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