Polytope of Type {4,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,2}*576
if this polytope has a name.
Group : SmallGroup(576,8418)
Rank : 4
Schlafli Type : {4,12,2}
Number of vertices, edges, etc : 12, 72, 36, 2
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,12,2,2} of size 1152
   {4,12,2,3} of size 1728
Vertex Figure Of :
   {2,4,12,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6,2}*288
   4-fold quotients : {4,6,2}*144
   9-fold quotients : {4,4,2}*64
   18-fold quotients : {2,4,2}*32, {4,2,2}*32
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,4}*1152b, {4,24,2}*1152a, {8,12,2}*1152a, {4,24,2}*1152b, {8,12,2}*1152b, {4,12,2}*1152
   3-fold covers : {4,12,2}*1728b, {12,12,2}*1728d, {12,12,2}*1728e, {4,12,2}*1728c, {12,12,2}*1728i, {4,12,6}*1728n, {12,12,2}*1728k
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope