(126,394)(127,395)
(128,396)(129,375)(130,376)(131,373)(132,374)(133,371)(134,372)(135,369)
(136,370)(137,381)(138,382)(139,383)(140,384)(141,377)(142,378)(143,379)
(144,380)(145,359)(146,360)(147,357)(148,358)(149,355)(150,356)(151,353)
(152,354)(153,365)(154,366)(155,367)(156,368)(157,361)(158,362)(159,363)
(160,364)(161,423)(162,424)(163,421)(164,422)(165,419)(166,420)(167,417)
(168,418)(169,429)(170,430)(171,431)(172,432)(173,425)(174,426)(175,427)
(176,428)(177,407)(178,408)(179,405)(180,406)(181,403)(182,404)(183,401)
(184,402)(185,413)(186,414)(187,415)(188,416)(189,409)(190,410)(191,411)
(192,412)(193,471)(194,472)(195,469)(196,470)(197,467)(198,468)(199,465)
(200,466)(201,477)(202,478)(203,479)(204,480)(205,473)(206,474)(207,475)
(208,476)(209,455)(210,456)(211,453)(212,454)(213,451)(214,452)(215,449)
(216,450)(217,461)(218,462)(219,463)(220,464)(221,457)(222,458)(223,459)
(224,460)(225,439)(226,440)(227,437)(228,438)(229,435)(230,436)(231,433)
(232,434)(233,445)(234,446)(235,447)(236,448)(237,441)(238,442)(239,443)
(240,444);
poly := sub<Sym(480)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1 >;
References : None.
to this polytope