Polytope of Type {5,2,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,6,6}*720a
if this polytope has a name.
Group : SmallGroup(720,813)
Rank : 5
Schlafli Type : {5,2,6,6}
Number of vertices, edges, etc : 5, 5, 6, 18, 6
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,6,6,2} of size 1440
Vertex Figure Of :
   {2,5,2,6,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {5,2,2,6}*240, {5,2,6,2}*240
   6-fold quotients : {5,2,2,3}*120, {5,2,3,2}*120
   9-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,6,12}*1440a, {5,2,12,6}*1440a, {10,2,6,6}*1440a
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (10,11)(14,15)(16,17)(18,19)(20,21)(22,23);;
s3 := ( 6,10)( 7,14)( 8,18)( 9,16)(12,22)(13,20)(17,19)(21,23);;
s4 := ( 6,12)( 7, 8)( 9,13)(10,20)(11,21)(14,16)(15,17)(18,22)(19,23);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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