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Polytope of Type {3,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,10,6}*1440
if this polytope has a name.
Group : SmallGroup(1440,5853)
Rank : 4
Schlafli Type : {3,10,6}
Number of vertices, edges, etc : 12, 60, 120, 6
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {3,10,6}*720
   3-fold quotients : {3,10,2}*480
   6-fold quotients : {3,5,2}*240, {3,10,2}*240a, {3,10,2}*240b
   12-fold quotients : {3,5,2}*120
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,15)(13,16);;
s1 := ( 1, 3)( 2, 4)( 7,10)( 8, 9)(11,14)(12,15)(13,16);;
s2 := ( 3, 7)( 4, 8)( 5, 9)( 6,10)(12,16)(13,15);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope