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