Polytope of Type {2,2,2,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,6}*96
if this polytope has a name.
Group : SmallGroup(96,230)
Rank : 5
Schlafli Type : {2,2,2,6}
Number of vertices, edges, etc : 2, 2, 2, 6, 6
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,2,6,2} of size 192
{2,2,2,6,3} of size 288
{2,2,2,6,4} of size 384
{2,2,2,6,3} of size 384
{2,2,2,6,4} of size 384
{2,2,2,6,4} of size 384
{2,2,2,6,4} of size 576
{2,2,2,6,6} of size 576
{2,2,2,6,6} of size 576
{2,2,2,6,6} of size 576
{2,2,2,6,8} of size 768
{2,2,2,6,4} of size 768
{2,2,2,6,6} of size 768
{2,2,2,6,9} of size 864
{2,2,2,6,3} of size 864
{2,2,2,6,6} of size 864
{2,2,2,6,4} of size 960
{2,2,2,6,5} of size 960
{2,2,2,6,6} of size 960
{2,2,2,6,5} of size 960
{2,2,2,6,5} of size 960
{2,2,2,6,10} of size 960
{2,2,2,6,12} of size 1152
{2,2,2,6,12} of size 1152
{2,2,2,6,12} of size 1152
{2,2,2,6,4} of size 1152
{2,2,2,6,3} of size 1152
{2,2,2,6,12} of size 1152
{2,2,2,6,14} of size 1344
{2,2,2,6,15} of size 1440
{2,2,2,6,4} of size 1728
{2,2,2,6,12} of size 1728
{2,2,2,6,12} of size 1728
{2,2,2,6,18} of size 1728
{2,2,2,6,18} of size 1728
{2,2,2,6,6} of size 1728
{2,2,2,6,6} of size 1728
{2,2,2,6,6} of size 1728
{2,2,2,6,12} of size 1728
{2,2,2,6,6} of size 1728
{2,2,2,6,20} of size 1920
{2,2,2,6,15} of size 1920
{2,2,2,6,20} of size 1920
{2,2,2,6,4} of size 1920
{2,2,2,6,4} of size 1920
{2,2,2,6,4} of size 1920
{2,2,2,6,5} of size 1920
{2,2,2,6,6} of size 1920
{2,2,2,6,6} of size 1920
{2,2,2,6,6} of size 1920
{2,2,2,6,10} of size 1920
{2,2,2,6,10} of size 1920
{2,2,2,6,5} of size 1920
{2,2,2,6,10} of size 1920
{2,2,2,6,10} of size 1920
{2,2,2,6,10} of size 1920
{2,2,2,6,10} of size 1920
Vertex Figure Of :
{2,2,2,2,6} of size 192
{3,2,2,2,6} of size 288
{4,2,2,2,6} of size 384
{5,2,2,2,6} of size 480
{6,2,2,2,6} of size 576
{7,2,2,2,6} of size 672
{8,2,2,2,6} of size 768
{9,2,2,2,6} of size 864
{10,2,2,2,6} of size 960
{11,2,2,2,6} of size 1056
{12,2,2,2,6} of size 1152
{13,2,2,2,6} of size 1248
{14,2,2,2,6} of size 1344
{15,2,2,2,6} of size 1440
{17,2,2,2,6} of size 1632
{18,2,2,2,6} of size 1728
{19,2,2,2,6} of size 1824
{20,2,2,2,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,3}*48
3-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,2,12}*192, {2,2,4,6}*192a, {2,4,2,6}*192, {4,2,2,6}*192
3-fold covers : {2,2,2,18}*288, {2,2,6,6}*288a, {2,2,6,6}*288b, {2,6,2,6}*288, {6,2,2,6}*288
4-fold covers : {2,2,4,12}*384a, {2,4,2,12}*384, {4,2,2,12}*384, {2,4,4,6}*384, {4,4,2,6}*384, {4,2,4,6}*384a, {2,2,2,24}*384, {2,2,8,6}*384, {2,8,2,6}*384, {8,2,2,6}*384, {2,2,4,6}*384
5-fold covers : {2,2,10,6}*480, {2,10,2,6}*480, {10,2,2,6}*480, {2,2,2,30}*480
6-fold covers : {2,2,2,36}*576, {2,2,4,18}*576a, {2,4,2,18}*576, {4,2,2,18}*576, {2,2,6,12}*576a, {2,2,6,12}*576b, {2,2,12,6}*576a, {2,6,2,12}*576, {2,12,2,6}*576, {6,2,2,12}*576, {12,2,2,6}*576, {2,4,6,6}*576a, {2,6,4,6}*576, {4,2,6,6}*576a, {4,2,6,6}*576b, {4,6,2,6}*576a, {6,2,4,6}*576a, {6,4,2,6}*576a, {2,2,12,6}*576c, {2,4,6,6}*576c
7-fold covers : {2,2,14,6}*672, {2,14,2,6}*672, {14,2,2,6}*672, {2,2,2,42}*672
8-fold covers : {4,4,4,6}*768, {2,4,4,12}*768, {4,4,2,12}*768, {4,2,4,12}*768a, {2,4,8,6}*768a, {2,8,4,6}*768a, {4,8,2,6}*768a, {8,4,2,6}*768a, {2,2,8,12}*768a, {2,2,4,24}*768a, {2,4,8,6}*768b, {2,8,4,6}*768b, {4,8,2,6}*768b, {8,4,2,6}*768b, {2,2,8,12}*768b, {2,2,4,24}*768b, {2,4,4,6}*768a, {4,4,2,6}*768, {2,2,4,12}*768a, {4,2,8,6}*768, {8,2,4,6}*768a, {2,8,2,12}*768, {8,2,2,12}*768, {2,4,2,24}*768, {4,2,2,24}*768, {2,2,16,6}*768, {2,16,2,6}*768, {16,2,2,6}*768, {2,2,2,48}*768, {2,2,4,12}*768b, {2,2,4,6}*768b, {2,2,4,12}*768c, {2,4,4,6}*768d, {4,2,4,6}*768, {2,2,8,6}*768b, {2,2,8,6}*768c
9-fold covers : {2,2,2,54}*864, {2,2,6,18}*864a, {2,2,6,18}*864b, {2,2,18,6}*864a, {2,6,2,18}*864, {2,18,2,6}*864, {6,2,2,18}*864, {18,2,2,6}*864, {2,2,6,6}*864a, {2,2,6,6}*864b, {2,6,6,6}*864a, {2,2,6,6}*864d, {2,6,6,6}*864b, {2,6,6,6}*864c, {2,6,6,6}*864d, {2,6,6,6}*864g, {6,2,6,6}*864a, {6,2,6,6}*864b, {6,6,2,6}*864a, {6,6,2,6}*864b, {6,6,2,6}*864c
10-fold covers : {2,2,10,12}*960, {2,10,2,12}*960, {10,2,2,12}*960, {2,2,20,6}*960a, {2,20,2,6}*960, {20,2,2,6}*960, {2,4,10,6}*960, {2,10,4,6}*960, {4,2,10,6}*960, {4,10,2,6}*960, {10,2,4,6}*960a, {10,4,2,6}*960, {2,2,2,60}*960, {2,2,4,30}*960a, {2,4,2,30}*960, {4,2,2,30}*960
11-fold covers : {2,2,22,6}*1056, {2,22,2,6}*1056, {22,2,2,6}*1056, {2,2,2,66}*1056
12-fold covers : {2,4,4,18}*1152, {4,4,2,18}*1152, {2,2,4,36}*1152a, {4,4,6,6}*1152a, {6,4,4,6}*1152, {4,4,6,6}*1152c, {2,4,12,6}*1152a, {2,6,4,12}*1152, {2,12,4,6}*1152, {4,12,2,6}*1152a, {6,2,4,12}*1152a, {12,4,2,6}*1152a, {2,4,12,6}*1152c, {2,2,12,12}*1152a, {2,2,12,12}*1152b, {4,2,4,18}*1152a, {2,4,2,36}*1152, {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, {6,4,2,12}*1152a, {12,2,4,6}*1152a, {2,4,6,12}*1152b, {2,4,6,12}*1152c, {2,12,2,12}*1152, {12,2,2,12}*1152, {2,2,8,18}*1152, {2,8,2,18}*1152, {8,2,2,18}*1152, {2,2,2,72}*1152, {2,6,8,6}*1152, {2,8,6,6}*1152a, {6,2,8,6}*1152, {6,8,2,6}*1152, {8,2,6,6}*1152a, {8,2,6,6}*1152b, {8,6,2,6}*1152, {2,2,24,6}*1152a, {2,8,6,6}*1152c, {2,2,6,24}*1152b, {2,2,6,24}*1152c, {2,2,24,6}*1152b, {2,6,2,24}*1152, {2,24,2,6}*1152, {6,2,2,24}*1152, {24,2,2,6}*1152, {2,2,4,18}*1152, {2,2,6,6}*1152a, {2,2,6,12}*1152a, {2,2,12,6}*1152a, {2,2,12,6}*1152b, {2,4,6,6}*1152a, {2,6,4,6}*1152a, {2,6,4,6}*1152b, {2,6,6,6}*1152b, {4,6,2,6}*1152, {6,2,4,6}*1152, {6,4,2,6}*1152, {6,6,2,6}*1152
13-fold covers : {2,2,26,6}*1248, {2,26,2,6}*1248, {26,2,2,6}*1248, {2,2,2,78}*1248
14-fold covers : {2,2,14,12}*1344, {2,14,2,12}*1344, {14,2,2,12}*1344, {2,2,28,6}*1344a, {2,28,2,6}*1344, {28,2,2,6}*1344, {2,4,14,6}*1344, {2,14,4,6}*1344, {4,2,14,6}*1344, {4,14,2,6}*1344, {14,2,4,6}*1344a, {14,4,2,6}*1344, {2,2,2,84}*1344, {2,2,4,42}*1344a, {2,4,2,42}*1344, {4,2,2,42}*1344
15-fold covers : {2,2,10,18}*1440, {2,10,2,18}*1440, {10,2,2,18}*1440, {2,2,2,90}*1440, {2,2,30,6}*1440a, {2,6,10,6}*1440, {2,10,6,6}*1440a, {2,10,6,6}*1440b, {6,2,10,6}*1440, {6,10,2,6}*1440, {10,2,6,6}*1440a, {10,2,6,6}*1440b, {10,6,2,6}*1440, {2,2,6,30}*1440b, {2,2,6,30}*1440c, {2,2,30,6}*1440b, {2,6,2,30}*1440, {2,30,2,6}*1440, {6,2,2,30}*1440, {30,2,2,6}*1440
17-fold covers : {2,2,34,6}*1632, {2,34,2,6}*1632, {34,2,2,6}*1632, {2,2,2,102}*1632
18-fold covers : {2,2,2,108}*1728, {2,2,4,54}*1728a, {2,4,2,54}*1728, {4,2,2,54}*1728, {2,2,12,18}*1728a, {2,2,18,12}*1728a, {2,12,2,18}*1728, {2,18,2,12}*1728, {12,2,2,18}*1728, {18,2,2,12}*1728, {2,2,6,36}*1728a, {2,2,6,36}*1728b, {2,2,36,6}*1728a, {2,6,2,36}*1728, {2,36,2,6}*1728, {6,2,2,36}*1728, {36,2,2,6}*1728, {2,2,6,12}*1728a, {2,2,6,12}*1728b, {2,2,12,6}*1728b, {2,6,6,12}*1728a, {2,12,6,6}*1728a, {2,4,6,18}*1728a, {2,4,18,6}*1728a, {2,6,4,18}*1728, {2,18,4,6}*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, {6,2,4,18}*1728a, {6,4,2,18}*1728a, {18,2,4,6}*1728a, {18,4,2,6}*1728a, {4,6,6,6}*1728a, {2,4,6,6}*1728b, {2,6,12,6}*1728a, {4,2,6,6}*1728a, {4,2,6,6}*1728b, {2,2,12,18}*1728b, {2,4,6,18}*1728b, {2,2,12,6}*1728c, {2,4,6,6}*1728c, {2,6,6,12}*1728b, {2,6,6,12}*1728c, {2,6,6,12}*1728d, {2,6,12,6}*1728b, {2,6,12,6}*1728c, {2,12,6,6}*1728b, {2,12,6,6}*1728d, {6,2,6,12}*1728a, {6,2,6,12}*1728b, {6,2,12,6}*1728a, {6,6,2,12}*1728a, {6,6,2,12}*1728b, {6,6,2,12}*1728c, {6,12,2,6}*1728a, {6,12,2,6}*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, {6,4,6,6}*1728a, {6,6,4,6}*1728a, {6,6,4,6}*1728b, {4,2,6,6}*1728d, {2,2,6,12}*1728g, {2,2,12,6}*1728g, {2,6,6,12}*1728e, {2,12,6,6}*1728e, {4,6,6,6}*1728g, {6,4,6,6}*1728c, {6,6,4,6}*1728c, {2,4,6,6}*1728h, {2,6,12,6}*1728f, {2,6,12,6}*1728g, {2,12,6,6}*1728f, {6,2,12,6}*1728c, {6,12,2,6}*1728c, {12,6,2,6}*1728c, {4,6,6,6}*1728i, {2,2,4,6}*1728b, {2,2,4,12}*1728b, {2,4,4,6}*1728b, {2,4,6,6}*1728j, {2,4,6,6}*1728k, {2,6,4,6}*1728b, {4,4,2,6}*1728, {4,6,2,6}*1728, {6,4,2,6}*1728, {2,2,6,12}*1728i
19-fold covers : {2,2,38,6}*1824, {2,38,2,6}*1824, {38,2,2,6}*1824, {2,2,2,114}*1824
20-fold covers : {2,4,4,30}*1920, {4,4,2,30}*1920, {2,2,4,60}*1920a, {4,4,10,6}*1920, {10,4,4,6}*1920, {2,10,4,12}*1920, {10,2,4,12}*1920a, {2,4,20,6}*1920, {2,20,4,6}*1920, {4,20,2,6}*1920, {20,4,2,6}*1920, {2,2,20,12}*1920, {4,2,4,30}*1920a, {2,4,2,60}*1920, {4,2,2,60}*1920, {4,10,4,6}*1920, {4,2,10,12}*1920, {4,10,2,12}*1920, {10,4,2,12}*1920, {4,2,20,6}*1920a, {20,2,4,6}*1920a, {2,4,10,12}*1920, {2,20,2,12}*1920, {20,2,2,12}*1920, {2,2,8,30}*1920, {2,8,2,30}*1920, {8,2,2,30}*1920, {2,2,2,120}*1920, {2,8,10,6}*1920, {2,10,8,6}*1920, {8,2,10,6}*1920, {8,10,2,6}*1920, {10,2,8,6}*1920, {10,8,2,6}*1920, {2,2,10,24}*1920, {2,10,2,24}*1920, {10,2,2,24}*1920, {2,2,40,6}*1920, {2,40,2,6}*1920, {40,2,2,6}*1920, {2,2,20,6}*1920a, {2,10,4,6}*1920, {10,2,4,6}*1920, {2,2,4,30}*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);;
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, 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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(12)!(1,2);
s1 := Sym(12)!(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*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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope