Polytope of Type {6,6,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,3,2}*432a
if this polytope has a name.
Group : SmallGroup(432,545)
Rank : 5
Schlafli Type : {6,6,3,2}
Number of vertices, edges, etc : 6, 18, 9, 3, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,6,3,2,2} of size 864
   {6,6,3,2,3} of size 1296
   {6,6,3,2,4} of size 1728
Vertex Figure Of :
   {2,6,6,3,2} of size 864
   {4,6,6,3,2} of size 1728
   {4,6,6,3,2} of size 1728
   {4,6,6,3,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,6,3,2}*216
   3-fold quotients : {6,2,3,2}*144
   6-fold quotients : {3,2,3,2}*72
   9-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,6,3,2}*864a, {6,6,6,2}*864a
   3-fold covers : {6,6,9,2}*1296a, {18,6,3,2}*1296a, {6,6,3,2}*1296a, {6,6,3,2}*1296b, {6,6,3,6}*1296a, {6,6,3,2}*1296e
   4-fold covers : {24,6,3,2}*1728a, {6,6,12,2}*1728a, {12,6,6,2}*1728a, {6,6,6,4}*1728a, {6,12,6,2}*1728a, {6,6,3,4}*1728a, {6,12,3,2}*1728a
Permutation Representation (GAP) : 
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18);;
s1 := ( 1,10)( 2,12)( 3,11)( 4,14)( 5,13)( 6,15)( 7,18)( 8,17)( 9,16);;
s2 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)(10,13)(11,15)(12,14)(17,18);;
s3 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17);;
s4 := (19,20);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(20)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18);
s1 := Sym(20)!( 1,10)( 2,12)( 3,11)( 4,14)( 5,13)( 6,15)( 7,18)( 8,17)( 9,16);
s2 := Sym(20)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)(10,13)(11,15)(12,14)(17,18);
s3 := Sym(20)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17);
s4 := Sym(20)!(19,20);
poly := sub<Sym(20)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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