Polytope of Type {4,6,3}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope