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