Polytope of Type {10,6,2}

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

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

Permutation Representation (Magma) :

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

to this polytope