Polytope of Type {3,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,2}*288
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 4
Schlafli Type : {3,6,2}
Number of vertices, edges, etc : 12, 36, 24, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,2,2} of size 576
   {3,6,2,3} of size 864
   {3,6,2,4} of size 1152
   {3,6,2,5} of size 1440
   {3,6,2,6} of size 1728
Vertex Figure Of :
   {2,3,6,2} of size 576
   {4,3,6,2} of size 1152
   {3,3,6,2} of size 1440
   {6,3,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,6,2}*96
   4-fold quotients : {3,6,2}*72
   6-fold quotients : {3,3,2}*48
   12-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,12,2}*576, {3,6,4}*576a, {6,6,2}*576b
   3-fold covers : {9,6,2}*864, {3,6,2}*864, {3,6,6}*864
   4-fold covers : {3,6,2}*1152, {3,6,4}*1152a, {3,6,8}*1152, {3,12,4}*1152b, {12,6,2}*1152a, {6,12,2}*1152c, {6,6,2}*1152b, {12,6,2}*1152d, {6,6,4}*1152f, {6,12,2}*1152e, {3,12,2}*1152
   5-fold covers : {3,6,10}*1440, {15,6,2}*1440e
   6-fold covers : {9,12,2}*1728, {9,6,4}*1728a, {3,12,2}*1728, {3,6,4}*1728a, {18,6,2}*1728, {6,6,2}*1728a, {3,12,6}*1728, {3,6,12}*1728, {6,6,6}*1728f, {6,6,2}*1728c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope