Polytope of Type {2,10,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,6,2}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240973)
Rank : 5
Schlafli Type : {2,10,6,2}
Number of vertices, edges, etc : 2, 40, 120, 24, 2
Order of s₀s₁s₂s₃s₄ : 8
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {2,5,6,2}*960a
   4-fold quotients : {2,5,6,2}*480a
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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);;
s4 := (43,44);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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(44)!(1,2);
s1 := Sym(44)!( 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(44)!( 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(44)!( 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);
s4 := Sym(44)!(43,44);
poly := sub<Sym(44)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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