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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,2,6}*384
if this polytope has a name.
Group : SmallGroup(384,18491)
Rank : 5
Schlafli Type : {4,4,2,6}
Number of vertices, edges, etc : 4, 8, 4, 6, 6
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,2,6,2} of size 768
   {4,4,2,6,3} of size 1152
Vertex Figure Of :
   {2,4,4,2,6} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,2,3}*192, {2,4,2,6}*192, {4,2,2,6}*192
   3-fold quotients : {4,4,2,2}*128
   4-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96, {2,2,2,6}*96
   6-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
   8-fold quotients : {2,2,2,3}*48
   12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,4,6}*768, {4,4,2,12}*768, {4,8,2,6}*768a, {8,4,2,6}*768a, {4,8,2,6}*768b, {8,4,2,6}*768b, {4,4,2,6}*768
   3-fold covers : {4,4,2,18}*1152, {4,4,6,6}*1152a, {4,4,6,6}*1152c, {4,12,2,6}*1152a, {12,4,2,6}*1152a
   5-fold covers : {4,4,2,30}*1920, {4,4,10,6}*1920, {4,20,2,6}*1920, {20,4,2,6}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope