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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,6}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240973)
Rank : 5
Schlafli Type : {2,2,10,6}
Number of vertices, edges, etc : 2, 2, 40, 120, 24
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 : {2,2,5,6}*960a
   4-fold quotients : {2,2,5,6}*480a
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7,21)( 8,17)(11,20)(12,19)(13,30)(14,18)(15,43)(16,32)(22,37)(23,38)
(24,34)(25,41)(26,42)(27,33)(28,44)(29,31)(35,40)(36,39);;
s3 := ( 5,13)( 6,14)( 7, 9)( 8,10)(11,24)(12,27)(15,30)(16,18)(17,29)(19,25)
(20,26)(21,28)(22,42)(23,33)(31,43)(32,44)(34,40)(39,41);;
s4 := ( 6, 9)( 7,17)( 8,21)(11,12)(13,18)(14,30)(15,42)(16,41)(19,20)(22,40)
(24,31)(25,32)(26,43)(27,44)(28,33)(29,34)(35,37);;
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, s1*s2*s1*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*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(44)!(1,2);
s1 := Sym(44)!(3,4);
s2 := Sym(44)!( 7,21)( 8,17)(11,20)(12,19)(13,30)(14,18)(15,43)(16,32)(22,37)
(23,38)(24,34)(25,41)(26,42)(27,33)(28,44)(29,31)(35,40)(36,39);
s3 := Sym(44)!( 5,13)( 6,14)( 7, 9)( 8,10)(11,24)(12,27)(15,30)(16,18)(17,29)
(19,25)(20,26)(21,28)(22,42)(23,33)(31,43)(32,44)(34,40)(39,41);
s4 := Sym(44)!( 6, 9)( 7,17)( 8,21)(11,12)(13,18)(14,30)(15,42)(16,41)(19,20)
(22,40)(24,31)(25,32)(26,43)(27,44)(28,33)(29,34)(35,37);
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, 
s1*s2*s1*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*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3*s2*s3 >;

to this polytope