Polytope of Type {4,6,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,2,7}*672a
if this polytope has a name.
Group : SmallGroup(672,1150)
Rank : 5
Schlafli Type : {4,6,2,7}
Number of vertices, edges, etc : 4, 12, 6, 7, 7
Order of s₀s₁s₂s₃s₄ : 84
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,6,2,7,2} of size 1344
Vertex Figure Of :
   {2,4,6,2,7} of size 1344
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,2,7}*336
   3-fold quotients : {4,2,2,7}*224
   4-fold quotients : {2,3,2,7}*168
   6-fold quotients : {2,2,2,7}*112
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,2,7}*1344a, {8,6,2,7}*1344, {4,6,2,14}*1344a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope