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