Polytope of Type {2,2,6,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,2}*96
if this polytope has a name.
Group : SmallGroup(96,230)
Rank : 5
Schlafli Type : {2,2,6,2}
Number of vertices, edges, etc : 2, 2, 6, 6, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,6,2,2} of size 192
{2,2,6,2,3} of size 288
{2,2,6,2,4} of size 384
{2,2,6,2,5} of size 480
{2,2,6,2,6} of size 576
{2,2,6,2,7} of size 672
{2,2,6,2,8} of size 768
{2,2,6,2,9} of size 864
{2,2,6,2,10} of size 960
{2,2,6,2,11} of size 1056
{2,2,6,2,12} of size 1152
{2,2,6,2,13} of size 1248
{2,2,6,2,14} of size 1344
{2,2,6,2,15} of size 1440
{2,2,6,2,17} of size 1632
{2,2,6,2,18} of size 1728
{2,2,6,2,19} of size 1824
{2,2,6,2,20} of size 1920
Vertex Figure Of :
{2,2,2,6,2} of size 192
{3,2,2,6,2} of size 288
{4,2,2,6,2} of size 384
{5,2,2,6,2} of size 480
{6,2,2,6,2} of size 576
{7,2,2,6,2} of size 672
{8,2,2,6,2} of size 768
{9,2,2,6,2} of size 864
{10,2,2,6,2} of size 960
{11,2,2,6,2} of size 1056
{12,2,2,6,2} of size 1152
{13,2,2,6,2} of size 1248
{14,2,2,6,2} of size 1344
{15,2,2,6,2} of size 1440
{17,2,2,6,2} of size 1632
{18,2,2,6,2} of size 1728
{19,2,2,6,2} of size 1824
{20,2,2,6,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,3,2}*48
3-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,12,2}*192, {2,2,6,4}*192a, {2,4,6,2}*192a, {4,2,6,2}*192
3-fold covers : {2,2,18,2}*288, {2,2,6,6}*288a, {2,2,6,6}*288c, {2,6,6,2}*288a, {2,6,6,2}*288b, {6,2,6,2}*288
4-fold covers : {2,2,12,4}*384a, {2,4,12,2}*384a, {4,2,12,2}*384, {4,4,6,2}*384, {2,4,6,4}*384a, {4,2,6,4}*384a, {2,2,24,2}*384, {2,2,6,8}*384, {2,8,6,2}*384, {8,2,6,2}*384, {2,2,6,4}*384, {2,4,6,2}*384
5-fold covers : {2,2,6,10}*480, {2,10,6,2}*480, {10,2,6,2}*480, {2,2,30,2}*480
6-fold covers : {2,2,36,2}*576, {2,2,18,4}*576a, {2,4,18,2}*576a, {4,2,18,2}*576, {2,2,6,12}*576a, {2,2,12,6}*576a, {2,2,12,6}*576b, {2,6,12,2}*576a, {2,6,12,2}*576b, {2,12,6,2}*576a, {6,2,12,2}*576, {12,2,6,2}*576, {2,4,6,6}*576a, {2,4,6,6}*576b, {2,6,6,4}*576a, {2,6,6,4}*576b, {4,2,6,6}*576a, {4,2,6,6}*576c, {4,6,6,2}*576a, {6,2,6,4}*576a, {6,4,6,2}*576, {2,2,6,12}*576c, {2,12,6,2}*576c, {4,6,6,2}*576c
7-fold covers : {2,2,6,14}*672, {2,14,6,2}*672, {14,2,6,2}*672, {2,2,42,2}*672
8-fold covers : {4,4,12,2}*768, {2,4,12,4}*768a, {4,4,6,4}*768a, {4,2,12,4}*768a, {4,8,6,2}*768a, {8,4,6,2}*768a, {2,2,12,8}*768a, {2,8,12,2}*768a, {2,2,24,4}*768a, {2,4,24,2}*768a, {4,8,6,2}*768b, {8,4,6,2}*768b, {2,2,12,8}*768b, {2,8,12,2}*768b, {2,2,24,4}*768b, {2,4,24,2}*768b, {4,4,6,2}*768a, {2,2,12,4}*768a, {2,4,12,2}*768a, {4,2,6,8}*768, {8,2,6,4}*768a, {2,4,6,8}*768a, {2,8,6,4}*768a, {8,2,12,2}*768, {4,2,24,2}*768, {2,2,6,16}*768, {2,16,6,2}*768, {16,2,6,2}*768, {2,2,48,2}*768, {2,2,12,4}*768b, {2,4,12,2}*768b, {2,2,6,4}*768b, {2,2,12,4}*768c, {2,4,6,2}*768b, {2,4,6,4}*768a, {2,4,6,4}*768b, {2,4,12,2}*768c, {4,2,6,4}*768, {4,4,6,2}*768d, {2,2,6,8}*768b, {2,8,6,2}*768b, {2,2,6,8}*768c, {2,8,6,2}*768c
9-fold covers : {2,2,54,2}*864, {2,2,6,18}*864a, {2,2,18,6}*864a, {2,2,18,6}*864b, {2,6,18,2}*864a, {2,6,18,2}*864b, {2,18,6,2}*864a, {6,2,18,2}*864, {18,2,6,2}*864, {2,2,6,6}*864b, {2,2,6,6}*864c, {2,6,6,2}*864a, {2,6,6,2}*864b, {6,6,6,2}*864a, {2,2,6,6}*864d, {2,6,6,2}*864d, {2,6,6,6}*864b, {2,6,6,6}*864d, {2,6,6,6}*864e, {2,6,6,6}*864f, {6,2,6,6}*864a, {6,2,6,6}*864c, {6,6,6,2}*864b, {6,6,6,2}*864c, {6,6,6,2}*864d, {6,6,6,2}*864g
10-fold covers : {2,2,12,10}*960, {2,10,12,2}*960, {10,2,12,2}*960, {2,2,6,20}*960a, {2,20,6,2}*960a, {20,2,6,2}*960, {2,4,6,10}*960a, {2,10,6,4}*960a, {4,2,6,10}*960, {4,10,6,2}*960, {10,2,6,4}*960a, {10,4,6,2}*960, {2,2,60,2}*960, {2,2,30,4}*960a, {2,4,30,2}*960a, {4,2,30,2}*960
11-fold covers : {2,2,6,22}*1056, {2,22,6,2}*1056, {22,2,6,2}*1056, {2,2,66,2}*1056
12-fold covers : {4,4,18,2}*1152, {2,2,36,4}*1152a, {2,4,36,2}*1152a, {4,4,6,6}*1152a, {4,4,6,6}*1152b, {2,4,12,6}*1152a, {2,4,12,6}*1152b, {2,6,12,4}*1152a, {2,6,12,4}*1152b, {4,12,6,2}*1152a, {6,2,12,4}*1152a, {6,4,12,2}*1152, {12,4,6,2}*1152, {4,12,6,2}*1152c, {2,2,12,12}*1152a, {2,2,12,12}*1152c, {2,12,12,2}*1152a, {2,12,12,2}*1152b, {4,2,18,4}*1152a, {2,4,18,4}*1152a, {4,2,36,2}*1152, {6,4,6,4}*1152a, {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, {2,4,6,12}*1152a, {2,12,6,4}*1152a, {2,4,6,12}*1152b, {2,12,6,4}*1152b, {4,6,12,2}*1152b, {4,6,12,2}*1152c, {12,2,12,2}*1152, {2,2,18,8}*1152, {2,8,18,2}*1152, {8,2,18,2}*1152, {2,2,72,2}*1152, {2,6,6,8}*1152a, {2,6,6,8}*1152b, {2,8,6,6}*1152a, {2,8,6,6}*1152b, {6,2,6,8}*1152, {6,8,6,2}*1152, {8,2,6,6}*1152a, {8,2,6,6}*1152c, {8,6,6,2}*1152a, {2,2,6,24}*1152a, {2,24,6,2}*1152a, {8,6,6,2}