Polytope of Type {12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*216b
if this polytope has a name.
Group : SmallGroup(216,87)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 18, 54, 9
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,6,2} of size 432
Vertex Figure Of :
   {2,12,6} of size 432
   {4,12,6} of size 864
   {6,12,6} of size 1296
   {8,12,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {4,6}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,6}*432e
   3-fold covers : {12,6}*648
   4-fold covers : {24,6}*864d, {12,12}*864d
   5-fold covers : {60,6}*1080a
   6-fold covers : {12,6}*1296k, {12,6}*1296n, {12,6}*1296o
   7-fold covers : {84,6}*1512a
   8-fold covers : {48,6}*1728e, {12,12}*1728e, {24,12}*1728h, {12,24}*1728j, {12,24}*1728l, {24,12}*1728n
   9-fold covers : {12,18}*1944a, {12,6}*1944b, {12,18}*1944c, {12,18}*1944e, {36,6}*1944
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 >;

References : None.
to this polytope