Polytope of Type {5,2,4,3,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,3,4}*960
if this polytope has a name.
Group : SmallGroup(960,11373)
Rank : 6
Schlafli Type : {5,2,4,3,4}
Number of vertices, edges, etc : 5, 5, 4, 6, 6, 4
Order of s₀s₁s₂s₃s₄s₅ : 15
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,4,3,4,2} of size 1920
Vertex Figure Of :
   {2,5,2,4,3,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,4,3,4}*1920a, {5,2,4,3,4}*1920b, {5,2,4,6,4}*1920d, {5,2,4,6,4}*1920e, {5,2,4,6,4}*1920f, {5,2,4,6,4}*1920g, {10,2,4,3,4}*1920
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8,11)( 9,10)(12,19)(13,20)(14,15)(16,18)(17,21);;
s3 := ( 7, 9)( 8,12)(11,16)(14,19)(15,18)(17,20);;
s4 := ( 8,13)( 9,10)(11,20)(14,21)(15,17)(16,18);;
s5 := ( 6,13)( 7,20)( 8,12)( 9,17)(10,21)(11,19)(14,16)(15,18);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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