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