Polytope of Type {2,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,6}*960a
if this polytope has a name.
Group : SmallGroup(960,10869)
Rank : 4
Schlafli Type : {2,10,6}
Number of vertices, edges, etc : 2, 40, 120, 24
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,10,6,2} of size 1920
Vertex Figure Of :
   {2,2,10,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,5,6}*480a
   4-fold quotients : {2,5,6}*240a
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,10,6}*1920a
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5,19)( 6,15)( 9,18)(10,17)(11,28)(12,16)(13,41)(14,30)(20,35)(21,36)
(22,32)(23,39)(24,40)(25,31)(26,42)(27,29)(33,38)(34,37);;
s2 := ( 3,11)( 4,12)( 5, 7)( 6, 8)( 9,22)(10,25)(13,28)(14,16)(15,27)(17,23)
(18,24)(19,26)(20,40)(21,31)(29,41)(30,42)(32,38)(37,39);;
s3 := ( 4, 7)( 5,15)( 6,19)( 9,10)(11,16)(12,28)(13,40)(14,39)(17,18)(20,38)
(22,29)(23,30)(24,41)(25,42)(26,31)(27,32)(33,35);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(42)!(1,2);
s1 := Sym(42)!( 5,19)( 6,15)( 9,18)(10,17)(11,28)(12,16)(13,41)(14,30)(20,35)
(21,36)(22,32)(23,39)(24,40)(25,31)(26,42)(27,29)(33,38)(34,37);
s2 := Sym(42)!( 3,11)( 4,12)( 5, 7)( 6, 8)( 9,22)(10,25)(13,28)(14,16)(15,27)
(17,23)(18,24)(19,26)(20,40)(21,31)(29,41)(30,42)(32,38)(37,39);
s3 := Sym(42)!( 4, 7)( 5,15)( 6,19)( 9,10)(11,16)(12,28)(13,40)(14,39)(17,18)
(20,38)(22,29)(23,30)(24,41)(25,42)(26,31)(27,32)(33,35);
poly := sub<Sym(42)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2 >;

to this polytope