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

Atlas Canonical Name : {2,3,2,6,4}*576a
if this polytope has a name.
Group : SmallGroup(576,8553)
Rank : 6
Schlafli Type : {2,3,2,6,4}
Number of vertices, edges, etc : 2, 3, 3, 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 :
{2,3,2,6,4,2} of size 1152
Vertex Figure Of :
{2,2,3,2,6,4} of size 1152
{3,2,3,2,6,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3,2,6,2}*288
3-fold quotients : {2,3,2,2,4}*192
4-fold quotients : {2,3,2,3,2}*144
6-fold quotients : {2,3,2,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,3,2,12,4}*1152a, {2,3,2,6,8}*1152, {2,6,2,6,4}*1152a
3-fold covers : {2,3,2,18,4}*1728a, {2,9,2,6,4}*1728a, {2,3,6,6,4}*1728a, {2,3,2,6,12}*1728a, {6,3,2,6,4}*1728a, {2,3,2,6,12}*1728c, {2,3,6,6,4}*1728d
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4);;
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*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,
s1*s2*s1*s2*s1*s2, 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)!(1,2);
s1 := Sym(17)!(4,5);
s2 := Sym(17)!(3,4);
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*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, s1*s2*s1*s2*s1*s2, 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 >;

to this polytope