Polytope of Type {10,92}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,92}*1840
Also Known As : {10,92|2}. if this polytope has another name.
Group : SmallGroup(1840,121)
Rank : 3
Schlafli Type : {10,92}
Number of vertices, edges, etc : 10, 460, 92
Order of s0s1s2 : 460
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {10,46}*920
5-fold quotients : {2,92}*368
10-fold quotients : {2,46}*184
20-fold quotients : {2,23}*92
23-fold quotients : {10,4}*80
46-fold quotients : {10,2}*40
92-fold quotients : {5,2}*20
115-fold quotients : {2,4}*16
230-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 24, 93)( 25, 94)( 26, 95)( 27, 96)( 28, 97)( 29, 98)( 30, 99)( 31,100)
( 32,101)( 33,102)( 34,103)( 35,104)( 36,105)( 37,106)( 38,107)( 39,108)
( 40,109)( 41,110)( 42,111)( 43,112)( 44,113)( 45,114)( 46,115)( 47, 70)
( 48, 71)( 49, 72)( 50, 73)( 51, 74)( 52, 75)( 53, 76)( 54, 77)( 55, 78)
( 56, 79)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)( 62, 85)( 63, 86)
( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)(139,208)(140,209)
(141,210)(142,211)(143,212)(144,213)(145,214)(146,215)(147,216)(148,217)
(149,218)(150,219)(151,220)(152,221)(153,222)(154,223)(155,224)(156,225)
(157,226)(158,227)(159,228)(160,229)(161,230)(162,185)(163,186)(164,187)
(165,188)(166,189)(167,190)(168,191)(169,192)(170,193)(171,194)(172,195)
(173,196)(174,197)(175,198)(176,199)(177,200)(178,201)(179,202)(180,203)
(181,204)(182,205)(183,206)(184,207)(254,323)(255,324)(256,325)(257,326)
(258,327)(259,328)(260,329)(261,330)(262,331)(263,332)(264,333)(265,334)
(266,335)(267,336)(268,337)(269,338)(270,339)(271,340)(272,341)(273,342)
(274,343)(275,344)(276,345)(277,300)(278,301)(279,302)(280,303)(281,304)
(282,305)(283,306)(284,307)(285,308)(286,309)(287,310)(288,311)(289,312)
(290,313)(291,314)(292,315)(293,316)(294,317)(295,318)(296,319)(297,320)
(298,321)(299,322)(369,438)(370,439)(371,440)(372,441)(373,442)(374,443)
(375,444)(376,445)(377,446)(378,447)(379,448)(380,449)(381,450)(382,451)
(383,452)(384,453)(385,454)(386,455)(387,456)(388,457)(389,458)(390,459)
(391,460)(392,415)(393,416)(394,417)(395,418)(396,419)(397,420)(398,421)
(399,422)(400,423)(401,424)(402,425)(403,426)(404,427)(405,428)(406,429)
(407,430)(408,431)(409,432)(410,433)(411,434)(412,435)(413,436)(414,437);;
s1 := ( 1, 24)( 2, 46)( 3, 45)( 4, 44)( 5, 43)( 6, 42)( 7, 41)( 8, 40)
( 9, 39)( 10, 38)( 11, 37)( 12, 36)( 13, 35)( 14, 34)( 15, 33)( 16, 32)
( 17, 31)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 47, 93)
( 48,115)( 49,114)( 50,113)( 51,112)( 52,111)( 53,110)( 54,109)( 55,108)
( 56,107)( 57,106)( 58,105)( 59,104)( 60,103)( 61,102)( 62,101)( 63,100)
( 64, 99)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 71, 92)( 72, 91)
( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 78, 85)( 79, 84)( 80, 83)
( 81, 82)(116,139)(117,161)(118,160)(119,159)(120,158)(121,157)(122,156)
(123,155)(124,154)(125,153)(126,152)(127,151)(128,150)(129,149)(130,148)
(131,147)(132,146)(133,145)(134,144)(135,143)(136,142)(137,141)(138,140)
(162,208)(163,230)(164,229)(165,228)(166,227)(167,226)(168,225)(169,224)
(170,223)(171,222)(172,221)(173,220)(174,219)(175,218)(176,217)(177,216)
(178,215)(179,214)(180,213)(181,212)(182,211)(183,210)(184,209)(186,207)
(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)
(195,198)(196,197)(231,369)(232,391)(233,390)(234,389)(235,388)(236,387)
(237,386)(238,385)(239,384)(240,383)(241,382)(242,381)(243,380)(244,379)
(245,378)(246,377)(247,376)(248,375)(249,374)(250,373)(251,372)(252,371)
(253,370)(254,346)(255,368)(256,367)(257,366)(258,365)(259,364)(260,363)
(261,362)(262,361)(263,360)(264,359)(265,358)(266,357)(267,356)(268,355)
(269,354)(270,353)(271,352)(272,351)(273,350)(274,349)(275,348)(276,347)
(277,438)(278,460)(279,459)(280,458)(281,457)(282,456)(283,455)(284,454)
(285,453)(286,452)(287,451)(288,450)(289,449)(290,448)(291,447)(292,446)
(293,445)(294,444)(295,443)(296,442)(297,441)(298,440)(299,439)(300,415)
(301,437)(302,436)(303,435)(304,434)(305,433)(306,432)(307,431)(308,430)
(309,429)(310,428)(311,427)(312,426)(313,425)(314,424)(315,423)(316,422)
(317,421)(318,420)(319,419)(320,418)(321,417)(322,416)(323,392)(324,414)
(325,413)(326,412)(327,411)(328,410)(329,409)(330,408)(331,407)(332,406)
(333,405)(334,404)(335,403)(336,402)(337,401)(338,400)(339,399)(340,398)
(341,397)(342,396)(343,395)(344,394)(345,393);;
s2 := ( 1,232)( 2,231)( 3,253)( 4,252)( 5,251)( 6,250)( 7,249)( 8,248)
( 9,247)( 10,246)( 11,245)( 12,244)( 13,243)( 14,242)( 15,241)( 16,240)
( 17,239)( 18,238)( 19,237)( 20,236)( 21,235)( 22,234)( 23,233)( 24,255)
( 25,254)( 26,276)( 27,275)( 28,274)( 29,273)( 30,272)( 31,271)( 32,270)
( 33,269)( 34,268)( 35,267)( 36,266)( 37,265)( 38,264)( 39,263)( 40,262)
( 41,261)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,278)( 48,277)
( 49,299)( 50,298)( 51,297)( 52,296)( 53,295)( 54,294)( 55,293)( 56,292)
( 57,291)( 58,290)( 59,289)( 60,288)( 61,287)( 62,286)( 63,285)( 64,284)
( 65,283)( 66,282)( 67,281)( 68,280)( 69,279)( 70,301)( 71,300)( 72,322)
( 73,321)( 74,320)( 75,319)( 76,318)( 77,317)( 78,316)( 79,315)( 80,314)
( 81,313)( 82,312)( 83,311)( 84,310)( 85,309)( 86,308)( 87,307)( 88,306)
( 89,305)( 90,304)( 91,303)( 92,302)( 93,324)( 94,323)( 95,345)( 96,344)
( 97,343)( 98,342)( 99,341)(100,340)(101,339)(102,338)(103,337)(104,336)
(105,335)(106,334)(107,333)(108,332)(109,331)(110,330)(111,329)(112,328)
(113,327)(114,326)(115,325)(116,347)(117,346)(118,368)(119,367)(120,366)
(121,365)(122,364)(123,363)(124,362)(125,361)(126,360)(127,359)(128,358)
(129,357)(130,356)(131,355)(132,354)(133,353)(134,352)(135,351)(136,350)
(137,349)(138,348)(139,370)(140,369)(141,391)(142,390)(143,389)(144,388)
(145,387)(146,386)(147,385)(148,384)(149,383)(150,382)(151,381)(152,380)
(153,379)(154,378)(155,377)(156,376)(157,375)(158,374)(159,373)(160,372)
(161,371)(162,393)(163,392)(164,414)(165,413)(166,412)(167,411)(168,410)
(169,409)(170,408)(171,407)(172,406)(173,405)(174,404)(175,403)(176,402)
(177,401)(178,400)(179,399)(180,398)(181,397)(182,396)(183,395)(184,394)
(185,416)(186,415)(187,437)(188,436)(189,435)(190,434)(191,433)(192,432)
(193,431)(194,430)(195,429)(196,428)(197,427)(198,426)(199,425)(200,424)
(201,423)(202,422)(203,421)(204,420)(205,419)(206,418)(207,417)(208,439)
