Polytope of Type {8,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240844)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 80, 480, 120
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 12
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 : {8,6}*960a, {4,12}*960a
   4-fold quotients : {8,6}*480a, {8,6}*480b, {4,6}*480
   8-fold quotients : {4,6}*240a, {4,6}*240b, {4,6}*240c
   16-fold quotients : {4,6}*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 := ( 1,37)( 2,36)( 3,39)( 4,33)( 5,32)( 6,29)( 7,25)( 8,40)( 9,19)(10,16)
(12,23)(14,21)(15,38)(17,35)(18,26)(22,24)(31,34)(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, 
s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 ];;
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)!( 1,37)( 2,36)( 3,39)( 4,33)( 5,32)( 6,29)( 7,25)( 8,40)( 9,19)
(10,16)(12,23)(14,21)(15,38)(17,35)(18,26)(22,24)(31,34)(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, 
s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 >;

References : None.
to this polytope