Polytope of Type {24,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,10}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240046)
Rank : 3
Schlafli Type : {24,10}
Number of vertices, edges, etc : 96, 480, 40
Order of s0s1s2 : 30
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,10}*960e
3-fold quotients : {8,10}*640c
6-fold quotients : {8,5}*320a, {4,10}*320b
12-fold quotients : {4,5}*160
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)
(161,323)(162,324)(163,321)(164,322)(165,327)(166,328)(167,325)(168,326)
(169,331)(170,332)(171,329)(172,330)(173,335)(174,336)(175,333)(176,334)
(177,339)(178,340)(179,337)(180,338)(181,343)(182,344)(183,341)(184,342)
(185,347)(186,348)(187,345)(188,346)(189,351)(190,352)(191,349)(192,350)
(193,355)(194,356)(195,353)(196,354)(197,359)(198,360)(199,357)(200,358)
(201,363)(202,364)(203,361)(204,362)(205,367)(206,368)(207,365)(208,366)
(209,371)(210,372)(211,369)(212,370)(213,375)(214,376)(215,373)(216,374)
(217,379)(218,380)(219,377)(220,378)(221,383)(222,384)(223,381)(224,382)
(225,387)(226,388)(227,385)(228,386)(229,391)(230,392)(231,389)(232,390)
(233,395)(234,396)(235,393)(236,394)(237,399)(238,400)(239,397)(240,398)
(241,403)(242,404)(243,401)(244,402)(245,407)(246,408)(247,405)(248,406)
(249,411)(250,412)(251,409)(252,410)(253,415)(254,416)(255,413)(256,414)
(257,419)(258,420)(259,417)(260,418)(261,423)(262,424)(263,421)(264,422)
(265,427)(266,428)(267,425)(268,426)(269,431)(270,432)(271,429)(272,430)
(273,435)(274,436)(275,433)(276,434)(277,439)(278,440)(279,437)(280,438)
(281,443)(282,444)(283,441)(284,442)(285,447)(286,448)(287,445)(288,446)
(289,451)(290,452)(291,449)(292,450)(293,455)(294,456)(295,453)(296,454)
(297,459)(298,460)(299,457)(300,458)(301,463)(302,464)(303,461)(304,462)
(305,467)(306,468)(307,465)(308,466)(309,471)(310,472)(311,469)(312,470)
(313,475)(314,476)(315,473)(316,474)(317,479)(318,480)(319,477)(320,478);;
s1 := ( 1,193)( 2,194)( 3,212)( 4,211)( 5,213)( 6,214)( 7,200)( 8,199)
( 9,224)( 10,223)( 11,205)( 12,206)( 13,203)( 14,204)( 15,218)( 16,217)
( 17,210)( 18,209)( 19,196)( 20,195)( 21,197)( 22,198)( 23,215)( 24,216)
( 25,208)( 26,207)( 27,222)( 28,221)( 29,220)( 30,219)( 31,202)( 32,201)
( 33,161)( 34,162)( 35,180)( 36,179)( 37,181)( 38,182)( 39,168)( 40,167)
( 41,192)( 42,191)( 43,173)( 44,174)( 45,171)( 46,172)( 47,186)( 48,185)
( 49,178)( 50,177)( 51,164)( 52,163)( 53,165)( 54,166)( 55,183)( 56,184)
( 57,176)( 58,175)( 59,190)( 60,189)( 61,188)( 62,187)( 63,170)( 64,169)
( 65,289)( 66,290)( 67,308)( 68,307)( 69,309)( 70,310)( 71,296)( 72,295)
( 73,320)( 74,319)( 75,301)( 76,302)( 77,299)( 78,300)( 79,314)( 80,313)
( 81,306)( 82,305)( 83,292)( 84,291)( 85,293)( 86,294)( 87,311)( 88,312)
( 89,304)( 90,303)( 91,318)( 92,317)( 93,316)( 94,315)( 95,298)( 96,297)
( 97,257)( 98,258)( 99,276)(100,275)(101,277)(102,278)(103,264)(104,263)
(105,288)(106,287)(107,269)(108,270)(109,267)(110,268)(111,282)(112,281)
(113,274)(114,273)(115,260)(116,259)(117,261)(118,262)(119,279)(120,280)
(121,272)(122,271)(123,286)(124,285)(125,284)(126,283)(127,266)(128,265)
