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# Polytope of Type {2,6,4}

Atlas Canonical Name : {2,6,4}*384b
if this polytope has a name.
Group : SmallGroup(384,20051)
Rank : 4
Schlafli Type : {2,6,4}
Number of vertices, edges, etc : 2, 24, 48, 16
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,4,2} of size 768
Vertex Figure Of :
{2,2,6,4} of size 768
{3,2,6,4} of size 1152
{5,2,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,4}*192
4-fold quotients : {2,6,4}*96a, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
8-fold quotients : {2,3,4}*48, {2,6,2}*48
12-fold quotients : {2,2,4}*32
16-fold quotients : {2,3,2}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12,4}*768d, {4,6,4}*768c, {2,6,8}*768f, {2,6,8}*768g, {2,6,4}*768b, {2,12,4}*768e
3-fold covers : {2,18,4}*1152b, {2,6,12}*1152b, {6,6,4}*1152c, {6,6,4}*1152d, {2,6,12}*1152f
5-fold covers : {2,6,20}*1920a, {10,6,4}*1920b, {2,30,4}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 7)( 4, 8)( 9,13)(10,14);;
s2 := ( 5, 7)( 6, 8)( 9,10)(11,14)(12,13);;
s3 := ( 3, 9)( 4,10)( 5,12)( 6,11)( 7,13)( 8,14);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;

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

to this polytope