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# Polytope of Type {4,2,12}

Atlas Canonical Name : {4,2,12}*192
if this polytope has a name.
Group : SmallGroup(192,1108)
Rank : 4
Schlafli Type : {4,2,12}
Number of vertices, edges, etc : 4, 4, 12, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,2,12,2} of size 384
{4,2,12,4} of size 768
{4,2,12,4} of size 768
{4,2,12,4} of size 768
{4,2,12,3} of size 768
{4,2,12,6} of size 1152
{4,2,12,6} of size 1152
{4,2,12,6} of size 1152
{4,2,12,3} of size 1152
{4,2,12,6} of size 1152
{4,2,12,4} of size 1728
{4,2,12,6} of size 1728
{4,2,12,6} of size 1728
{4,2,12,6} of size 1728
{4,2,12,10} of size 1920
Vertex Figure Of :
{2,4,2,12} of size 384
{3,4,2,12} of size 576
{4,4,2,12} of size 768
{6,4,2,12} of size 1152
{3,4,2,12} of size 1152
{6,4,2,12} of size 1152
{6,4,2,12} of size 1152
{9,4,2,12} of size 1728
{4,4,2,12} of size 1728
{6,4,2,12} of size 1728
{10,4,2,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,12}*96, {4,2,6}*96
3-fold quotients : {4,2,4}*64
4-fold quotients : {4,2,3}*48, {2,2,6}*48
6-fold quotients : {2,2,4}*32, {4,2,2}*32
8-fold quotients : {2,2,3}*24
12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,12}*384, {4,2,24}*384, {8,2,12}*384
3-fold covers : {4,2,36}*576, {12,2,12}*576, {4,6,12}*576a, {4,6,12}*576b
4-fold covers : {8,2,24}*768, {8,4,12}*768a, {4,4,24}*768a, {8,4,12}*768b, {4,4,24}*768b, {4,8,12}*768a, {4,4,12}*768a, {4,4,12}*768b, {4,8,12}*768b, {4,8,12}*768c, {4,8,12}*768d, {16,2,12}*768, {4,2,48}*768, {4,4,12}*768e
5-fold covers : {20,2,12}*960, {4,10,12}*960, {4,2,60}*960
6-fold covers : {4,4,36}*1152, {4,12,12}*1152b, {4,12,12}*1152c, {12,4,12}*1152, {8,2,36}*1152, {4,2,72}*1152, {8,6,12}*1152b, {8,6,12}*1152c, {4,6,24}*1152b, {4,6,24}*1152c, {12,2,24}*1152, {24,2,12}*1152
7-fold covers : {28,2,12}*1344, {4,14,12}*1344, {4,2,84}*1344
9-fold covers : {4,2,108}*1728, {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {4,6,36}*1728a, {4,18,12}*1728a, {4,6,12}*1728a, {4,6,36}*1728b, {4,6,12}*1728b, {12,6,12}*1728b, {12,6,12}*1728c, {12,6,12}*1728e, {12,6,12}*1728f, {4,6,12}*1728h, {4,6,12}*1728k, {4,6,12}*1728l, {4,6,12}*1728n
10-fold covers : {4,4,60}*1920, {4,20,12}*1920, {20,4,12}*1920, {8,2,60}*1920, {4,2,120}*1920, {8,10,12}*1920, {4,10,24}*1920, {40,2,12}*1920, {20,2,24}*1920
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(11,14)(12,13)(15,16);;
s3 := ( 5,11)( 6, 8)( 7,15)( 9,12)(10,13)(14,16);;
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,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

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

to this polytope