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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,2,6,2}*576
if this polytope has a name.
Group : SmallGroup(576,8675)
Rank : 6
Schlafli Type : {2,6,2,6,2}
Number of vertices, edges, etc : 2, 6, 6, 6, 6, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,2,6,2,2} of size 1152
   {2,6,2,6,2,3} of size 1728
Vertex Figure Of :
   {2,2,6,2,6,2} of size 1152
   {3,2,6,2,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,2,6,2}*288, {2,6,2,3,2}*288
   3-fold quotients : {2,2,2,6,2}*192, {2,6,2,2,2}*192
   4-fold quotients : {2,3,2,3,2}*144
   6-fold quotients : {2,2,2,3,2}*96, {2,3,2,2,2}*96
   9-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,2,6,4}*1152a, {2,6,4,6,2}*1152, {4,6,2,6,2}*1152a, {2,6,2,12,2}*1152, {2,12,2,6,2}*1152
   3-fold covers : {2,6,2,18,2}*1728, {2,18,2,6,2}*1728, {2,6,6,6,2}*1728a, {2,6,2,6,6}*1728a, {2,6,2,6,6}*1728c, {2,6,6,6,2}*1728b, {2,6,6,6,2}*1728c, {2,6,6,6,2}*1728g, {6,6,2,6,2}*1728a, {6,6,2,6,2}*1728b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (5,6)(7,8);;
s2 := (3,7)(4,5)(6,8);;
s3 := (11,12)(13,14);;
s4 := ( 9,13)(10,11)(12,14);;
s5 := (15,16);;
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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(16)!(1,2);
s1 := Sym(16)!(5,6)(7,8);
s2 := Sym(16)!(3,7)(4,5)(6,8);
s3 := Sym(16)!(11,12)(13,14);
s4 := Sym(16)!( 9,13)(10,11)(12,14);
s5 := Sym(16)!(15,16);
poly := sub<Sym(16)|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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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