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

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

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

Permutation Representation (Magma) :

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

to this polytope