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