Polytope of Type {60,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,14}*1680
Also Known As : {60,14|2}. if this polytope has another name.
Group : SmallGroup(1680,716)
Rank : 3
Schlafli Type : {60,14}
Number of vertices, edges, etc : 60, 420, 14
Order of s0s1s2 : 420
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 : {30,14}*840
3-fold quotients : {20,14}*560
5-fold quotients : {12,14}*336
6-fold quotients : {10,14}*280
7-fold quotients : {60,2}*240
10-fold quotients : {6,14}*168
14-fold quotients : {30,2}*120
15-fold quotients : {4,14}*112
21-fold quotients : {20,2}*80
28-fold quotients : {15,2}*60
30-fold quotients : {2,14}*56
35-fold quotients : {12,2}*48
42-fold quotients : {10,2}*40
60-fold quotients : {2,7}*28
70-fold quotients : {6,2}*24
84-fold quotients : {5,2}*20
105-fold quotients : {4,2}*16
140-fold quotients : {3,2}*12
210-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 8, 29)( 9, 30)( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)( 15, 22)
( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 36, 71)( 37, 72)
( 38, 73)( 39, 74)( 40, 75)( 41, 76)( 42, 77)( 43, 99)( 44,100)( 45,101)
( 46,102)( 47,103)( 48,104)( 49,105)( 50, 92)( 51, 93)( 52, 94)( 53, 95)
( 54, 96)( 55, 97)( 56, 98)( 57, 85)( 58, 86)( 59, 87)( 60, 88)( 61, 89)
( 62, 90)( 63, 91)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)( 69, 83)
( 70, 84)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)
(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)(141,176)
(142,177)(143,178)(144,179)(145,180)(146,181)(147,182)(148,204)(149,205)
(150,206)(151,207)(152,208)(153,209)(154,210)(155,197)(156,198)(157,199)
(158,200)(159,201)(160,202)(161,203)(162,190)(163,191)(164,192)(165,193)
(166,194)(167,195)(168,196)(169,183)(170,184)(171,185)(172,186)(173,187)
(174,188)(175,189)(211,316)(212,317)(213,318)(214,319)(215,320)(216,321)
(217,322)(218,344)(219,345)(220,346)(221,347)(222,348)(223,349)(224,350)
(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)(232,330)
(233,331)(234,332)(235,333)(236,334)(237,335)(238,336)(239,323)(240,324)
(241,325)(242,326)(243,327)(244,328)(245,329)(246,386)(247,387)(248,388)
(249,389)(250,390)(251,391)(252,392)(253,414)(254,415)(255,416)(256,417)
(257,418)(258,419)(259,420)(260,407)(261,408)(262,409)(263,410)(264,411)
(265,412)(266,413)(267,400)(268,401)(269,402)(270,403)(271,404)(272,405)
(273,406)(274,393)(275,394)(276,395)(277,396)(278,397)(279,398)(280,399)
(281,351)(282,352)(283,353)(284,354)(285,355)(286,356)(287,357)(288,379)
(289,380)(290,381)(291,382)(292,383)(293,384)(294,385)(295,372)(296,373)
(297,374)(298,375)(299,376)(300,377)(301,378)(302,365)(303,366)(304,367)
(305,368)(306,369)(307,370)(308,371)(309,358)(310,359)(311,360)(312,361)
(313,362)(314,363)(315,364);;
s1 := ( 1,253)( 2,259)( 3,258)( 4,257)( 5,256)( 6,255)( 7,254)( 8,246)
( 9,252)( 10,251)( 11,250)( 12,249)( 13,248)( 14,247)( 15,274)( 16,280)
( 17,279)( 18,278)( 19,277)( 20,276)( 21,275)( 22,267)( 23,273)( 24,272)
( 25,271)( 26,270)( 27,269)( 28,268)( 29,260)( 30,266)( 31,265)( 32,264)
( 33,263)( 34,262)( 35,261)( 36,218)( 37,224)( 38,223)( 39,222)( 40,221)
( 41,220)( 42,219)( 43,211)( 44,217)( 45,216)( 46,215)( 47,214)( 48,213)
( 49,212)( 50,239)( 51,245)( 52,244)( 53,243)( 54,242)( 55,241)( 56,240)
( 57,232)( 58,238)( 59,237)( 60,236)( 61,235)( 62,234)( 63,233)( 64,225)
( 65,231)( 66,230)( 67,229)( 68,228)( 69,227)( 70,226)( 71,288)( 72,294)
( 73,293)( 74,292)( 75,291)( 76,290)( 77,289)( 78,281)( 79,287)( 80,286)
( 81,285)( 82,284)( 83,283)( 84,282)( 85,309)( 86,315)( 87,314)( 88,313)
( 89,312)( 90,311)( 91,310)( 92,302)( 93,308)( 94,307)( 95,306)( 96,305)
( 97,304)( 98,303)( 99,295)(100,301)(101,300)(102,299)(103,298)(104,297)
(105,296)(106,358)(107,364)(108,363)(109,362)(110,361)(111,360)(112,359)
(113,351)(114,357)(115,356)(116,355)(117,354)(118,353)(119,352)(120,379)
(121,385)(122,384)(123,383)(124,382)(125,381)(126,380)(127,372)(128,378)
(129,377)(130,376)(131,375)(132,374)(133,373)(134,365)(135,371)(136,370)
(137,369)(138,368)(139,367)(140,366)(141,323)(142,329)(143,328)(144,327)
(145,326)(146,325)(147,324)(148,316)(149,322)(150,321)(151,320)(152,319)
(153,318)(154,317)(155,344)(156,350)(157,349)(158,348)(159,347)(160,346)
(161,345)(162,337)(163,343)(164,342)(165,341)(166,340)(167,339)(168,338)
(169,330)(170,336)(171,335)(172,334)(173,333)(174,332)(175,331)(176,393)
(177,399)(178,398)(179,397)(180,396)(181,395)(182,394)(183,386)(184,392)
(185,391)(186,390)(187,389)(188,388)(189,387)(190,414)(191,420)(192,419)
(193,418)(194,417)(195,416)(196,415)(197,407)(198,413)(199,412)(200,411)
(201,410)(202,409)(203,408)(204,400)(205,406)(206,405)(207,404)(208,403)
(209,402)(210,401);;
s2 := ( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)
( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)
( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)
( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)
( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)
( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)(109,111)
(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)(129,133)
(130,132)(134,135)(136,140)(137,139)(141,142)(143,147)(144,146)(148,149)
(150,154)(151,153)(155,156)(157,161)(158,160)(162,163)(164,168)(165,167)
(169,170)(171,175)(172,174)(176,177)(178,182)(179,181)(183,184)(185,189)
(186,188)(190,191)(192,196)(193,195)(197,198)(199,203)(200,202)(204,205)
(206,210)(207,209)(211,212)(213,217)(214,216)(218,219)(220,224)(221,223)
(225,226)(227,231)(228,230)(232,233)(234,238)(235,237)(239,240)(241,245)
(242,244)(246,247)(248,252)(249,251)(253,254)(255,259)(256,258)(260,261)
(262,266)(263,265)(267,268)(269,273)(270,272)(274,275)(276,280)(277,279)
(281,282)(283,287)(284,286)(288,289)(290,294)(291,293)(295,296)(297,301)
(298,300)(302,303)(304,308)(305,307)(309,310)(311,315)(312,314)(316,317)
(318,322)(319,321)(323,324)(325,329)(326,328)(330,331)(332,336)(333,335)
(337,338)(339,343)(340,342)(344,345)(346,350)(347,349)(351,352)(353,357)
(354,356)(358,359)(360,364)(361,363)(365,366)(367,371)(368,370)(372,373)
(374,378)(375,377)(379,380)(381,385)(382,384)(386,387)(388,392)(389,391)
(393,394)(395,399)(396,398)(400,401)(402,406)(403,405)(407,408)(409,413)
(410,412)(414,415)(416,420)(417,419);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(420)!( 8, 29)( 9, 30)( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)
( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 36, 71)
( 37, 72)( 38, 73)( 39, 74)( 40, 75)( 41, 76)( 42, 77)( 43, 99)( 44,100)
( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)( 50, 92)( 51, 93)( 52, 94)
( 53, 95)( 54, 96)( 55, 97)( 56, 98)( 57, 85)( 58, 86)( 59, 87)( 60, 88)
( 61, 89)( 62, 90)( 63, 91)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)
( 69, 83)( 70, 84)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)
(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)
(141,176)(142,177)(143,178)(144,179)(145,180)(146,181)(147,182)(148,204)
(149,205)(150,206)(151,207)(152,208)(153,209)(154,210)(155,197)(156,198)
(157,199)(158,200)(159,201)(160,202)(161,203)(162,190)(163,191)(164,192)
(165,193)(166,194)(167,195)(168,196)(169,183)(170,184)(171,185)(172,186)
(173,187)(174,188)(175,189)(211,316)(212,317)(213,318)(214,319)(215,320)
(216,321)(217,322)(218,344)(219,345)(220,346)(221,347)(222,348)(223,349)
(224,350)(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)
(232,330)(233,331)(234,332)(235,333)(236,334)(237,335)(238,336)(239,323)
(240,324)(241,325)(242,326)(243,327)(244,328)(245,329)(246,386)(247,387)
(248,388)(249,389)(250,390)(251,391)(252,392)(253,414)(254,415)(255,416)
(256,417)(257,418)(258,419)(259,420)(260,407)(261,408)(262,409)(263,410)
(264,411)(265,412)(266,413)(267,400)(268,401)(269,402)(270,403)(271,404)
(272,405)(273,406)(274,393)(275,394)(276,395)(277,396)(278,397)(279,398)
(280,399)(281,351)(282,352)(283,353)(284,354)(285,355)(286,356)(287,357)
(288,379)(289,380)(290,381)(291,382)(292,383)(293,384)(294,385)(295,372)
(296,373)(297,374)(298,375)(299,376)(300,377)(301,378)(302,365)(303,366)
(304,367)(305,368)(306,369)(307,370)(308,371)(309,358)(310,359)(311,360)
(312,361)(313,362)(314,363)(315,364);
s1 := Sym(420)!( 1,253)( 2,259)( 3,258)( 4,257)( 5,256)( 6,255)( 7,254)
( 8,246)( 9,252)( 10,251)( 11,250)( 12,249)( 13,248)( 14,247)( 15,274)
( 16,280)( 17,279)( 18,278)( 19,277)( 20,276)( 21,275)( 22,267)( 23,273)
( 24,272)( 25,271)( 26,270)( 27,269)( 28,268)( 29,260)( 30,266)( 31,265)
( 32,264)( 33,263)( 34,262)( 35,261)( 36,218)( 37,224)( 38,223)( 39,222)
( 40,221)( 41,220)( 42,219)( 43,211)( 44,217)( 45,216)( 46,215)( 47,214)
( 48,213)( 49,212)( 50,239)( 51,245)( 52,244)( 53,243)( 54,242)( 55,241)
( 56,240)( 57,232)( 58,238)( 59,237)( 60,236)( 61,235)( 62,234)( 63,233)
( 64,225)( 65,231)( 66,230)( 67,229)( 68,228)( 69,227)( 70,226)( 71,288)
( 72,294)( 73,293)( 74,292)( 75,291)( 76,290)( 77,289)( 78,281)( 79,287)
( 80,286)( 81,285)( 82,284)( 83,283)( 84,282)( 85,309)( 86,315)( 87,314)
( 88,313)( 89,312)( 90,311)( 91,310)( 92,302)( 93,308)( 94,307)( 95,306)
( 96,305)( 97,304)( 98,303)( 99,295)(100,301)(101,300)(102,299)(103,298)
(104,297)(105,296)(106,358)(107,364)(108,363)(109,362)(110,361)(111,360)
(112,359)(113,351)(114,357)(115,356)(116,355)(117,354)(118,353)(119,352)
(120,379)(121,385)(122,384)(123,383)(124,382)(125,381)(126,380)(127,372)
(128,378)(129,377)(130,376)(131,375)(132,374)(133,373)(134,365)(135,371)
(136,370)(137,369)(138,368)(139,367)(140,366)(141,323)(142,329)(143,328)
(144,327)(145,326)(146,325)(147,324)(148,316)(149,322)(150,321)(151,320)
(152,319)(153,318)(154,317)(155,344)(156,350)(157,349)(158,348)(159,347)
(160,346)(161,345)(162,337)(163,343)(164,342)(165,341)(166,340)(167,339)
(168,338)(169,330)(170,336)(171,335)(172,334)(173,333)(174,332)(175,331)
(176,393)(177,399)(178,398)(179,397)(180,396)(181,395)(182,394)(183,386)
(184,392)(185,391)(186,390)(187,389)(188,388)(189,387)(190,414)(191,420)
(192,419)(193,418)(194,417)(195,416)(196,415)(197,407)(198,413)(199,412)
(200,411)(201,410)(202,409)(203,408)(204,400)(205,406)(206,405)(207,404)
(208,403)(209,402)(210,401);
s2 := Sym(420)!( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 16)
( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)
( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)
( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)
( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)
( 92, 93)( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)
(109,111)(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)
(129,133)(130,132)(134,135)(136,140)(137,139)(141,142)(143,147)(144,146)
(148,149)(150,154)(151,153)(155,156)(157,161)(158,160)(162,163)(164,168)
(165,167)(169,170)(171,175)(172,174)(176,177)(178,182)(179,181)(183,184)
(185,189)(186,188)(190,191)(192,196)(193,195)(197,198)(199,203)(200,202)
(204,205)(206,210)(207,209)(211,212)(213,217)(214,216)(218,219)(220,224)
(221,223)(225,226)(227,231)(228,230)(232,233)(234,238)(235,237)(239,240)
(241,245)(242,244)(246,247)(248,252)(249,251)(253,254)(255,259)(256,258)
(260,261)(262,266)(263,265)(267,268)(269,273)(270,272)(274,275)(276,280)
(277,279)(281,282)(283,287)(284,286)(288,289)(290,294)(291,293)(295,296)
(297,301)(298,300)(302,303)(304,308)(305,307)(309,310)(311,315)(312,314)
(316,317)(318,322)(319,321)(323,324)(325,329)(326,328)(330,331)(332,336)
(333,335)(337,338)(339,343)(340,342)(344,345)(346,350)(347,349)(351,352)
(353,357)(354,356)(358,359)(360,364)(361,363)(365,366)(367,371)(368,370)
(372,373)(374,378)(375,377)(379,380)(381,385)(382,384)(386,387)(388,392)
(389,391)(393,394)(395,399)(396,398)(400,401)(402,406)(403,405)(407,408)
(409,413)(410,412)(414,415)(416,420)(417,419);
poly := sub<Sym(420)|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 >;
References : None.
to this polytope