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# Polytope of Type {16,2,6}

Atlas Canonical Name : {16,2,6}*384
if this polytope has a name.
Group : SmallGroup(384,14592)
Rank : 4
Schlafli Type : {16,2,6}
Number of vertices, edges, etc : 16, 16, 6, 6
Order of s0s1s2s3 : 48
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{16,2,6,2} of size 768
{16,2,6,3} of size 1152
Vertex Figure Of :
{2,16,2,6} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {16,2,3}*192, {8,2,6}*192
3-fold quotients : {16,2,2}*128
4-fold quotients : {8,2,3}*96, {4,2,6}*96
6-fold quotients : {8,2,2}*64
8-fold quotients : {4,2,3}*48, {2,2,6}*48
12-fold quotients : {4,2,2}*32
16-fold quotients : {2,2,3}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {16,4,6}*768a, {16,2,12}*768, {32,2,6}*768
3-fold covers : {16,2,18}*1152, {16,6,6}*1152a, {16,6,6}*1152c, {48,2,6}*1152
5-fold covers : {16,2,30}*1920, {16,10,6}*1920, {80,2,6}*1920
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s2 := (19,20)(21,22);;
s3 := (17,21)(18,19)(20,22);;
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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(22)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(22)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s2 := Sym(22)!(19,20)(21,22);
s3 := Sym(22)!(17,21)(18,19)(20,22);
poly := sub<Sym(22)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope