Polytope of Type {3,2,2,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,6,4}*576a
if this polytope has a name.
Group : SmallGroup(576,8553)
Rank : 6
Schlafli Type : {3,2,2,6,4}
Number of vertices, edges, etc : 3, 3, 2, 6, 12, 4
Order of s₀s₁s₂s₃s₄s₅ : 12
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,2,6,4,2} of size 1152
Vertex Figure Of :
   {2,3,2,2,6,4} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,2,6,2}*288
   3-fold quotients : {3,2,2,2,4}*192
   4-fold quotients : {3,2,2,3,2}*144
   6-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,2,12,4}*1152a, {3,2,4,6,4}*1152a, {3,2,2,6,8}*1152, {6,2,2,6,4}*1152a
   3-fold covers : {3,2,2,18,4}*1728a, {9,2,2,6,4}*1728a, {3,2,2,6,12}*1728a, {3,2,6,6,4}*1728a, {3,2,6,6,4}*1728b, {3,6,2,6,4}*1728a, {3,2,2,6,12}*1728c
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 8, 9)(11,12)(14,15)(16,17);;
s4 := ( 6, 8)( 7,14)(10,11)(12,15)(13,16);;
s5 := ( 6, 7)( 8,11)( 9,12)(10,13)(14,16)(15,17);;
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*s2*s0*s2, s1*s2*s1*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, 
s0*s1*s0*s1*s0*s1, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(17)!(2,3);
s1 := Sym(17)!(1,2);
s2 := Sym(17)!(4,5);
s3 := Sym(17)!( 8, 9)(11,12)(14,15)(16,17);
s4 := Sym(17)!( 6, 8)( 7,14)(10,11)(12,15)(13,16);
s5 := Sym(17)!( 6, 7)( 8,11)( 9,12)(10,13)(14,16)(15,17);
poly := sub<Sym(17)|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*s2*s0*s2, s1*s2*s1*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, s0*s1*s0*s1*s0*s1, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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