Polytope of Type {2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12}*288d
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 4
Schlafli Type : {2,6,12}
Number of vertices, edges, etc : 2, 6, 36, 12
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,12,2} of size 576
   {2,6,12,4} of size 1152
   {2,6,12,6} of size 1728
Vertex Figure Of :
   {2,2,6,12} of size 576
   {3,2,6,12} of size 864
   {4,2,6,12} of size 1152
   {5,2,6,12} of size 1440
   {6,2,6,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,6,4}*96b
   6-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,12}*576a
   3-fold covers : {2,6,36}*864c, {2,18,12}*864c, {2,6,12}*864d, {6,6,12}*864h
   4-fold covers : {2,6,24}*1152a, {2,12,12}*1152d, {2,6,12}*1152b, {4,6,12}*1152b, {2,6,24}*1152c, {2,6,24}*1152e, {2,12,12}*1152j, {2,12,12}*1152l, {4,6,12}*1152g
   5-fold covers : {2,30,12}*1440d, {2,6,60}*1440d
   6-fold covers : {2,6,36}*1728, {2,18,12}*1728a, {2,6,12}*1728b, {6,6,12}*1728a, {6,6,12}*1728b, {2,6,12}*1728c
Permutation Representation (GAP) :

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

to this polytope