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