Polytope of Type {10,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,16}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240469)
Rank : 3
Schlafli Type : {10,16}
Number of vertices, edges, etc : 60, 480, 96
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {10,8}*960a
   4-fold quotients : {10,4}*480a
   8-fold quotients : {10,4}*240a
   16-fold quotients : {5,4}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := ( 1, 2)( 3, 4)( 6,14)( 7,15)( 8,17)( 9,16)(10,20)(11,21)(12,18)(13,19)
(22,30)(23,31)(24,33)(25,32)(26,36)(27,37)(28,34)(29,35);;
s2 := ( 2, 3)( 6,22)( 7,23)( 8,25)( 9,24)(10,28)(11,29)(12,26)(13,27)(14,34)
(15,35)(16,37)(17,36)(18,30)(19,31)(20,33)(21,32);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(37)!(2,3)(4,5);
s1 := Sym(37)!( 1, 2)( 3, 4)( 6,14)( 7,15)( 8,17)( 9,16)(10,20)(11,21)(12,18)
(13,19)(22,30)(23,31)(24,33)(25,32)(26,36)(27,37)(28,34)(29,35);
s2 := Sym(37)!( 2, 3)( 6,22)( 7,23)( 8,25)( 9,24)(10,28)(11,29)(12,26)(13,27)
(14,34)(15,35)(16,37)(17,36)(18,30)(19,31)(20,33)(21,32);
poly := sub<Sym(37)|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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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*s1*s2*s1*s2 >;

References : None.
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