(129,225)(130,226)(131,244)(132,243)(133,245)(134,246)(135,232)(136,231)
(137,256)(138,255)(139,237)(140,238)(141,235)(142,236)(143,250)(144,249)
(145,242)(146,241)(147,228)(148,227)(149,229)(150,230)(151,247)(152,248)
(153,240)(154,239)(155,254)(156,253)(157,252)(158,251)(159,234)(160,233)
(321,353)(322,354)(323,372)(324,371)(325,373)(326,374)(327,360)(328,359)
(329,384)(330,383)(331,365)(332,366)(333,363)(334,364)(335,378)(336,377)
(337,370)(338,369)(339,356)(340,355)(341,357)(342,358)(343,375)(344,376)
(345,368)(346,367)(347,382)(348,381)(349,380)(350,379)(351,362)(352,361)
(385,449)(386,450)(387,468)(388,467)(389,469)(390,470)(391,456)(392,455)
(393,480)(394,479)(395,461)(396,462)(397,459)(398,460)(399,474)(400,473)
(401,466)(402,465)(403,452)(404,451)(405,453)(406,454)(407,471)(408,472)
(409,464)(410,463)(411,478)(412,477)(413,476)(414,475)(415,458)(416,457)
(419,436)(420,435)(421,437)(422,438)(423,424)(425,448)(426,447)(427,429)
(428,430)(431,442)(432,441)(433,434)(443,446)(444,445);;
s2 := ( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9, 12)( 10, 11)( 17, 31)( 18, 32)
( 19, 29)( 20, 30)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 33,130)( 34,129)
( 35,132)( 36,131)( 37,135)( 38,136)( 39,133)( 40,134)( 41,140)( 42,139)
( 43,138)( 44,137)( 45,141)( 46,142)( 47,143)( 48,144)( 49,159)( 50,160)
( 51,157)( 52,158)( 53,153)( 54,154)( 55,155)( 56,156)( 57,149)( 58,150)
( 59,151)( 60,152)( 61,147)( 62,148)( 63,145)( 64,146)( 65, 98)( 66, 97)
( 67,100)( 68, 99)( 69,103)( 70,104)( 71,101)( 72,102)( 73,108)( 74,107)
( 75,106)( 76,105)( 77,109)( 78,110)( 79,111)( 80,112)( 81,127)( 82,128)
( 83,125)( 84,126)( 85,121)( 86,122)( 87,123)( 88,124)( 89,117)( 90,118)
( 91,119)( 92,120)( 93,115)( 94,116)( 95,113)( 96,114)(161,162)(163,164)
(165,167)(166,168)(169,172)(170,171)(177,191)(178,192)(179,189)(180,190)
(181,185)(182,186)(183,187)(184,188)(193,290)(194,289)(195,292)(196,291)
(197,295)(198,296)(199,293)(200,294)(201,300)(202,299)(203,298)(204,297)
(205,301)(206,302)(207,303)(208,304)(209,319)(210,320)(211,317)(212,318)
(213,313)(214,314)(215,315)(216,316)(217,309)(218,310)(219,311)(220,312)
(221,307)(222,308)(223,305)(224,306)(225,258)(226,257)(227,260)(228,259)
(229,263)(230,264)(231,261)(232,262)(233,268)(234,267)(235,266)(236,265)
(237,269)(238,270)(239,271)(240,272)(241,287)(242,288)(243,285)(244,286)
(245,281)(246,282)(247,283)(248,284)(249,277)(250,278)(251,279)(252,280)
(253,275)(254,276)(255,273)(256,274)(321,322)(323,324)(325,327)(326,328)
(329,332)(330,331)(337,351)(338,352)(339,349)(340,350)(341,345)(342,346)
(343,347)(344,348)(353,450)(354,449)(355,452)(356,451)(357,455)(358,456)
(359,453)(360,454)(361,460)(362,459)(363,458)(364,457)(365,461)(366,462)
(367,463)(368,464)(369,479)(370,480)(371,477)(372,478)(373,473)(374,474)
(375,475)(376,476)(377,469)(378,470)(379,471)(380,472)(381,467)(382,468)
(383,465)(384,466)(385,418)(386,417)(387,420)(388,419)(389,423)(390,424)
(391,421)(392,422)(393,428)(394,427)(395,426)(396,425)(397,429)(398,430)
(399,431)(400,432)(401,447)(402,448)(403,445)(404,446)(405,441)(406,442)
(407,443)(408,444)(409,437)(410,438)(411,439)(412,440)(413,435)(414,436)
(415,433)(416,434);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
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)(161,323)(162,324)(163,321)(164,322)(165,327)(166,328)(167,325)
(168,326)(169,331)(170,332)(171,329)(172,330)(173,335)(174,336)(175,333)
(176,334)(177,339)(178,340)(179,337)(180,338)(181,343)(182,344)(183,341)
(184,342)(185,347)(186,348)(187,345)(188,346)(189,351)(190,352)(191,349)
(192,350)(193,355)(194,356)(195,353)(196,354)(197,359)(198,360)(199,357)
(200,358)(201,363)(202,364)(203,361)(204,362)(205,367)(206,368)(207,365)
(208,366)(209,371)(210,372)(211,369)(212,370)(213,375)(214,376)(215,373)
(216,374)(217,379)(218,380)(219,377)(220,378)(221,383)(222,384)(223,381)
(224,382)(225,387)(226,388)(227,385)(228,386)(229,391)(230,392)(231,389)
(232,390)(233,395)(234,396)(235,393)(236,394)(237,399)(238,400)(239,397)
(240,398)(241,403)(242,404)(243,401)(244,402)(245,407)(246,408)(247,405)
(248,406)(249,411)(250,412)(251,409)(252,410)(253,415)(254,416)(255,413)
(256,414)(257,419)(258,420)(259,417)(260,418)(261,423)(262,424)(263,421)
(264,422)(265,427)(266,428)(267,425)(268,426)(269,431)(270,432)(271,429)
(272,430)(273,435)(274,436)(275,433)(276,434)(277,439)(278,440)(279,437)
(280,438)(281,443)(282,444)(283,441)(284,442)(285,447)(286,448)(287,445)
(288,446)(289,451)(290,452)(291,449)(292,450)(293,455)(294,456)(295,453)
(296,454)(297,459)(298,460)(299,457)(300,458)(301,463)(302,464)(303,461)
(304,462)(305,467)(306,468)(307,465)(308,466)(309,471)(310,472)(311,469)
(312,470)(313,475)(314,476)(315,473)(316,474)(317,479)(318,480)(319,477)
(320,478);
s1 := Sym(480)!( 1,193)( 2,194)( 3,212)( 4,211)( 5,213)( 6,214)( 7,200)
( 8,199)( 9,224)( 10,223)( 11,205)( 12,206)( 13,203)( 14,204)( 15,218)
( 16,217)( 17,210)( 18,209)( 19,196)( 20,195)( 21,197)( 22,198)( 23,215)
( 24,216)( 25,208)( 26,207)( 27,222)( 28,221)( 29,220)( 30,219)( 31,202)
( 32,201)( 33,161)( 34,162)( 35,180)( 36,179)( 37,181)( 38,182)( 39,168)
( 40,167)( 41,192)( 42,191)( 43,173)( 44,174)( 45,171)( 46,172)( 47,186)
( 48,185)( 49,178)( 50,177)( 51,164)( 52,163)( 53,165)( 54,166)( 55,183)
( 56,184)( 57,176)( 58,175)( 59,190)( 60,189)( 61,188)( 62,187)( 63,170)
( 64,169)( 65,289)( 66,290)( 67,308)( 68,307)( 69,309)( 70,310)( 71,296)
( 72,295)( 73,320)( 74,319)( 75,301)( 76,302)( 77,299)( 78,300)( 79,314)
( 80,313)( 81,306)( 82,305)( 83,292)( 84,291)( 85,293)( 86,294)( 87,311)
( 88,312)( 89,304)( 90,303)( 91,318)( 92,317)( 93,316)( 94,315)( 95,298)
( 96,297)( 97,257)( 98,258)( 99,276)(100,275)(101,277)(102,278)(103,264)
(104,263)(105,288)(106,287)(107,269)(108,270)(109,267)(110,268)(111,282)
(112,281)(113,274)(114,273)(115,260)(116,259)(117,261)(118,262)(119,279)
(120,280)(121,272)(122,271)(123,286)(124,285)(125,284)(126,283)(127,266)
(128,265)(129,225)(130,226)(131,244)(132,243)(133,245)(134,246)(135,232)
(136,231)(137,256)(138,255)(139,237)(140,238)(141,235)(142,236)(143,250)
(144,249)(145,242)(146,241)(147,228)(148,227)(149,229)(150,230)(151,247)
