Polytope of Type {2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,8}*384a
if this polytope has a name.
Group : SmallGroup(384,17949)
Rank : 4
Schlafli Type : {2,6,8}
Number of vertices, edges, etc : 2, 12, 48, 16
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,8,2} of size 768
Vertex Figure Of :
   {2,2,6,8} of size 768
   {3,2,6,8} of size 1152
   {5,2,6,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {2,6,4}*96b
   8-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,8}*768c, {2,12,8}*768d, {2,6,8}*768d
   3-fold covers : {2,18,8}*1152a, {2,6,24}*1152a, {6,6,8}*1152a
   5-fold covers : {2,6,40}*1920a, {2,30,8}*1920a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope