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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,7,2,6}*336
if this polytope has a name.
Group : SmallGroup(336,219)
Rank : 5
Schlafli Type : {2,7,2,6}
Number of vertices, edges, etc : 2, 7, 7, 6, 6
Order of s₀s₁s₂s₃s₄ : 42
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,7,2,6,2} of size 672
   {2,7,2,6,3} of size 1008
   {2,7,2,6,4} of size 1344
   {2,7,2,6,3} of size 1344
   {2,7,2,6,4} of size 1344
   {2,7,2,6,4} of size 1344
Vertex Figure Of :
   {2,2,7,2,6} of size 672
   {3,2,7,2,6} of size 1008
   {4,2,7,2,6} of size 1344
   {5,2,7,2,6} of size 1680
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,7,2,3}*168
   3-fold quotients : {2,7,2,2}*112
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,7,2,12}*672, {2,14,2,6}*672
   3-fold covers : {2,7,2,18}*1008, {2,21,2,6}*1008
   4-fold covers : {2,7,2,24}*1344, {2,14,2,12}*1344, {2,28,2,6}*1344, {2,14,4,6}*1344, {4,14,2,6}*1344
   5-fold covers : {2,7,2,30}*1680, {2,35,2,6}*1680
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope