Polytope of Type {2,2,2,6,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,6,2}*192
if this polytope has a name.
Group : SmallGroup(192,1542)
Rank : 6
Schlafli Type : {2,2,2,6,2}
Number of vertices, edges, etc : 2, 2, 2, 6, 6, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,2,6,2,2} of size 384
{2,2,2,6,2,3} of size 576
{2,2,2,6,2,4} of size 768
{2,2,2,6,2,5} of size 960
{2,2,2,6,2,6} of size 1152
{2,2,2,6,2,7} of size 1344
{2,2,2,6,2,9} of size 1728
{2,2,2,6,2,10} of size 1920
Vertex Figure Of :
{2,2,2,2,6,2} of size 384
{3,2,2,2,6,2} of size 576
{4,2,2,2,6,2} of size 768
{5,2,2,2,6,2} of size 960
{6,2,2,2,6,2} of size 1152
{7,2,2,2,6,2} of size 1344
{9,2,2,2,6,2} of size 1728
{10,2,2,2,6,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,3,2}*96
3-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,2,12,2}*384, {2,2,2,6,4}*384a, {2,2,4,6,2}*384a, {2,4,2,6,2}*384, {4,2,2,6,2}*384
3-fold covers : {2,2,2,18,2}*576, {2,2,2,6,6}*576a, {2,2,2,6,6}*576c, {2,2,6,6,2}*576a, {2,2,6,6,2}*576b, {2,6,2,6,2}*576, {6,2,2,6,2}*576
4-fold covers : {2,4,4,6,2}*768, {4,4,2,6,2}*768, {2,2,2,12,4}*768a, {2,2,4,12,2}*768a, {2,4,2,6,4}*768a, {4,2,2,6,4}*768a, {4,2,4,6,2}*768a, {2,2,4,6,4}*768a, {2,4,2,12,2}*768, {4,2,2,12,2}*768, {2,2,2,6,8}*768, {2,2,8,6,2}*768, {2,8,2,6,2}*768, {8,2,2,6,2}*768, {2,2,2,24,2}*768, {2,2,2,6,4}*768, {2,2,4,6,2}*768
5-fold covers : {2,2,2,6,10}*960, {2,2,10,6,2}*960, {2,10,2,6,2}*960, {10,2,2,6,2}*960, {2,2,2,30,2}*960
6-fold covers : {2,2,2,18,4}*1152a, {2,2,4,18,2}*1152a, {2,4,2,18,2}*1152, {4,2,2,18,2}*1152, {2,2,2,36,2}*1152, {2,2,4,6,6}*1152a, {2,2,4,6,6}*1152b, {2,2,6,6,4}*1152a, {2,2,6,6,4}*1152b, {2,4,2,6,6}*1152a, {2,4,2,6,6}*1152c, {2,4,6,6,2}*1152a, {2,6,2,6,4}*1152a, {2,6,4,6,2}*1152, {4,2,2,6,6}*1152a, {4,2,2,6,6}*1152c, {4,2,6,6,2}*1152a, {4,2,6,6,2}*1152b, {4,6,2,6,2}*1152a, {6,2,2,6,4}*1152a, {6,2,4,6,2}*1152a, {6,4,2,6,2}*1152a, {2,2,2,6,12}*1152a, {2,2,12,6,2}*1152a, {2,4,6,6,2}*1152c, {2,2,2,6,12}*1152b, {2,2,2,12,6}*1152b, {2,2,2,12,6}*1152c, {2,2,6,12,2}*1152b, {2,2,6,12,2}*1152c, {2,2,12,6,2}*1152b, {2,6,2,12,2}*1152, {2,12,2,6,2}*1152, {6,2,2,12,2}*1152, {12,2,2,6,2}*1152
7-fold covers : {2,2,2,6,14}*1344, {2,2,14,6,2}*1344, {2,14,2,6,2}*1344, {14,2,2,6,2}*1344, {2,2,2,42,2}*1344
9-fold covers : {2,2,2,54,2}*1728, {2,2,2,6,18}*1728a, {2,2,2,18,6}*1728a, {2,2,2,18,6}*1728b, {2,2,6,18,2}*1728a, {2,2,6,18,2}*1728b, {2,2,18,6,2}*1728a, {2,6,2,18,2}*1728, {2,18,2,6,2}*1728, {6,2,2,18,2}*1728, {18,2,2,6,2}*1728, {2,2,2,6,6}*1728b, {2,2,2,6,6}*1728c, {2,2,6,6,2}*1728a, {2,2,6,6,2}*1728b, {2,6,6,6,2}*1728a, {2,2,2,6,6}*1728d, {2,2,6,6,2}*1728d, {2,2,6,6,6}*1728b, {2,2,6,6,6}*1728d, {2,2,6,6,6}*1728e, {2,2,6,6,6}*1728f, {2,6,2,6,6}*1728a, {2,6,2,6,6}*1728c, {2,6,6,6,2}*1728b, {2,6,6,6,2}*1728c, {2,6,6,6,2}*1728d, {2,6,6,6,2}*1728g, {6,2,2,6,6}*1728a, {6,2,2,6,6}*1728c, {6,2,6,6,2}*1728a, {6,2,6,6,2}*1728b, {6,6,2,6,2}*1728a, {6,6,2,6,2}*1728b, {6,6,2,6,2}*1728c
10-fold covers : {2,2,2,30,4}*1920a, {2,2,4,30,2}*1920a, {2,4,2,30,2}*1920, {4,2,2,30,2}*1920, {2,2,2,60,2}*1920, {2,2,4,6,10}*1920a, {2,2,10,6,4}*1920a, {2,4,2,6,10}*1920, {2,4,10,6,2}*1920, {2,10,2,6,4}*1920a, {2,10,4,6,2}*1920, {4,2,2,6,10}*1920, {4,2,10,6,2}*1920, {4,10,2,6,2}*1920, {10,2,2,6,4}*1920a, {10,2,4,6,2}*1920a, {10,4,2,6,2}*1920, {2,2,2,12,10}*1920, {2,2,10,12,2}*1920, {2,10,2,12,2}*1920, {10,2,2,12,2}*1920, {2,2,2,6,20}*1920a, {2,2,20,6,2}*1920a, {2,20,2,6,2}*1920, {20,2,2,6,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 9,10)(11,12);;
s4 := ( 7,11)( 8, 9)(10,12);;
s5 := (13,14);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(14)!(1,2);
s1 := Sym(14)!(3,4);
s2 := Sym(14)!(5,6);
s3 := Sym(14)!( 9,10)(11,12);
s4 := Sym(14)!( 7,11)( 8, 9)(10,12);
s5 := Sym(14)!(13,14);
poly := sub<Sym(14)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope