Polytope of Type {2,3,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,4,4}*384b
if this polytope has a name.
Group : SmallGroup(384,20051)
Rank : 5
Schlafli Type : {2,3,4,4}
Number of vertices, edges, etc : 2, 6, 12, 16, 4
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,4,4,2} of size 768
Vertex Figure Of :
   {2,2,3,4,4} of size 768
   {3,2,3,4,4} of size 1152
   {5,2,3,4,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,4,2}*192
   4-fold quotients : {2,3,2,4}*96, {2,3,4,2}*96
   8-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,8,4}*768, {2,3,4,8}*768, {2,6,4,4}*768d
   3-fold covers : {2,9,4,4}*1152b, {2,3,4,12}*1152, {6,3,4,4}*1152b, {2,3,12,4}*1152
   5-fold covers : {2,3,4,20}*1920, {2,15,4,4}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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