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