(209,438)(210,460)(211,459)(212,458)(213,457)(214,456)(215,455)(216,454)
(217,453)(218,452)(219,451)(220,450)(221,449)(222,448)(223,447)(224,446)
(225,445)(226,444)(227,443)(228,442)(229,441)(230,440);;
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*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(460)!( 24, 93)( 25, 94)( 26, 95)( 27, 96)( 28, 97)( 29, 98)( 30, 99)
( 31,100)( 32,101)( 33,102)( 34,103)( 35,104)( 36,105)( 37,106)( 38,107)
( 39,108)( 40,109)( 41,110)( 42,111)( 43,112)( 44,113)( 45,114)( 46,115)
( 47, 70)( 48, 71)( 49, 72)( 50, 73)( 51, 74)( 52, 75)( 53, 76)( 54, 77)
( 55, 78)( 56, 79)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)( 62, 85)
( 63, 86)( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)(139,208)
(140,209)(141,210)(142,211)(143,212)(144,213)(145,214)(146,215)(147,216)
(148,217)(149,218)(150,219)(151,220)(152,221)(153,222)(154,223)(155,224)
(156,225)(157,226)(158,227)(159,228)(160,229)(161,230)(162,185)(163,186)
(164,187)(165,188)(166,189)(167,190)(168,191)(169,192)(170,193)(171,194)
(172,195)(173,196)(174,197)(175,198)(176,199)(177,200)(178,201)(179,202)
(180,203)(181,204)(182,205)(183,206)(184,207)(254,323)(255,324)(256,325)
(257,326)(258,327)(259,328)(260,329)(261,330)(262,331)(263,332)(264,333)
(265,334)(266,335)(267,336)(268,337)(269,338)(270,339)(271,340)(272,341)
(273,342)(274,343)(275,344)(276,345)(277,300)(278,301)(279,302)(280,303)
(281,304)(282,305)(283,306)(284,307)(285,308)(286,309)(287,310)(288,311)
(289,312)(290,313)(291,314)(292,315)(293,316)(294,317)(295,318)(296,319)
(297,320)(298,321)(299,322)(369,438)(370,439)(371,440)(372,441)(373,442)
(374,443)(375,444)(376,445)(377,446)(378,447)(379,448)(380,449)(381,450)
(382,451)(383,452)(384,453)(385,454)(386,455)(387,456)(388,457)(389,458)
(390,459)(391,460)(392,415)(393,416)(394,417)(395,418)(396,419)(397,420)
(398,421)(399,422)(400,423)(401,424)(402,425)(403,426)(404,427)(405,428)
(406,429)(407,430)(408,431)(409,432)(410,433)(411,434)(412,435)(413,436)
(414,437);
s1 := Sym(460)!( 1, 24)( 2, 46)( 3, 45)( 4, 44)( 5, 43)( 6, 42)( 7, 41)
( 8, 40)( 9, 39)( 10, 38)( 11, 37)( 12, 36)( 13, 35)( 14, 34)( 15, 33)
( 16, 32)( 17, 31)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)
( 47, 93)( 48,115)( 49,114)( 50,113)( 51,112)( 52,111)( 53,110)( 54,109)
( 55,108)( 56,107)( 57,106)( 58,105)( 59,104)( 60,103)( 61,102)( 62,101)
( 63,100)( 64, 99)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 71, 92)
( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 78, 85)( 79, 84)
( 80, 83)( 81, 82)(116,139)(117,161)(118,160)(119,159)(120,158)(121,157)
(122,156)(123,155)(124,154)(125,153)(126,152)(127,151)(128,150)(129,149)
(130,148)(131,147)(132,146)(133,145)(134,144)(135,143)(136,142)(137,141)
(138,140)(162,208)(163,230)(164,229)(165,228)(166,227)(167,226)(168,225)
(169,224)(170,223)(171,222)(172,221)(173,220)(174,219)(175,218)(176,217)
(177,216)(178,215)(179,214)(180,213)(181,212)(182,211)(183,210)(184,209)
(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)
(194,199)(195,198)(196,197)(231,369)(232,391)(233,390)(234,389)(235,388)
(236,387)(237,386)(238,385)(239,384)(240,383)(241,382)(242,381)(243,380)
(244,379)(245,378)(246,377)(247,376)(248,375)(249,374)(250,373)(251,372)
(252,371)(253,370)(254,346)(255,368)(256,367)(257,366)(258,365)(259,364)
(260,363)(261,362)(262,361)(263,360)(264,359)(265,358)(266,357)(267,356)
(268,355)(269,354)(270,353)(271,352)(272,351)(273,350)(274,349)(275,348)
(276,347)(277,438)(278,460)(279,459)(280,458)(281,457)(282,456)(283,455)
(284,454)(285,453)(286,452)(287,451)(288,450)(289,449)(290,448)(291,447)
(292,446)(293,445)(294,444)(295,443)(296,442)(297,441)(298,440)(299,439)
(300,415)(301,437)(302,436)(303,435)(304,434)(305,433)(306,432)(307,431)
(308,430)(309,429)(310,428)(311,427)(312,426)(313,425)(314,424)(315,423)
(316,422)(317,421)(318,420)(319,419)(320,418)(321,417)(322,416)(323,392)
(324,414)(325,413)(326,412)(327,411)(328,410)(329,409)(330,408)(331,407)
(332,406)(333,405)(334,404)(335,403)(336,402)(337,401)(338,400)(339,399)
(340,398)(341,397)(342,396)(343,395)(344,394)(345,393);
s2 := Sym(460)!( 1,232)( 2,231)( 3,253)( 4,252)( 5,251)( 6,250)( 7,249)
( 8,248)( 9,247)( 10,246)( 11,245)( 12,244)( 13,243)( 14,242)( 15,241)
( 16,240)( 17,239)( 18,238)( 19,237)( 20,236)( 21,235)( 22,234)( 23,233)
( 24,255)( 25,254)( 26,276)( 27,275)( 28,274)( 29,273)( 30,272)( 31,271)
( 32,270)( 33,269)( 34,268)( 35,267)( 36,266)( 37,265)( 38,264)( 39,263)
( 40,262)( 41,261)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,278)
( 48,277)( 49,299)( 50,298)( 51,297)( 52,296)( 53,295)( 54,294)( 55,293)
( 56,292)( 57,291)( 58,290)( 59,289)( 60,288)( 61,287)( 62,286)( 63,285)
( 64,284)( 65,283)( 66,282)( 67,281)( 68,280)( 69,279)( 70,301)( 71,300)
( 72,322)( 73,321)( 74,320)( 75,319)( 76,318)( 77,317)( 78,316)( 79,315)
( 80,314)( 81,313)( 82,312)( 83,311)( 84,310)( 85,309)( 86,308)( 87,307)
( 88,306)( 89,305)( 90,304)( 91,303)( 92,302)( 93,324)( 94,323)( 95,345)
( 96,344)( 97,343)( 98,342)( 99,341)(100,340)(101,339)(102,338)(103,337)
(104,336)(105,335)(106,334)(107,333)(108,332)(109,331)(110,330)(111,329)
(112,328)(113,327)(114,326)(115,325)(116,347)(117,346)(118,368)(119,367)
(120,366)(121,365)(122,364)(123,363)(124,362)(125,361)(126,360)(127,359)
(128,358)(129,357)(130,356)(131,355)(132,354)(133,353)(134,352)(135,351)
(136,350)(137,349)(138,348)(139,370)(140,369)(141,391)(142,390)(143,389)
(144,388)(145,387)(146,386)(147,385)(148,384)(149,383)(150,382)(151,381)
(152,380)(153,379)(154,378)(155,377)(156,376)(157,375)(158,374)(159,373)
(160,372)(161,371)(162,393)(163,392)(164,414)(165,413)(166,412)(167,411)
(168,410)(169,409)(170,408)(171,407)(172,406)(173,405)(174,404)(175,403)
(176,402)(177,401)(178,400)(179,399)(180,398)(181,397)(182,396)(183,395)
(184,394)(185,416)(186,415)(187,437)(188,436)(189,435)(190,434)(191,433)
(192,432)(193,431)(194,430)(195,429)(196,428)(197,427)(198,426)(199,425)
(200,424)(201,423)(202,422)(203,421)(204,420)(205,419)(206,418)(207,417)
(208,439)(209,438)(210,460)(211,459)(212,458)(213,457)(214,456)(215,455)
(216,454)(217,453)(218,452)(219,451)(220,450)(221,449)(222,448)(223,447)
(224,446)(225,445)(226,444)(227,443)(228,442)(229,441)(230,440);
poly := sub<Sym(460)|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*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope