Polytope of Type {8,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240844)
Rank : 3
Schlafli Type : {8,20}
Number of vertices, edges, etc : 48, 480, 120
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 6
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 : {8,10}*960c, {4,20}*960c
   4-fold quotients : {8,5}*480, {4,10}*480c
   8-fold quotients : {4,5}*240, {4,10}*240a, {4,10}*240b
   16-fold quotients : {4,5}*120
   120-fold quotients : {2,4}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,38)( 2,33)( 3,21)( 4,36)( 5,19)( 6,34)( 7,17)( 8,22)( 9,32)(10,16)
(11,30)(12,26)(13,20)(14,39)(15,37)(18,23)(24,40)(25,35)(29,31);;
s1 := ( 1, 7)( 2,36)( 4,26)( 5,17)( 6,38)( 8,16)( 9,30)(10,29)(11,20)(13,21)
(14,34)(15,33)(18,40)(19,24)(22,27)(23,35)(25,39)(28,31)(42,44);;
s2 := ( 1,15)( 2, 4)( 3,14)( 5, 9)( 6,31)( 7,35)( 8,24)(11,30)(12,18)(13,20)
(17,25)(19,32)(21,39)(22,40)(23,26)(29,34)(33,36)(37,38)(41,44)(42,43);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2, 
s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
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