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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,6,2}*576a
if this polytope has a name.
Group : SmallGroup(576,8675)
Rank : 6
Schlafli Type : {2,2,6,6,2}
Number of vertices, edges, etc : 2, 2, 6, 18, 6, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,6,6,2,2} of size 1152
   {2,2,6,6,2,3} of size 1728
Vertex Figure Of :
   {2,2,2,6,6,2} of size 1152
   {3,2,2,6,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,2,6,2}*192, {2,2,6,2,2}*192
   6-fold quotients : {2,2,2,3,2}*96, {2,2,3,2,2}*96
   9-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,6,6,4}*1152a, {2,4,6,6,2}*1152a, {4,2,6,6,2}*1152a, {2,2,6,12,2}*1152b, {2,2,12,6,2}*1152b
   3-fold covers : {2,2,6,18,2}*1728a, {2,2,18,6,2}*1728a, {2,2,6,6,2}*1728b, {2,2,6,6,2}*1728d, {2,2,6,6,6}*1728b, {2,2,6,6,6}*1728e, {2,6,6,6,2}*1728b, {2,6,6,6,2}*1728d, {6,2,6,6,2}*1728a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 9,10)(13,14)(15,16)(17,18)(19,20)(21,22);;
s3 := ( 5, 9)( 6,13)( 7,17)( 8,15)(11,21)(12,19)(16,18)(20,22);;
s4 := ( 5,11)( 6, 7)( 8,12)( 9,19)(10,20)(13,15)(14,16)(17,21)(18,22);;
s5 := (23,24);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(24)!(1,2);
s1 := Sym(24)!(3,4);
s2 := Sym(24)!( 9,10)(13,14)(15,16)(17,18)(19,20)(21,22);
s3 := Sym(24)!( 5, 9)( 6,13)( 7,17)( 8,15)(11,21)(12,19)(16,18)(20,22);
s4 := Sym(24)!( 5,11)( 6, 7)( 8,12)( 9,19)(10,20)(13,15)(14,16)(17,21)(18,22);
s5 := Sym(24)!(23,24);
poly := sub<Sym(24)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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