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

Atlas Canonical Name : {6,4,2,3}*288c
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 5
Schlafli Type : {6,4,2,3}
Number of vertices, edges, etc : 6, 12, 4, 3, 3
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,4,2,3,2} of size 576
{6,4,2,3,3} of size 1152
{6,4,2,3,4} of size 1152
{6,4,2,3,6} of size 1728
Vertex Figure Of :
{2,6,4,2,3} of size 576
{4,6,4,2,3} of size 1152
{4,6,4,2,3} of size 1152
{4,6,4,2,3} of size 1152
{6,6,4,2,3} of size 1728
{6,6,4,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,4,2,3}*144
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,4,2,3}*576b, {12,4,2,3}*576c, {6,4,2,3}*576, {6,4,2,6}*576c
3-fold covers : {6,4,2,9}*864c, {18,4,2,3}*864b
4-fold covers : {6,4,2,3}*1152a, {24,4,2,3}*1152c, {24,4,2,3}*1152d, {12,4,2,3}*1152b, {12,4,2,6}*1152b, {12,4,2,6}*1152c, {6,4,2,12}*1152c, {6,4,2,3}*1152b, {12,4,2,3}*1152c, {6,8,2,3}*1152b, {6,8,2,3}*1152c, {6,4,2,6}*1152
5-fold covers : {30,4,2,3}*1440b, {6,4,2,15}*1440c
6-fold covers : {12,4,2,9}*1728b, {12,4,2,9}*1728c, {36,4,2,3}*1728b, {36,4,2,3}*1728c, {6,4,2,9}*1728, {6,4,2,18}*1728c, {18,4,2,3}*1728, {18,4,2,6}*1728b, {6,4,6,3}*1728b, {6,12,2,3}*1728a, {6,12,2,3}*1728b
Permutation Representation (GAP) :
s0 := (1,4)(2,6);;
s1 := (1,2)(3,4)(5,6);;
s2 := (1,2)(4,6);;
s3 := (8,9);;
s4 := (7,8);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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,
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(9)!(1,4)(2,6);
s1 := Sym(9)!(1,2)(3,4)(5,6);
s2 := Sym(9)!(1,2)(4,6);
s3 := Sym(9)!(8,9);
s4 := Sym(9)!(7,8);
poly := sub<Sym(9)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, 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, s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope