Polytope of Type {3,10,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,10,4,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240508)
Rank : 5
Schlafli Type : {3,10,4,4}
Number of vertices, edges, etc : 6, 30, 40, 8, 4
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-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 : {3,10,2,4}*960b, {3,10,4,2}*960
   4-fold quotients : {3,5,2,4}*480, {3,10,2,2}*480b
   8-fold quotients : {3,5,2,2}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (10,11)(12,13);;
s1 := ( 9,12)(10,11);;
s2 := ( 1, 6)( 2, 8)( 3, 7)( 4, 5)(10,12)(11,13);;
s3 := (1,8)(2,5)(3,4)(6,7);;
s4 := (1,6)(2,7)(3,8)(4,5);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(13)!(10,11)(12,13);
s1 := Sym(13)!( 9,12)(10,11);
s2 := Sym(13)!( 1, 6)( 2, 8)( 3, 7)( 4, 5)(10,12)(11,13);
s3 := Sym(13)!(1,8)(2,5)(3,4)(6,7);
s4 := Sym(13)!(1,6)(2,7)(3,8)(4,5);
poly := sub<Sym(13)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 >;

References : None.
to this polytope