Polytope of Type {2,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4}*576
if this polytope has a name.
Group : SmallGroup(576,8418)
Rank : 4
Schlafli Type : {2,4,4}
Number of vertices, edges, etc : 2, 36, 72, 36
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,4,2} of size 1152
Vertex Figure Of :
   {2,2,4,4} of size 1152
   {3,2,4,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,4}*288
   4-fold quotients : {2,4,4}*144
   9-fold quotients : {2,4,4}*64
   18-fold quotients : {2,2,4}*32, {2,4,2}*32
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,4}*1152a, {2,4,8}*1152a, {2,8,4}*1152a, {2,4,8}*1152b, {2,8,4}*1152b, {2,4,4}*1152
   3-fold covers : {2,4,12}*1728a, {2,12,4}*1728a, {2,4,12}*1728d, {2,12,4}*1728c, {6,4,4}*1728b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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