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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,4,2}*384c
if this polytope has a name.
Group : SmallGroup(384,20051)
Rank : 5
Schlafli Type : {4,6,4,2}
Number of vertices, edges, etc : 4, 12, 12, 4, 2
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,6,4,2,2} of size 768
   {4,6,4,2,3} of size 1152
   {4,6,4,2,5} of size 1920
Vertex Figure Of :
   {2,4,6,4,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6,2,2}*192c
   4-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,4,2}*768d, {4,12,4,2}*768e, {4,6,4,4}*768b, {4,6,8,2}*768b, {4,6,4,2}*768b
   3-fold covers : {4,18,4,2}*1152c, {4,6,12,2}*1152d, {4,6,4,6}*1152b, {4,6,12,2}*1152e
   5-fold covers : {4,6,20,2}*1920b, {4,6,4,10}*1920b, {4,30,4,2}*1920c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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