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