Polytope of Type {2,12,6}

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

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

Permutation Representation (Magma) :

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

to this polytope