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Polytope of Type {2,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6}*432a
if this polytope has a name.
Group : SmallGroup(432,545)
Rank : 4
Schlafli Type : {2,6,6}
Number of vertices, edges, etc : 2, 18, 54, 18
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,6,2} of size 864
   {2,6,6,4} of size 1728
   {2,6,6,4} of size 1728
   {2,6,6,4} of size 1728
Vertex Figure Of :
   {2,2,6,6} of size 864
   {3,2,6,6} of size 1296
   {4,2,6,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,3}*216
   3-fold quotients : {2,6,6}*144b
   6-fold quotients : {2,6,3}*72
   9-fold quotients : {2,2,6}*48
   18-fold quotients : {2,2,3}*24
   27-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,12}*864a, {4,6,6}*864c, {2,12,6}*864c
   3-fold covers : {2,6,18}*1296a, {2,6,18}*1296c, {2,6,18}*1296d, {2,6,18}*1296e, {2,6,6}*1296c, {2,18,6}*1296h, {6,6,6}*1296f, {2,6,6}*1296f
   4-fold covers : {2,6,24}*1728a, {2,12,12}*1728b, {4,6,12}*1728b, {8,6,6}*1728c, {2,24,6}*1728c, {4,12,6}*1728c, {2,6,6}*1728b, {2,12,6}*1728a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20);;
s2 := ( 6,10)( 7,11)( 8, 9)(15,19)(16,20)(17,18);;
s3 := ( 3,15)( 4,16)( 5,17)( 6,12)( 7,13)( 8,14)( 9,18)(10,19)(11,20);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(20)!(1,2);
s1 := Sym(20)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20);
s2 := Sym(20)!( 6,10)( 7,11)( 8, 9)(15,19)(16,20)(17,18);
s3 := Sym(20)!( 3,15)( 4,16)( 5,17)( 6,12)( 7,13)( 8,14)( 9,18)(10,19)(11,20);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2 >; 
 

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