*1152c, {2,2,6,24}*1152b, {2,2,24,6}*1152b, {2,2,24,6}*1152c, {2,6,24,2}*1152b, {2,6,24,2}*1152c, {2,24,6,2}*1152b, {6,2,24,2}*1152, {24,2,6,2}*1152, {2,2,18,4}*1152, {2,4,18,2}*1152, {2,2,6,6}*1152b, {2,2,6,12}*1152a, {2,2,6,12}*1152b, {2,2,12,6}*1152a, {2,4,6,6}*1152a, {2,4,6,6}*1152b, {2,6,6,2}*1152a, {2,6,6,4}*1152a, {2,6,6,4}*1152b, {2,6,12,2}*1152a, {2,12,6,2}*1152a, {2,12,6,2}*1152b, {4,6,6,2}*1152a, {6,2,6,4}*1152, {6,4,6,2}*1152a, {6,4,6,2}*1152b, {6,6,6,2}*1152b
13-fold covers : {2,2,6,26}*1248, {2,26,6,2}*1248, {26,2,6,2}*1248, {2,2,78,2}*1248
14-fold covers : {2,2,12,14}*1344, {2,14,12,2}*1344, {14,2,12,2}*1344, {2,2,6,28}*1344a, {2,28,6,2}*1344a, {28,2,6,2}*1344, {2,4,6,14}*1344a, {2,14,6,4}*1344a, {4,2,6,14}*1344, {4,14,6,2}*1344, {14,2,6,4}*1344a, {14,4,6,2}*1344, {2,2,84,2}*1344, {2,2,42,4}*1344a, {2,4,42,2}*1344a, {4,2,42,2}*1344
15-fold covers : {2,2,18,10}*1440, {2,10,18,2}*1440, {10,2,18,2}*1440, {2,2,90,2}*1440, {2,2,6,30}*1440a, {2,6,6,10}*1440a, {2,6,6,10}*1440b, {2,10,6,6}*1440a, {2,10,6,6}*1440c, {2,30,6,2}*1440a, {6,2,6,10}*1440, {6,10,6,2}*1440, {10,2,6,6}*1440a, {10,2,6,6}*1440c, {10,6,6,2}*1440a, {10,6,6,2}*1440b, {2,2,6,30}*1440b, {2,2,30,6}*1440b, {2,2,30,6}*1440c, {2,6,30,2}*1440b, {2,6,30,2}*1440c, {2,30,6,2}*1440b, {6,2,30,2}*1440, {30,2,6,2}*1440
17-fold covers : {2,2,6,34}*1632, {2,34,6,2}*1632, {34,2,6,2}*1632, {2,2,102,2}*1632
18-fold covers : {2,2,108,2}*1728, {2,2,54,4}*1728a, {2,4,54,2}*1728a, {4,2,54,2}*1728, {2,2,12,18}*1728a, {2,2,18,12}*1728a, {2,12,18,2}*1728a, {2,18,12,2}*1728a, {12,2,18,2}*1728, {18,2,12,2}*1728, {2,2,6,36}*1728a, {2,2,36,6}*1728a, {2,2,36,6}*1728b, {2,6,36,2}*1728a, {2,6,36,2}*1728b, {2,36,6,2}*1728a, {6,2,36,2}*1728, {36,2,6,2}*1728, {2,2,6,12}*1728b, {2,2,12,6}*1728a, {2,2,12,6}*1728b, {2,6,12,2}*1728a, {2,6,12,2}*1728b, {2,12,6,2}*1728b, {6,6,12,2}*1728a, {12,6,6,2}*1728a, {2,4,6,18}*1728a, {2,4,18,6}*1728a, {2,4,18,6}*1728b, {2,6,18,4}*1728a, {2,6,18,4}*1728b, {2,18,6,4}*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, {6,2,18,4}*1728a, {6,4,18,2}*1728, {18,2,6,4}*1728a, {18,4,6,2}*1728, {6,6,6,4}*1728a, {2,4,6,6}*1728a, {2,4,6,6}*1728b, {2,6,6,4}*1728a, {2,6,6,4}*1728b, {4,2,6,6}*1728b, {4,2,6,6}*1728c, {4,6,6,2}*1728b, {6,12,6,2}*1728a, {2,2,18,12}*1728b, {2,12,18,2}*1728b, {4,6,18,2}