Polytope of Type {3,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,20}*1440a
if this polytope has a name.
Group : SmallGroup(1440,4642)
Rank : 3
Schlafli Type : {3,20}
Number of vertices, edges, etc : 36, 360, 240
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 20
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 : {3,10}*720b
   3-fold quotients : {3,20}*480
   4-fold quotients : {3,10}*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
   120-fold quotients : {3,2}*12
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)( 2,34)( 3,45)( 5,43)( 6,27)( 7,25)( 8,30)( 9,36)(10,38)(11,40)
(12,37)(13,29)(14,42)(15,31)(16,23)(17,44)(18,24)(19,26)(20,21)(22,46)(28,32)
(33,48)(35,39)(41,47);;
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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*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)( 2,34)( 3,45)( 5,43)( 6,27)( 7,25)( 8,30)( 9,36)(10,38)
(11,40)(12,37)(13,29)(14,42)(15,31)(16,23)(17,44)(18,24)(19,26)(20,21)(22,46)
(28,32)(33,48)(35,39)(41,47);
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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope