Polytope of Type {4,2,2,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,2,6}*192
if this polytope has a name.
Group : SmallGroup(192,1514)
Rank : 5
Schlafli Type : {4,2,2,6}
Number of vertices, edges, etc : 4, 4, 2, 6, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,2,2,6,2} of size 384
{4,2,2,6,3} of size 576
{4,2,2,6,4} of size 768
{4,2,2,6,3} of size 768
{4,2,2,6,4} of size 768
{4,2,2,6,4} of size 768
{4,2,2,6,4} of size 1152
{4,2,2,6,6} of size 1152
{4,2,2,6,6} of size 1152
{4,2,2,6,6} of size 1152
{4,2,2,6,9} of size 1728
{4,2,2,6,3} of size 1728
{4,2,2,6,6} of size 1728
{4,2,2,6,10} of size 1920
{4,2,2,6,4} of size 1920
{4,2,2,6,5} of size 1920
{4,2,2,6,6} of size 1920
{4,2,2,6,5} of size 1920
{4,2,2,6,5} of size 1920
Vertex Figure Of :
{2,4,2,2,6} of size 384
{3,4,2,2,6} of size 576
{4,4,2,2,6} of size 768
{6,4,2,2,6} of size 1152
{3,4,2,2,6} of size 1152
{6,4,2,2,6} of size 1152
{6,4,2,2,6} of size 1152
{9,4,2,2,6} of size 1728
{4,4,2,2,6} of size 1728
{6,4,2,2,6} of size 1728
{10,4,2,2,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96
3-fold quotients : {4,2,2,2}*64
4-fold quotients : {2,2,2,3}*48
6-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,2,2,12}*384, {4,4,2,6}*384, {4,2,4,6}*384a, {8,2,2,6}*384
3-fold covers : {4,2,2,18}*576, {12,2,2,6}*576, {4,2,6,6}*576a, {4,2,6,6}*576b, {4,6,2,6}*576a
4-fold covers : {4,4,4,6}*768, {4,4,2,12}*768, {4,2,4,12}*768a, {4,8,2,6}*768a, {8,4,2,6}*768a, {4,8,2,6}*768b, {8,4,2,6}*768b, {4,4,2,6}*768, {4,2,8,6}*768, {8,2,4,6}*768a, {8,2,2,12}*768, {4,2,2,24}*768, {16,2,2,6}*768, {4,2,4,6}*768
5-fold covers : {20,2,2,6}*960, {4,2,10,6}*960, {4,10,2,6}*960, {4,2,2,30}*960
6-fold covers : {4,4,2,18}*1152, {4,4,6,6}*1152a, {4,4,6,6}*1152c, {4,12,2,6}*1152a, {12,4,2,6}*1152a, {4,2,4,18}*1152a, {4,2,2,36}*1152, {4,6,4,6}*1152a, {4,2,12,6}*1152a, {4,2,6,12}*1152b, {4,2,6,12}*1152c, {4,2,12,6}*1152b, {4,6,2,12}*1152a, {12,2,4,6}*1152a, {12,2,2,12}*1152, {8,2,2,18}*1152, {8,2,6,6}*1152a, {8,2,6,6}*1152b, {8,6,2,6}*1152, {24,2,2,6}*1152
7-fold covers : {28,2,2,6}*1344, {4,2,14,6}*1344, {4,14,2,6}*1344, {4,2,2,42}*1344
9-fold covers : {4,2,2,54}*1728, {12,2,2,18}*1728, {36,2,2,6}*1728, {4,2,6,18}*1728a, {4,2,6,18}*1728b, {4,2,18,6}*1728a, {4,6,2,18}*1728a, {4,18,2,6}*1728a, {4,6,6,6}*1728a, {4,2,6,6}*1728a, {4,2,6,6}*1728b, {12,2,6,6}*1728a, {12,2,6,6}*1728b, {12,6,2,6}*1728a, {12,6,2,6}*1728b, {4,6,6,6}*1728d, {4,6,6,6}*1728f, {4,2,6,6}*1728d, {4,6,6,6}*1728g, {12,6,2,6}*1728c, {4,6,6,6}*1728i, {4,6,2,6}*1728
10-fold covers : {4,4,2,30}*1920, {4,4,10,6}*1920, {4,20,2,6}*1920, {20,4,2,6}*1920, {4,2,4,30}*1920a, {4,2,2,60}*1920, {4,10,4,6}*1920, {4,2,10,12}*1920, {4,10,2,12}*1920, {4,2,20,6}*1920a, {20,2,4,6}*1920a, {20,2,2,12}*1920, {8,2,2,30}*1920, {8,2,10,6}*1920, {8,10,2,6}*1920, {40,2,2,6}*1920
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := (5,6);;
s3 := ( 9,10)(11,12);;
s4 := ( 7,11)( 8, 9)(10,12);;
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,
s1*s2*s1*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*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(12)!(2,3);
s1 := Sym(12)!(1,2)(3,4);
s2 := Sym(12)!(5,6);
s3 := Sym(12)!( 9,10)(11,12);
s4 := Sym(12)!( 7,11)( 8, 9)(10,12);
poly := sub<Sym(12)|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, s1*s2*s1*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*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope