Polytope of Type {5,10,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,10,8}*1920
if this polytope has a name.
Group : SmallGroup(1920,240561)
Rank : 4
Schlafli Type : {5,10,8}
Number of vertices, edges, etc : 12, 60, 96, 8
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
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 : {5,10,8}*960, {5,10,4}*960
   4-fold quotients : {5,10,4}*480, {5,10,2}*480
   8-fold quotients : {5,5,2}*240, {5,10,2}*240a, {5,10,2}*240b
   16-fold quotients : {5,5,2}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(18,21)(19,20);;
s1 := ( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,20)(19,21);;
s2 := ( 1,11)( 2, 9)( 3,15)( 4,13)( 5, 7)( 6,16)( 8,14)(10,12)(18,19)(20,21);;
s3 := ( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(21)!( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(18,21)
(19,20);
s1 := Sym(21)!( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,20)
(19,21);
s2 := Sym(21)!( 1,11)( 2, 9)( 3,15)( 4,13)( 5, 7)( 6,16)( 8,14)(10,12)(18,19)
(20,21);
s3 := Sym(21)!( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
poly := sub<Sym(21)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

References : None.
to this polytope