Polytope of Type {3,2,14,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,14,2}*336
if this polytope has a name.
Group : SmallGroup(336,219)
Rank : 5
Schlafli Type : {3,2,14,2}
Number of vertices, edges, etc : 3, 3, 14, 14, 2
Order of s₀s₁s₂s₃s₄ : 42
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,14,2,2} of size 672
   {3,2,14,2,3} of size 1008
   {3,2,14,2,4} of size 1344
   {3,2,14,2,5} of size 1680
Vertex Figure Of :
   {2,3,2,14,2} of size 672
   {3,3,2,14,2} of size 1344
   {4,3,2,14,2} of size 1344
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,7,2}*168
   7-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,28,2}*672, {3,2,14,4}*672, {6,2,14,2}*672
   3-fold covers : {9,2,14,2}*1008, {3,2,14,6}*1008, {3,6,14,2}*1008, {3,2,42,2}*1008
   4-fold covers : {3,2,28,4}*1344, {3,2,56,2}*1344, {3,2,14,8}*1344, {12,2,14,2}*1344, {6,2,28,2}*1344, {6,2,14,4}*1344, {6,4,14,2}*1344, {3,4,14,2}*1344
   5-fold covers : {3,2,14,10}*1680, {15,2,14,2}*1680, {3,2,70,2}*1680
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope