Polytope of Type {6,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,2}*432c
if this polytope has a name.
Group : SmallGroup(432,756)
Rank : 4
Schlafli Type : {6,12,2}
Number of vertices, edges, etc : 9, 54, 18, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,12,2,2} of size 864
   {6,12,2,3} of size 1296
   {6,12,2,4} of size 1728
Vertex Figure Of :
   {2,6,12,2} of size 864
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,4,2}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,12,4}*864c, {6,12,2}*864i
   3-fold covers : {6,36,2}*1296a, {6,12,2}*1296, {6,36,2}*1296b, {6,36,2}*1296c, {6,12,6}*1296g, {6,12,6}*1296h
   4-fold covers : {6,12,8}*1728c, {6,24,2}*1728h, {6,12,4}*1728q, {12,12,2}*1728l, {6,12,4}*1728r, {12,12,2}*1728o
Permutation Representation (GAP) :

s0 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18);;
s1 := ( 2, 3)( 5, 6)( 8, 9)(10,13)(11,15)(12,14)(17,18);;
s2 := ( 1,11)( 2,10)( 3,12)( 4,14)( 5,13)( 6,15)( 7,17)( 8,16)( 9,18);;
s3 := (19,20);;
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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(20)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18);
s1 := Sym(20)!( 2, 3)( 5, 6)( 8, 9)(10,13)(11,15)(12,14)(17,18);
s2 := Sym(20)!( 1,11)( 2,10)( 3,12)( 4,14)( 5,13)( 6,15)( 7,17)( 8,16)( 9,18);
s3 := Sym(20)!(19,20);
poly := sub<Sym(20)|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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 >;

to this polytope