Polytope of Type {14,62}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,62}*1736
Also Known As : {14,62|2}. if this polytope has another name.
Group : SmallGroup(1736,31)
Rank : 3
Schlafli Type : {14,62}
Number of vertices, edges, etc : 14, 434, 62
Order of s0s1s2 : 434
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) :
7-fold quotients : {2,62}*248
14-fold quotients : {2,31}*124
31-fold quotients : {14,2}*56
62-fold quotients : {7,2}*28
217-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 32,187)( 33,188)( 34,189)( 35,190)( 36,191)( 37,192)( 38,193)( 39,194)
( 40,195)( 41,196)( 42,197)( 43,198)( 44,199)( 45,200)( 46,201)( 47,202)
( 48,203)( 49,204)( 50,205)( 51,206)( 52,207)( 53,208)( 54,209)( 55,210)
( 56,211)( 57,212)( 58,213)( 59,214)( 60,215)( 61,216)( 62,217)( 63,156)
( 64,157)( 65,158)( 66,159)( 67,160)( 68,161)( 69,162)( 70,163)( 71,164)
( 72,165)( 73,166)( 74,167)( 75,168)( 76,169)( 77,170)( 78,171)( 79,172)
( 80,173)( 81,174)( 82,175)( 83,176)( 84,177)( 85,178)( 86,179)( 87,180)
( 88,181)( 89,182)( 90,183)( 91,184)( 92,185)( 93,186)( 94,125)( 95,126)
( 96,127)( 97,128)( 98,129)( 99,130)(100,131)(101,132)(102,133)(103,134)
(104,135)(105,136)(106,137)(107,138)(108,139)(109,140)(110,141)(111,142)
(112,143)(113,144)(114,145)(115,146)(116,147)(117,148)(118,149)(119,150)
(120,151)(121,152)(122,153)(123,154)(124,155)(249,404)(250,405)(251,406)
(252,407)(253,408)(254,409)(255,410)(256,411)(257,412)(258,413)(259,414)
(260,415)(261,416)(262,417)(263,418)(264,419)(265,420)(266,421)(267,422)
(268,423)(269,424)(270,425)(271,426)(272,427)(273,428)(274,429)(275,430)
(276,431)(277,432)(278,433)(279,434)(280,373)(281,374)(282,375)(283,376)
(284,377)(285,378)(286,379)(287,380)(288,381)(289,382)(290,383)(291,384)
(292,385)(293,386)(294,387)(295,388)(296,389)(297,390)(298,391)(299,392)
(300,393)(301,394)(302,395)(303,396)(304,397)(305,398)(306,399)(307,400)
(308,401)(309,402)(310,403)(311,342)(312,343)(313,344)(314,345)(315,346)
(316,347)(317,348)(318,349)(319,350)(320,351)(321,352)(322,353)(323,354)
(324,355)(325,356)(326,357)(327,358)(328,359)(329,360)(330,361)(331,362)
(332,363)(333,364)(334,365)(335,366)(336,367)(337,368)(338,369)(339,370)
(340,371)(341,372);;
s1 := ( 1, 32)( 2, 62)( 3, 61)( 4, 60)( 5, 59)( 6, 58)( 7, 57)( 8, 56)
( 9, 55)( 10, 54)( 11, 53)( 12, 52)( 13, 51)( 14, 50)( 15, 49)( 16, 48)
( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)( 24, 40)
( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 31, 33)( 63,187)
( 64,217)( 65,216)( 66,215)( 67,214)( 68,213)( 69,212)( 70,211)( 71,210)
( 72,209)( 73,208)( 74,207)( 75,206)( 76,205)( 77,204)( 78,203)( 79,202)
( 80,201)( 81,200)( 82,199)( 83,198)( 84,197)( 85,196)( 86,195)( 87,194)
( 88,193)( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,156)( 95,186)
( 96,185)( 97,184)( 98,183)( 99,182)(100,181)(101,180)(102,179)(103,178)
(104,177)(105,176)(106,175)(107,174)(108,173)(109,172)(110,171)(111,170)
(112,169)(113,168)(114,167)(115,166)(116,165)(117,164)(118,163)(119,162)
(120,161)(121,160)(122,159)(123,158)(124,157)(126,155)(127,154)(128,153)
(129,152)(130,151)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)
(137,144)(138,143)(139,142)(140,141)(218,249)(219,279)(220,278)(221,277)
(222,276)(223,275)(224,274)(225,273)(226,272)(227,271)(228,270)(229,269)
(230,268)(231,267)(232,266)(233,265)(234,264)(235,263)(236,262)(237,261)
(238,260)(239,259)(240,258)(241,257)(242,256)(243,255)(244,254)(245,253)
(246,252)(247,251)(248,250)(280,404)(281,434)(282,433)(283,432)(284,431)
(285,430)(286,429)(287,428)(288,427)(289,426)(290,425)(291,424)(292,423)
(293,422)(294,421)(295,420)(296,419)(297,418)(298,417)(299,416)(300,415)
(301,414)(302,413)(303,412)(304,411)(305,410)(306,409)(307,408)(308,407)
(309,406)(310,405)(311,373)(312,403)(313,402)(314,401)(315,400)(316,399)
(317,398)(318,397)(319,396)(320,395)(321,394)(322,393)(323,392)(324,391)
(325,390)(326,389)(327,388)(328,387)(329,386)(330,385)(331,384)(332,383)
(333,382)(334,381)(335,380)(336,379)(337,378)(338,377)(339,376)(340,375)
(341,374)(343,372)(344,371)(345,370)(346,369)(347,368)(348,367)(349,366)
(350,365)(351,364)(352,363)(353,362)(354,361)(355,360)(356,359)(357,358);;
s2 := ( 1,219)( 2,218)( 3,248)( 4,247)( 5,246)( 6,245)( 7,244)( 8,243)
( 9,242)( 10,241)( 11,240)( 12,239)( 13,238)( 14,237)( 15,236)( 16,235)
( 17,234)( 18,233)( 19,232)( 20,231)( 21,230)( 22,229)( 23,228)( 24,227)
( 25,226)( 26,225)( 27,224)( 28,223)( 29,222)( 30,221)( 31,220)( 32,250)
( 33,249)( 34,279)( 35,278)( 36,277)( 37,276)( 38,275)( 39,274)( 40,273)
( 41,272)( 42,271)( 43,270)( 44,269)( 45,268)( 46,267)( 47,266)( 48,265)
( 49,264)( 50,263)( 51,262)( 52,261)( 53,260)( 54,259)( 55,258)( 56,257)
( 57,256)( 58,255)( 59,254)( 60,253)( 61,252)( 62,251)( 63,281)( 64,280)
( 65,310)( 66,309)( 67,308)( 68,307)( 69,306)( 70,305)( 71,304)( 72,303)
( 73,302)( 74,301)( 75,300)( 76,299)( 77,298)( 78,297)( 79,296)( 80,295)
( 81,294)( 82,293)( 83,292)( 84,291)( 85,290)( 86,289)( 87,288)( 88,287)
( 89,286)( 90,285)( 91,284)( 92,283)( 93,282)( 94,312)( 95,311)( 96,341)
( 97,340)( 98,339)( 99,338)(100,337)(101,336)(102,335)(103,334)(104,333)
(105,332)(106,331)(107,330)(108,329)(109,328)(110,327)(111,326)(112,325)
(113,324)(114,323)(115,322)(116,321)(117,320)(118,319)(119,318)(120,317)
(121,316)(122,315)(123,314)(124,313)(125,343)(126,342)(127,372)(128,371)
(129,370)(130,369)(131,368)(132,367)(133,366)(134,365)(135,364)(136,363)
(137,362)(138,361)(139,360)(140,359)(141,358)(142,357)(143,356)(144,355)
(145,354)(146,353)(147,352)(148,351)(149,350)(150,349)(151,348)(152,347)
(153,346)(154,345)(155,344)(156,374)(157,373)(158,403)(159,402)(160,401)
(161,400)(162,399)(163,398)(164,397)(165,396)(166,395)(167,394)(168,393)
(169,392)(170,391)(171,390)(172,389)(173,388)(174,387)(175,386)(176,385)
(177,384)(178,383)(179,382)(180,381)(181,380)(182,379)(183,378)(184,377)
(185,376)(186,375)(187,405)(188,404)(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)(208,415)
(209,414)(210,413)(211,412)(212,411)(213,410)(214,409)(215,408)(216,407)
(217,406);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(434)!( 32,187)( 33,188)( 34,189)( 35,190)( 36,191)( 37,192)( 38,193)
( 39,194)( 40,195)( 41,196)( 42,197)( 43,198)( 44,199)( 45,200)( 46,201)
( 47,202)( 48,203)( 49,204)( 50,205)( 51,206)( 52,207)( 53,208)( 54,209)
( 55,210)( 56,211)( 57,212)( 58,213)( 59,214)( 60,215)( 61,216)( 62,217)
( 63,156)( 64,157)( 65,158)( 66,159)( 67,160)( 68,161)( 69,162)( 70,163)
( 71,164)( 72,165)( 73,166)( 74,167)( 75,168)( 76,169)( 77,170)( 78,171)
( 79,172)( 80,173)( 81,174)( 82,175)( 83,176)( 84,177)( 85,178)( 86,179)
( 87,180)( 88,181)( 89,182)( 90,183)( 91,184)( 92,185)( 93,186)( 94,125)
( 95,126)( 96,127)( 97,128)( 98,129)( 99,130)(100,131)(101,132)(102,133)
(103,134)(104,135)(105,136)(106,137)(107,138)(108,139)(109,140)(110,141)
(111,142)(112,143)(113,144)(114,145)(115,146)(116,147)(117,148)(118,149)
(119,150)(120,151)(121,152)(122,153)(123,154)(124,155)(249,404)(250,405)
(251,406)(252,407)(253,408)(254,409)(255,410)(256,411)(257,412)(258,413)
(259,414)(260,415)(261,416)(262,417)(263,418)(264,419)(265,420)(266,421)
(267,422)(268,423)(269,424)(270,425)(271,426)(272,427)(273,428)(274,429)
(275,430)(276,431)(277,432)(278,433)(279,434)(280,373)(281,374)(282,375)
(283,376)(284,377)(285,378)(286,379)(287,380)(288,381)(289,382)(290,383)
(291,384)(292,385)(293,386)(294,387)(295,388)(296,389)(297,390)(298,391)
(299,392)(300,393)(301,394)(302,395)(303,396)(304,397)(305,398)(306,399)
(307,400)(308,401)(309,402)(310,403)(311,342)(312,343)(313,344)(314,345)
(315,346)(316,347)(317,348)(318,349)(319,350)(320,351)(321,352)(322,353)
(323,354)(324,355)(325,356)(326,357)(327,358)(328,359)(329,360)(330,361)
(331,362)(332,363)(333,364)(334,365)(335,366)(336,367)(337,368)(338,369)
(339,370)(340,371)(341,372);
s1 := Sym(434)!( 1, 32)( 2, 62)( 3, 61)( 4, 60)( 5, 59)( 6, 58)( 7, 57)
( 8, 56)( 9, 55)( 10, 54)( 11, 53)( 12, 52)( 13, 51)( 14, 50)( 15, 49)
( 16, 48)( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)
( 24, 40)( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 31, 33)
( 63,187)( 64,217)( 65,216)( 66,215)( 67,214)( 68,213)( 69,212)( 70,211)
( 71,210)( 72,209)( 73,208)( 74,207)( 75,206)( 76,205)( 77,204)( 78,203)
( 79,202)( 80,201)( 81,200)( 82,199)( 83,198)( 84,197)( 85,196)( 86,195)
( 87,194)( 88,193)( 89,192)( 90,191)( 91,190)( 92,189)( 93,188)( 94,156)
( 95,186)( 96,185)( 97,184)( 98,183)( 99,182)(100,181)(101,180)(102,179)
(103,178)(104,177)(105,176)(106,175)(107,174)(108,173)(109,172)(110,171)
(111,170)(112,169)(113,168)(114,167)(115,166)(116,165)(117,164)(118,163)
(119,162)(120,161)(121,160)(122,159)(123,158)(124,157)(126,155)(127,154)
(128,153)(129,152)(130,151)(131,150)(132,149)(133,148)(134,147)(135,146)
(136,145)(137,144)(138,143)(139,142)(140,141)(218,249)(219,279)(220,278)
(221,277)(222,276)(223,275)(224,274)(225,273)(226,272)(227,271)(228,270)
(229,269)(230,268)(231,267)(232,266)(233,265)(234,264)(235,263)(236,262)
(237,261)(238,260)(239,259)(240,258)(241,257)(242,256)(243,255)(244,254)
(245,253)(246,252)(247,251)(248,250)(280,404)(281,434)(282,433)(283,432)
(284,431)(285,430)(286,429)(287,428)(288,427)(289,426)(290,425)(291,424)
(292,423)(293,422)(294,421)(295,420)(296,419)(297,418)(298,417)(299,416)
(300,415)(301,414)(302,413)(303,412)(304,411)(305,410)(306,409)(307,408)
(308,407)(309,406)(310,405)(311,373)(312,403)(313,402)(314,401)(315,400)
(316,399)(317,398)(318,397)(319,396)(320,395)(321,394)(322,393)(323,392)
(324,391)(325,390)(326,389)(327,388)(328,387)(329,386)(330,385)(331,384)
(332,383)(333,382)(334,381)(335,380)(336,379)(337,378)(338,377)(339,376)
(340,375)(341,374)(343,372)(344,371)(345,370)(346,369)(347,368)(348,367)
(349,366)(350,365)(351,364)(352,363)(353,362)(354,361)(355,360)(356,359)
(357,358);
s2 := Sym(434)!( 1,219)( 2,218)( 3,248)( 4,247)( 5,246)( 6,245)( 7,244)
( 8,243)( 9,242)( 10,241)( 11,240)( 12,239)( 13,238)( 14,237)( 15,236)
( 16,235)( 17,234)( 18,233)( 19,232)( 20,231)( 21,230)( 22,229)( 23,228)
( 24,227)( 25,226)( 26,225)( 27,224)( 28,223)( 29,222)( 30,221)( 31,220)
( 32,250)( 33,249)( 34,279)( 35,278)( 36,277)( 37,276)( 38,275)( 39,274)
( 40,273)( 41,272)( 42,271)( 43,270)( 44,269)( 45,268)( 46,267)( 47,266)
( 48,265)( 49,264)( 50,263)( 51,262)( 52,261)( 53,260)( 54,259)( 55,258)
( 56,257)( 57,256)( 58,255)( 59,254)( 60,253)( 61,252)( 62,251)( 63,281)
( 64,280)( 65,310)( 66,309)( 67,308)( 68,307)( 69,306)( 70,305)( 71,304)
( 72,303)( 73,302)( 74,301)( 75,300)( 76,299)( 77,298)( 78,297)( 79,296)
( 80,295)( 81,294)( 82,293)( 83,292)( 84,291)( 85,290)( 86,289)( 87,288)
( 88,287)( 89,286)( 90,285)( 91,284)( 92,283)( 93,282)( 94,312)( 95,311)
( 96,341)( 97,340)( 98,339)( 99,338)(100,337)(101,336)(102,335)(103,334)
(104,333)(105,332)(106,331)(107,330)(108,329)(109,328)(110,327)(111,326)
(112,325)(113,324)(114,323)(115,322)(116,321)(117,320)(118,319)(119,318)
(120,317)(121,316)(122,315)(123,314)(124,313)(125,343)(126,342)(127,372)
(128,371)(129,370)(130,369)(131,368)(132,367)(133,366)(134,365)(135,364)
(136,363)(137,362)(138,361)(139,360)(140,359)(141,358)(142,357)(143,356)
(144,355)(145,354)(146,353)(147,352)(148,351)(149,350)(150,349)(151,348)
(152,347)(153,346)(154,345)(155,344)(156,374)(157,373)(158,403)(159,402)
(160,401)(161,400)(162,399)(163,398)(164,397)(165,396)(166,395)(167,394)
(168,393)(169,392)(170,391)(171,390)(172,389)(173,388)(174,387)(175,386)
(176,385)(177,384)(178,383)(179,382)(180,381)(181,380)(182,379)(183,378)
(184,377)(185,376)(186,375)(187,405)(188,404)(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)
(208,415)(209,414)(210,413)(211,412)(212,411)(213,410)(214,409)(215,408)
(216,407)(217,406);
poly := sub<Sym(434)|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 >;
References : None.
to this polytope