*1728b, {2,2,6,12}*1728c, {2,12,6,2}*1728c, {4,6,6,2}*1728c, {2,6,6,12}*1728b, {2,6,6,12}*1728d, {2,6,12,6}*1728b, {2,6,12,6}*1728c, {2,6,12,6}*1728d, {2,6,12,6}*1728e, {2,12,6,6}*1728b, {2,12,6,6}*1728c, {6,2,6,12}*1728a, {6,2,12,6}*1728a, {6,2,12,6}*1728b, {6,6,12,2}*1728b, {6,6,12,2}*1728c, {6,6,12,2}*1728d, {6,12,6,2}*1728b, {6,12,6,2}*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, {6,4,6,6}*1728a, {6,4,6,6}*1728b, {6,6,6,4}*1728d, {6,6,6,4}*1728e, {6,6,6,4}*1728f, {4,2,6,6}*1728d, {2,2,6,12}*1728g, {2,2,12,6}*1728g, {2,6,12,2}*1728g, {2,12,6,2}*1728g, {6,6,12,2}*1728e, {12,6,6,2}*1728e, {4,6,6,6}*1728g, {4,6,6,6}*1728h, {2,4,6,6}*1728h, {2,6,6,4}*1728h, {2,6,6,12}*1728f, {2,6,6,12}*1728g, {2,12,6,6}*1728f, {2,12,6,6}*1728g, {4,6,6,2}*1728h, {6,2,6,12}*1728c, {6,12,6,2}*1728f, {6,12,6,2}*1728g, {12,6,6,2}*1728f, {6,6,6,4}*1728i, {2,2,6,4}*1728b, {2,2,12,4}*1728b, {2,4,6,2}*1728b, {2,4,12,2}*1728b, {4,4,6,2}*1728b, {4,6,6,2}*1728j, {4,6,6,2}*1728k, {6,4,6,2}*1728b, {2,2,12,6}*1728i, {2,6,12,2}*1728i
19-fold covers : {2,2,6,38}*1824, {2,38,6,2}*1824, {38,2,6,2}*1824, {2,2,114,2}*1824
20-fold covers : {4,4,30,2}*1920, {2,2,60,4}*1920a, {2,4,60,2}*1920a, {4,4,6,10}*1920, {2,4,12,10}*1920a, {2,10,12,4}*1920a, {10,2,12,4}*1920a, {10,4,12,2}*1920, {4,20,6,2}*1920, {20,4,6,2}*1920, {2,2,12,20}*1920, {2,20,12,2}*1920, {4,2,30,4}*1920a, {2,4,30,4}*1920a, {4,2,60,2}*1920, {10,4,6,4}*1920a, {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, {2,4,6,20}*1920a, {2,20,6,4}*1920a, {20,2,12,2}*1920, {2,2,30,8}*1920, {2,8,30,2}*1920, {8,2,30,2}*1920, {2,2,120,2}*1920, {2,8,6,10}*1920, {2,10,6,8}*1920, {8,2,6,10}*1920, {8,10,6,2}*1920, {10,2,6,8}*1920, {10,8,6,2}*1920, {2,2,24,10}*1920, {2,10,24,2}*1920, {10,2,24,2}*1920, {2,2,6,40}*1920, {2,40,6,2}*1920, {40,2,6,2}*1920, {2,2,6,20}*1920a, {2,4,6,10}*1920a, {2,10,6,4}*1920a, {2,20,6,2}*1920a, {10,2,6,4}*1920, {10,4,6,2}*1920, {2,2,30,4}*1920, {2,4,30,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (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*s1*s0*s1,
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(12)!(1,2);
s1 := Sym(12)!(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*s1*s0*s1, 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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope