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