Polytope of Type {22,42}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,42}*1848
Also Known As : {22,42|2}. if this polytope has another name.
Group : SmallGroup(1848,147)
Rank : 3
Schlafli Type : {22,42}
Number of vertices, edges, etc : 22, 462, 42
Order of s0s1s2 : 462
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) :
3-fold quotients : {22,14}*616
7-fold quotients : {22,6}*264
11-fold quotients : {2,42}*168
21-fold quotients : {22,2}*88
22-fold quotients : {2,21}*84
33-fold quotients : {2,14}*56
42-fold quotients : {11,2}*44
66-fold quotients : {2,7}*28
77-fold quotients : {2,6}*24
154-fold quotients : {2,3}*12
231-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)
( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)
( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)
( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)
( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)
(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)
(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)(137,140)
(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)(157,164)
(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)(171,172)
(178,187)(179,186)(180,185)(181,184)(182,183)(189,198)(190,197)(191,196)
(192,195)(193,194)(200,209)(201,208)(202,207)(203,206)(204,205)(211,220)
(212,219)(213,218)(214,217)(215,216)(222,231)(223,230)(224,229)(225,228)
(226,227)(233,242)(234,241)(235,240)(236,239)(237,238)(244,253)(245,252)
(246,251)(247,250)(248,249)(255,264)(256,263)(257,262)(258,261)(259,260)
(266,275)(267,274)(268,273)(269,272)(270,271)(277,286)(278,285)(279,284)
(280,283)(281,282)(288,297)(289,296)(290,295)(291,294)(292,293)(299,308)
(300,307)(301,306)(302,305)(303,304)(310,319)(311,318)(312,317)(313,316)
(314,315)(321,330)(322,329)(323,328)(324,327)(325,326)(332,341)(333,340)
(334,339)(335,338)(336,337)(343,352)(344,351)(345,350)(346,349)(347,348)
(354,363)(355,362)(356,361)(357,360)(358,359)(365,374)(366,373)(367,372)
(368,371)(369,370)(376,385)(377,384)(378,383)(379,382)(380,381)(387,396)
(388,395)(389,394)(390,393)(391,392)(398,407)(399,406)(400,405)(401,404)
(402,403)(409,418)(410,417)(411,416)(412,415)(413,414)(420,429)(421,428)
(422,427)(423,426)(424,425)(431,440)(432,439)(433,438)(434,437)(435,436)
(442,451)(443,450)(444,449)(445,448)(446,447)(453,462)(454,461)(455,460)
(456,459)(457,458);;
s1 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 68)( 13, 67)( 14, 77)
( 15, 76)( 16, 75)( 17, 74)( 18, 73)( 19, 72)( 20, 71)( 21, 70)( 22, 69)
( 23, 57)( 24, 56)( 25, 66)( 26, 65)( 27, 64)( 28, 63)( 29, 62)( 30, 61)
( 31, 60)( 32, 59)( 33, 58)( 34, 46)( 35, 45)( 36, 55)( 37, 54)( 38, 53)
( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 78,156)( 79,155)
( 80,165)( 81,164)( 82,163)( 83,162)( 84,161)( 85,160)( 86,159)( 87,158)
( 88,157)( 89,222)( 90,221)( 91,231)( 92,230)( 93,229)( 94,228)( 95,227)
( 96,226)( 97,225)( 98,224)( 99,223)(100,211)(101,210)(102,220)(103,219)
(104,218)(105,217)(106,216)(107,215)(108,214)(109,213)(110,212)(111,200)
(112,199)(113,209)(114,208)(115,207)(116,206)(117,205)(118,204)(119,203)
(120,202)(121,201)(122,189)(123,188)(124,198)(125,197)(126,196)(127,195)
(128,194)(129,193)(130,192)(131,191)(132,190)(133,178)(134,177)(135,187)
(136,186)(137,185)(138,184)(139,183)(140,182)(141,181)(142,180)(143,179)
(144,167)(145,166)(146,176)(147,175)(148,174)(149,173)(150,172)(151,171)
(152,170)(153,169)(154,168)(232,233)(234,242)(235,241)(236,240)(237,239)
(243,299)(244,298)(245,308)(246,307)(247,306)(248,305)(249,304)(250,303)
(251,302)(252,301)(253,300)(254,288)(255,287)(256,297)(257,296)(258,295)
(259,294)(260,293)(261,292)(262,291)(263,290)(264,289)(265,277)(266,276)
(267,286)(268,285)(269,284)(270,283)(271,282)(272,281)(273,280)(274,279)
(275,278)(309,387)(310,386)(311,396)(312,395)(313,394)(314,393)(315,392)
(316,391)(317,390)(318,389)(319,388)(320,453)(321,452)(322,462)(323,461)
(324,460)(325,459)(326,458)(327,457)(328,456)(329,455)(330,454)(331,442)
(332,441)(333,451)(334,450)(335,449)(336,448)(337,447)(338,446)(339,445)
(340,444)(341,443)(342,431)(343,430)(344,440)(345,439)(346,438)(347,437)
(348,436)(349,435)(350,434)(351,433)(352,432)(353,420)(354,419)(355,429)
(356,428)(357,427)(358,426)(359,425)(360,424)(361,423)(362,422)(363,421)
(364,409)(365,408)(366,418)(367,417)(368,416)(369,415)(370,414)(371,413)
(372,412)(373,411)(374,410)(375,398)(376,397)(377,407)(378,406)(379,405)
(380,404)(381,403)(382,402)(383,401)(384,400)(385,399);;
s2 := ( 1,320)( 2,321)( 3,322)( 4,323)( 5,324)( 6,325)( 7,326)( 8,327)
( 9,328)( 10,329)( 11,330)( 12,309)( 13,310)( 14,311)( 15,312)( 16,313)
( 17,314)( 18,315)( 19,316)( 20,317)( 21,318)( 22,319)( 23,375)( 24,376)
( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)( 32,384)
( 33,385)( 34,364)( 35,365)( 36,366)( 37,367)( 38,368)( 39,369)( 40,370)
( 41,371)( 42,372)( 43,373)( 44,374)( 45,353)( 46,354)( 47,355)( 48,356)
( 49,357)( 50,358)( 51,359)( 52,360)( 53,361)( 54,362)( 55,363)( 56,342)
( 57,343)( 58,344)( 59,345)( 60,346)( 61,347)( 62,348)( 63,349)( 64,350)
( 65,351)( 66,352)( 67,331)( 68,332)( 69,333)( 70,334)( 71,335)( 72,336)
( 73,337)( 74,338)( 75,339)( 76,340)( 77,341)( 78,243)( 79,244)( 80,245)
( 81,246)( 82,247)( 83,248)( 84,249)( 85,250)( 86,251)( 87,252)( 88,253)
( 89,232)( 90,233)( 91,234)( 92,235)( 93,236)( 94,237)( 95,238)( 96,239)
( 97,240)( 98,241)( 99,242)(100,298)(101,299)(102,300)(103,301)(104,302)
(105,303)(106,304)(107,305)(108,306)(109,307)(110,308)(111,287)(112,288)
(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)(120,296)
(121,297)(122,276)(123,277)(124,278)(125,279)(126,280)(127,281)(128,282)
(129,283)(130,284)(131,285)(132,286)(133,265)(134,266)(135,267)(136,268)
(137,269)(138,270)(139,271)(140,272)(141,273)(142,274)(143,275)(144,254)
(145,255)(146,256)(147,257)(148,258)(149,259)(150,260)(151,261)(152,262)
(153,263)(154,264)(155,397)(156,398)(157,399)(158,400)(159,401)(160,402)
(161,403)(162,404)(163,405)(164,406)(165,407)(166,386)(167,387)(168,388)
(169,389)(170,390)(171,391)(172,392)(173,393)(174,394)(175,395)(176,396)
(177,452)(178,453)(179,454)(180,455)(181,456)(182,457)(183,458)(184,459)
(185,460)(186,461)(187,462)(188,441)(189,442)(190,443)(191,444)(192,445)
(193,446)(194,447)(195,448)(196,449)(197,450)(198,451)(199,430)(200,431)
(201,432)(202,433)(203,434)(204,435)(205,436)(206,437)(207,438)(208,439)
(209,440)(210,419)(211,420)(212,421)(213,422)(214,423)(215,424)(216,425)
(217,426)(218,427)(219,428)(220,429)(221,408)(222,409)(223,410)(224,411)
(225,412)(226,413)(227,414)(228,415)(229,416)(230,417)(231,418);;
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(462)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)
( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)
( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)
(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)
(123,132)(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)
(137,140)(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)
(157,164)(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)
(171,172)(178,187)(179,186)(180,185)(181,184)(182,183)(189,198)(190,197)
(191,196)(192,195)(193,194)(200,209)(201,208)(202,207)(203,206)(204,205)
(211,220)(212,219)(213,218)(214,217)(215,216)(222,231)(223,230)(224,229)
(225,228)(226,227)(233,242)(234,241)(235,240)(236,239)(237,238)(244,253)
(245,252)(246,251)(247,250)(248,249)(255,264)(256,263)(257,262)(258,261)
(259,260)(266,275)(267,274)(268,273)(269,272)(270,271)(277,286)(278,285)
(279,284)(280,283)(281,282)(288,297)(289,296)(290,295)(291,294)(292,293)
(299,308)(300,307)(301,306)(302,305)(303,304)(310,319)(311,318)(312,317)
(313,316)(314,315)(321,330)(322,329)(323,328)(324,327)(325,326)(332,341)
(333,340)(334,339)(335,338)(336,337)(343,352)(344,351)(345,350)(346,349)
(347,348)(354,363)(355,362)(356,361)(357,360)(358,359)(365,374)(366,373)
(367,372)(368,371)(369,370)(376,385)(377,384)(378,383)(379,382)(380,381)
(387,396)(388,395)(389,394)(390,393)(391,392)(398,407)(399,406)(400,405)
(401,404)(402,403)(409,418)(410,417)(411,416)(412,415)(413,414)(420,429)
(421,428)(422,427)(423,426)(424,425)(431,440)(432,439)(433,438)(434,437)
(435,436)(442,451)(443,450)(444,449)(445,448)(446,447)(453,462)(454,461)
(455,460)(456,459)(457,458);
s1 := Sym(462)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 68)( 13, 67)
( 14, 77)( 15, 76)( 16, 75)( 17, 74)( 18, 73)( 19, 72)( 20, 71)( 21, 70)
( 22, 69)( 23, 57)( 24, 56)( 25, 66)( 26, 65)( 27, 64)( 28, 63)( 29, 62)
( 30, 61)( 31, 60)( 32, 59)( 33, 58)( 34, 46)( 35, 45)( 36, 55)( 37, 54)
( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 78,156)
( 79,155)( 80,165)( 81,164)( 82,163)( 83,162)( 84,161)( 85,160)( 86,159)
( 87,158)( 88,157)( 89,222)( 90,221)( 91,231)( 92,230)( 93,229)( 94,228)
( 95,227)( 96,226)( 97,225)( 98,224)( 99,223)(100,211)(101,210)(102,220)
(103,219)(104,218)(105,217)(106,216)(107,215)(108,214)(109,213)(110,212)
(111,200)(112,199)(113,209)(114,208)(115,207)(116,206)(117,205)(118,204)
(119,203)(120,202)(121,201)(122,189)(123,188)(124,198)(125,197)(126,196)
(127,195)(128,194)(129,193)(130,192)(131,191)(132,190)(133,178)(134,177)
(135,187)(136,186)(137,185)(138,184)(139,183)(140,182)(141,181)(142,180)
(143,179)(144,167)(145,166)(146,176)(147,175)(148,174)(149,173)(150,172)
(151,171)(152,170)(153,169)(154,168)(232,233)(234,242)(235,241)(236,240)
(237,239)(243,299)(244,298)(245,308)(246,307)(247,306)(248,305)(249,304)
(250,303)(251,302)(252,301)(253,300)(254,288)(255,287)(256,297)(257,296)
(258,295)(259,294)(260,293)(261,292)(262,291)(263,290)(264,289)(265,277)
(266,276)(267,286)(268,285)(269,284)(270,283)(271,282)(272,281)(273,280)
(274,279)(275,278)(309,387)(310,386)(311,396)(312,395)(313,394)(314,393)
(315,392)(316,391)(317,390)(318,389)(319,388)(320,453)(321,452)(322,462)
(323,461)(324,460)(325,459)(326,458)(327,457)(328,456)(329,455)(330,454)
(331,442)(332,441)(333,451)(334,450)(335,449)(336,448)(337,447)(338,446)
(339,445)(340,444)(341,443)(342,431)(343,430)(344,440)(345,439)(346,438)
(347,437)(348,436)(349,435)(350,434)(351,433)(352,432)(353,420)(354,419)
(355,429)(356,428)(357,427)(358,426)(359,425)(360,424)(361,423)(362,422)
(363,421)(364,409)(365,408)(366,418)(367,417)(368,416)(369,415)(370,414)
(371,413)(372,412)(373,411)(374,410)(375,398)(376,397)(377,407)(378,406)
(379,405)(380,404)(381,403)(382,402)(383,401)(384,400)(385,399);
s2 := Sym(462)!( 1,320)( 2,321)( 3,322)( 4,323)( 5,324)( 6,325)( 7,326)
( 8,327)( 9,328)( 10,329)( 11,330)( 12,309)( 13,310)( 14,311)( 15,312)
( 16,313)( 17,314)( 18,315)( 19,316)( 20,317)( 21,318)( 22,319)( 23,375)
( 24,376)( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)
( 32,384)( 33,385)( 34,364)( 35,365)( 36,366)( 37,367)( 38,368)( 39,369)
( 40,370)( 41,371)( 42,372)( 43,373)( 44,374)( 45,353)( 46,354)( 47,355)
( 48,356)( 49,357)( 50,358)( 51,359)( 52,360)( 53,361)( 54,362)( 55,363)
( 56,342)( 57,343)( 58,344)( 59,345)( 60,346)( 61,347)( 62,348)( 63,349)
( 64,350)( 65,351)( 66,352)( 67,331)( 68,332)( 69,333)( 70,334)( 71,335)
( 72,336)( 73,337)( 74,338)( 75,339)( 76,340)( 77,341)( 78,243)( 79,244)
( 80,245)( 81,246)( 82,247)( 83,248)( 84,249)( 85,250)( 86,251)( 87,252)
( 88,253)( 89,232)( 90,233)( 91,234)( 92,235)( 93,236)( 94,237)( 95,238)
( 96,239)( 97,240)( 98,241)( 99,242)(100,298)(101,299)(102,300)(103,301)
(104,302)(105,303)(106,304)(107,305)(108,306)(109,307)(110,308)(111,287)
(112,288)(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)
(120,296)(121,297)(122,276)(123,277)(124,278)(125,279)(126,280)(127,281)
(128,282)(129,283)(130,284)(131,285)(132,286)(133,265)(134,266)(135,267)
(136,268)(137,269)(138,270)(139,271)(140,272)(141,273)(142,274)(143,275)
(144,254)(145,255)(146,256)(147,257)(148,258)(149,259)(150,260)(151,261)
(152,262)(153,263)(154,264)(155,397)(156,398)(157,399)(158,400)(159,401)
(160,402)(161,403)(162,404)(163,405)(164,406)(165,407)(166,386)(167,387)
(168,388)(169,389)(170,390)(171,391)(172,392)(173,393)(174,394)(175,395)
(176,396)(177,452)(178,453)(179,454)(180,455)(181,456)(182,457)(183,458)
(184,459)(185,460)(186,461)(187,462)(188,441)(189,442)(190,443)(191,444)
(192,445)(193,446)(194,447)(195,448)(196,449)(197,450)(198,451)(199,430)
(200,431)(201,432)(202,433)(203,434)(204,435)(205,436)(206,437)(207,438)
(208,439)(209,440)(210,419)(211,420)(212,421)(213,422)(214,423)(215,424)
(216,425)(217,426)(218,427)(219,428)(220,429)(221,408)(222,409)(223,410)
(224,411)(225,412)(226,413)(227,414)(228,415)(229,416)(230,417)(231,418);
poly := sub<Sym(462)|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*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 >;
References : None.
to this polytope