(152,248)(153,240)(154,239)(155,254)(156,253)(157,252)(158,251)(159,234)
(160,233)(321,353)(322,354)(323,372)(324,371)(325,373)(326,374)(327,360)
(328,359)(329,384)(330,383)(331,365)(332,366)(333,363)(334,364)(335,378)
(336,377)(337,370)(338,369)(339,356)(340,355)(341,357)(342,358)(343,375)
(344,376)(345,368)(346,367)(347,382)(348,381)(349,380)(350,379)(351,362)
(352,361)(385,449)(386,450)(387,468)(388,467)(389,469)(390,470)(391,456)
(392,455)(393,480)(394,479)(395,461)(396,462)(397,459)(398,460)(399,474)
(400,473)(401,466)(402,465)(403,452)(404,451)(405,453)(406,454)(407,471)
(408,472)(409,464)(410,463)(411,478)(412,477)(413,476)(414,475)(415,458)
(416,457)(419,436)(420,435)(421,437)(422,438)(423,424)(425,448)(426,447)
(427,429)(428,430)(431,442)(432,441)(433,434)(443,446)(444,445);
s2 := Sym(480)!( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9, 12)( 10, 11)( 17, 31)
( 18, 32)( 19, 29)( 20, 30)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 33,130)
( 34,129)( 35,132)( 36,131)( 37,135)( 38,136)( 39,133)( 40,134)( 41,140)
( 42,139)( 43,138)( 44,137)( 45,141)( 46,142)( 47,143)( 48,144)( 49,159)
( 50,160)( 51,157)( 52,158)( 53,153)( 54,154)( 55,155)( 56,156)( 57,149)
( 58,150)( 59,151)( 60,152)( 61,147)( 62,148)( 63,145)( 64,146)( 65, 98)
( 66, 97)( 67,100)( 68, 99)( 69,103)( 70,104)( 71,101)( 72,102)( 73,108)
( 74,107)( 75,106)( 76,105)( 77,109)( 78,110)( 79,111)( 80,112)( 81,127)
( 82,128)( 83,125)( 84,126)( 85,121)( 86,122)( 87,123)( 88,124)( 89,117)
( 90,118)( 91,119)( 92,120)( 93,115)( 94,116)( 95,113)( 96,114)(161,162)
(163,164)(165,167)(166,168)(169,172)(170,171)(177,191)(178,192)(179,189)
(180,190)(181,185)(182,186)(183,187)(184,188)(193,290)(194,289)(195,292)
(196,291)(197,295)(198,296)(199,293)(200,294)(201,300)(202,299)(203,298)
(204,297)(205,301)(206,302)(207,303)(208,304)(209,319)(210,320)(211,317)
(212,318)(213,313)(214,314)(215,315)(216,316)(217,309)(218,310)(219,311)
(220,312)(221,307)(222,308)(223,305)(224,306)(225,258)(226,257)(227,260)
(228,259)(229,263)(230,264)(231,261)(232,262)(233,268)(234,267)(235,266)
(236,265)(237,269)(238,270)(239,271)(240,272)(241,287)(242,288)(243,285)
(244,286)(245,281)(246,282)(247,283)(248,284)(249,277)(250,278)(251,279)
(252,280)(253,275)(254,276)(255,273)(256,274)(321,322)(323,324)(325,327)
(326,328)(329,332)(330,331)(337,351)(338,352)(339,349)(340,350)(341,345)
(342,346)(343,347)(344,348)(353,450)(354,449)(355,452)(356,451)(357,455)
(358,456)(359,453)(360,454)(361,460)(362,459)(363,458)(364,457)(365,461)
(366,462)(367,463)(368,464)(369,479)(370,480)(371,477)(372,478)(373,473)
(374,474)(375,475)(376,476)(377,469)(378,470)(379,471)(380,472)(381,467)
(382,468)(383,465)(384,466)(385,418)(386,417)(387,420)(388,419)(389,423)
(390,424)(391,421)(392,422)(393,428)(394,427)(395,426)(396,425)(397,429)
(398,430)(399,431)(400,432)(401,447)(402,448)(403,445)(404,446)(405,441)
(406,442)(407,443)(408,444)(409,437)(410,438)(411,439)(412,440)(413,435)
(414,436)(415,433)(416,434);
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 >;
References : None.
to this polytope