Polytope of Type {3,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,4}*432b
if this polytope has a name.
Group : SmallGroup(432,741)
Rank : 4
Schlafli Type : {3,6,4}
Number of vertices, edges, etc : 3, 27, 36, 12
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 6
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,4,2} of size 864
   {3,6,4,4} of size 1728
Vertex Figure Of :
   {2,3,6,4} of size 864
   {4,3,6,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   9-fold quotients : {3,2,4}*48
   18-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,6,8}*864b, {6,6,4}*864k
   3-fold covers : {9,6,4}*1296e, {3,6,4}*1296b, {3,6,12}*1296f
   4-fold covers : {3,6,16}*1728b, {12,6,4}*1728l, {6,6,8}*1728g, {6,12,4}*1728p, {3,12,4}*1728b
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17);;
s1 := ( 1, 8)( 2, 7)( 3, 9)( 4, 5)(10,14)(11,13)(12,15)(16,17);;
s2 := (4,7)(5,8)(6,9);;
s3 := ( 1,10)( 2,11)( 3,12)( 4,16)( 5,17)( 6,18)( 7,13)( 8,14)( 9,15);;
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, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(18)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17);
s1 := Sym(18)!( 1, 8)( 2, 7)( 3, 9)( 4, 5)(10,14)(11,13)(12,15)(16,17);
s2 := Sym(18)!(4,7)(5,8)(6,9);
s3 := Sym(18)!( 1,10)( 2,11)( 3,12)( 4,16)( 5,17)( 6,18)( 7,13)( 8,14)( 9,15);
poly := sub<Sym(18)|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, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;

References : None.
to this polytope