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Polytope of Type {3,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,60}*1440
if this polytope has a name.
Group : SmallGroup(1440,4642)
Rank : 3
Schlafli Type : {3,60}
Number of vertices, edges, etc : 12, 360, 240
Order of s0s1s2 : 20
Order of s0s1s2s1 : 60
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {3,30}*720
3-fold quotients : {3,20}*480
4-fold quotients : {3,15}*360
6-fold quotients : {3,10}*240
12-fold quotients : {3,5}*120, {3,10}*120a, {3,10}*120b
24-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2,39)( 3,43)( 5,45)( 6, 7)( 8,13)( 9,22)(10,18)(11,41)(14,16)(17,33)
(19,20)(21,26)(23,42)(24,38)(25,27)(29,30)(34,35)(36,46)(40,47)(44,48)
(50,51);;
s1 := ( 1,19)( 2,37)( 4,14)( 5, 6)( 7,34)( 9,26)(10,12)(11,32)(13,28)(15,17)
(21,30)(22,29)(23,27)(24,36)(25,47)(31,43)(35,45)(38,44)(40,42)(46,48)
(49,50);;
s2 := ( 1, 4)( 2,35)( 3, 5)( 6,25)( 7,27)( 8,29)( 9,46)(10,24)(11,47)(12,37)
(13,30)(14,23)(15,31)(16,42)(17,48)(18,38)(19,21)(20,26)(22,36)(28,32)(33,44)
(34,39)(40,41)(43,45)(50,51);;
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*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(51)!( 2,39)( 3,43)( 5,45)( 6, 7)( 8,13)( 9,22)(10,18)(11,41)(14,16)
(17,33)(19,20)(21,26)(23,42)(24,38)(25,27)(29,30)(34,35)(36,46)(40,47)(44,48)
(50,51);
s1 := Sym(51)!( 1,19)( 2,37)( 4,14)( 5, 6)( 7,34)( 9,26)(10,12)(11,32)(13,28)
(15,17)(21,30)(22,29)(23,27)(24,36)(25,47)(31,43)(35,45)(38,44)(40,42)(46,48)
(49,50);
s2 := Sym(51)!( 1, 4)( 2,35)( 3, 5)( 6,25)( 7,27)( 8,29)( 9,46)(10,24)(11,47)
(12,37)(13,30)(14,23)(15,31)(16,42)(17,48)(18,38)(19,21)(20,26)(22,36)(28,32)
(33,44)(34,39)(40,41)(43,45)(50,51);
poly := sub<Sym(51)|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*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;

References : None.
to this polytope