Polytope of Type {10,5,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,5,2,3}*720a
if this polytope has a name.
Group : SmallGroup(720,771)
Rank : 5
Schlafli Type : {10,5,2,3}
Number of vertices, edges, etc : 12, 30, 6, 3, 3
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,5,2,3,2} of size 1440
Vertex Figure Of :
   {2,10,5,2,3} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,5,2,3}*360
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,5,2,3}*1440, {10,5,2,6}*1440a, {10,10,2,3}*1440b, {10,10,2,3}*1440c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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