Polytope of Type {10,2,4,3,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,4,3,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240408)
Rank : 6
Schlafli Type : {10,2,4,3,4}
Number of vertices, edges, etc : 10, 10, 4, 6, 6, 4
Order of s₀s₁s₂s₃s₄s₅ : 30
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {5,2,4,3,4}*960
   5-fold quotients : {2,2,4,3,4}*384
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (11,12)(13,16)(14,15)(17,24)(18,25)(19,20)(21,23)(22,26);;
s3 := (12,14)(13,17)(16,21)(19,24)(20,23)(22,25);;
s4 := (13,18)(14,15)(16,25)(19,26)(20,22)(21,23);;
s5 := (11,18)(12,25)(13,17)(14,22)(15,26)(16,24)(19,21)(20,23);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5, 
s4*s2*s3*s4*s2*s3*s4*s2*s3, s3*s5*s4*s3*s5*s4*s3*s5*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(26)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(26)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(26)!(11,12)(13,16)(14,15)(17,24)(18,25)(19,20)(21,23)(22,26);
s3 := Sym(26)!(12,14)(13,17)(16,21)(19,24)(20,23)(22,25);
s4 := Sym(26)!(13,18)(14,15)(16,25)(19,26)(20,22)(21,23);
s5 := Sym(26)!(11,18)(12,25)(13,17)(14,22)(15,26)(16,24)(19,21)(20,23);
poly := sub<Sym(26)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s5*s4*s5*s4*s5*s4*s5, s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s3*s5*s4*s3*s5*s4*s3*s5*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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