Polytope of Type {2,2,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12}*96
if this polytope has a name.
Group : SmallGroup(96,207)
Rank : 4
Schlafli Type : {2,2,12}
Number of vertices, edges, etc : 2, 2, 12, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,12,2} of size 192
{2,2,12,4} of size 384
{2,2,12,4} of size 384
{2,2,12,4} of size 384
{2,2,12,3} of size 384
{2,2,12,6} of size 576
{2,2,12,6} of size 576
{2,2,12,6} of size 576
{2,2,12,3} of size 576
{2,2,12,6} of size 576
{2,2,12,8} of size 768
{2,2,12,8} of size 768
{2,2,12,4} of size 768
{2,2,12,4} of size 768
{2,2,12,4} of size 768
{2,2,12,6} of size 768
{2,2,12,6} of size 768
{2,2,12,4} of size 864
{2,2,12,6} of size 864
{2,2,12,6} of size 864
{2,2,12,6} of size 864
{2,2,12,10} of size 960
{2,2,12,12} of size 1152
{2,2,12,12} of size 1152
{2,2,12,12} of size 1152
{2,2,12,4} of size 1152
{2,2,12,3} of size 1152
{2,2,12,6} of size 1152
{2,2,12,6} of size 1152
{2,2,12,14} of size 1344
{2,2,12,18} of size 1728
{2,2,12,6} of size 1728
{2,2,12,6} of size 1728
{2,2,12,18} of size 1728
{2,2,12,6} of size 1728
{2,2,12,9} of size 1728
{2,2,12,18} of size 1728
{2,2,12,3} of size 1728
{2,2,12,6} of size 1728
{2,2,12,4} of size 1728
{2,2,12,6} of size 1728
{2,2,12,6} of size 1728
{2,2,12,6} of size 1728
{2,2,12,4} of size 1728
{2,2,12,6} of size 1728
{2,2,12,6} of size 1728
{2,2,12,20} of size 1920
{2,2,12,15} of size 1920
{2,2,12,4} of size 1920
{2,2,12,4} of size 1920
{2,2,12,6} of size 1920
{2,2,12,6} of size 1920
{2,2,12,10} of size 1920
{2,2,12,10} of size 1920
{2,2,12,10} of size 1920
{2,2,12,10} of size 1920
{2,2,12,5} of size 1920
Vertex Figure Of :
{2,2,2,12} of size 192
{3,2,2,12} of size 288
{4,2,2,12} of size 384
{5,2,2,12} of size 480
{6,2,2,12} of size 576
{7,2,2,12} of size 672
{8,2,2,12} of size 768
{9,2,2,12} of size 864
{10,2,2,12} of size 960
{11,2,2,12} of size 1056
{12,2,2,12} of size 1152
{13,2,2,12} of size 1248
{14,2,2,12} of size 1344
{15,2,2,12} of size 1440
{17,2,2,12} of size 1632
{18,2,2,12} of size 1728
{19,2,2,12} of size 1824
{20,2,2,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,6}*48
3-fold quotients : {2,2,4}*32
4-fold quotients : {2,2,3}*24
6-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,4,12}*192a, {4,2,12}*192, {2,2,24}*192
3-fold covers : {2,2,36}*288, {2,6,12}*288a, {2,6,12}*288b, {6,2,12}*288
4-fold covers : {4,4,12}*384, {2,4,24}*384a, {2,4,12}*384a, {2,4,24}*384b, {2,8,12}*384a, {2,8,12}*384b, {4,2,24}*384, {8,2,12}*384, {2,2,48}*384, {2,4,12}*384b
5-fold covers : {2,10,12}*480, {10,2,12}*480, {2,2,60}*480
6-fold covers : {2,4,36}*576a, {4,2,36}*576, {2,2,72}*576, {12,2,12}*576, {6,4,12}*576, {4,6,12}*576a, {2,6,24}*576a, {2,6,24}*576b, {6,2,24}*576, {2,12,12}*576a, {2,12,12}*576b, {4,6,12}*576b
7-fold covers : {2,14,12}*672, {14,2,12}*672, {2,2,84}*672
8-fold covers : {2,8,12}*768a, {2,4,24}*768a, {2,8,24}*768a, {2,8,24}*768b, {2,8,24}*768c, {2,8,24}*768d, {8,2,24}*768, {8,4,12}*768a, {4,4,24}*768a, {8,4,12}*768b, {4,4,24}*768b, {4,8,12}*768a, {4,4,12}*768a, {4,4,12}*768b, {4,8,12}*768b, {4,8,12}*768c, {4,8,12}*768d, {2,16,12}*768a, {2,4,48}*768a, {2,16,12}*768b, {2,4,48}*768b, {2,4,12}*768a, {2,4,24}*768b, {2,8,12}*768b, {16,2,12}*768, {4,2,48}*768, {2,2,96}*768, {2,4,12}*768d, {4,4,12}*768e, {2,8,12}*768e, {2,8,12}*768f, {2,4,24}*768c, {2,4,24}*768d
9-fold covers : {2,2,108}*864, {2,6,36}*864a, {2,6,36}*864b, {6,2,36}*864, {2,18,12}*864a, {18,2,12}*864, {6,6,12}*864a, {2,6,12}*864a, {2,6,12}*864b, {6,6,12}*864b, {6,6,12}*864c, {6,6,12}*864d, {6,6,12}*864e, {2,6,12}*864g, {2,6,12}*864i
10-fold covers : {20,2,12}*960, {10,4,12}*960, {4,10,12}*960, {2,10,24}*960, {10,2,24}*960, {2,20,12}*960, {2,4,60}*960a, {4,2,60}*960, {2,2,120}*960
11-fold covers : {2,22,12}*1056, {22,2,12}*1056, {2,2,132}*1056
12-fold covers : {4,4,36}*1152, {4,12,12}*1152b, {4,12,12}*1152c, {12,4,12}*1152, {2,8,36}*1152a, {2,4,72}*1152a, {6,8,12}*1152a, {6,4,24}*1152a, {2,12,24}*1152a, {2,12,24}*1152b, {2,24,12}*1152a, {2,24,12}*1152c, {2,8,36}*1152b, {2,4,72}*1152b, {6,8,12}*1152b, {6,4,24}*1152b, {2,12,24}*1152d, {2,12,24}*1152e, {2,24,12}*1152d, {2,24,12}*1152f, {2,4,36}*1152a, {6,4,12}*1152a, {2,12,12}*1152a, {2,12,12}*1152b, {8,2,36}*1152, {4,2,72}*1152, {8,6,12}*1152b, {8,6,12}*1152c, {4,6,24}*1152b, {4,6,24}*1152c, {12,2,24}*1152, {24,2,12}*1152, {2,2,144}*1152, {2,6,48}*1152b, {2,6,48}*1152c, {6,2,48}*1152, {2,4,36}*1152b, {6,4,12}*1152b, {2,12,12}*1152f, {2,12,12}*1152g, {4,6,12}*1152a, {6,4,12}*1152c, {6,6,12}*1152a, {2,6,12}*1152a, {2,6,12}*1152b
13-fold covers : {2,26,12}*1248, {26,2,12}*1248, {2,2,156}*1248
14-fold covers : {28,2,12}*1344, {4,14,12}*1344, {14,4,12}*1344, {2,14,24}*1344, {14,2,24}*1344, {2,28,12}*1344, {2,4,84}*1344a, {4,2,84}*1344, {2,2,168}*1344
15-fold covers : {2,10,36}*1440, {10,2,36}*1440, {2,2,180}*1440, {6,10,12}*1440, {10,6,12}*1440a, {10,6,12}*1440b, {2,30,12}*1440a, {2,30,12}*1440b, {30,2,12}*1440, {2,6,60}*1440b, {2,6,60}*1440c, {6,2,60}*1440
17-fold covers : {2,34,12}*1632, {34,2,12}*1632, {2,2,204}*1632
18-fold covers : {2,4,108}*1728a, {4,2,108}*1728, {2,2,216}*1728, {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {4,6,36}*1728a, {4,18,12}*1728a, {18,4,12}*1728, {6,4,36}*1728, {4,6,12}*1728a, {6,12,12}*1728a, {2,6,72}*1728a, {2,6,72}*1728b, {6,2,72}*1728, {2,18,24}*1728a, {18,2,24}*1728, {6,6,24}*1728a, {2,6,24}*1728a, {2,6,24}*1728b, {2,12,36}*1728a, {2,12,36}*1728b, {2,36,12}*1728a, {4,6,36}*1728b, {2,12,12}*1728b, {2,12,12}*1728c, {4,6,12}*1728b, {6,6,24}*1728b, {6,6,24}*1728c, {6,6,24}*1728d, {6,6,24}*1728e, {2,6,24}*1728f, {12,6,12}*1728b, {12,6,12}*1728c, {12,6,12}*1728e, {12,6,12}*1728f, {6,12,12}*1728b, {6,12,12}*1728c, {6,12,12}*1728d, {2,12,12}*1728h, {6,12,12}*1728g, {4,6,12}*1728h, {4,4,12}*1728b, {4,6,12}*1728k, {4,6,12}*1728l, {6,4,12}*1728a, {2,4,12}*1728c, {2,4,12}*1728d, {2,6,24}*1728h, {4,6,12}*1728n, {2,12,12}*1728l
19-fold covers : {2,38,12}*1824, {38,2,12}*1824, {2,2,228}*1824
20-fold covers : {4,4,60}*1920, {4,20,12}*1920, {20,4,12}*1920, {2,8,60}*1920a, {2,4,120}*1920a, {10,8,12}*1920a, {10,4,24}*1920a, {2,40,12}*1920a, {2,20,24}*1920a, {2,8,60}*1920b, {2,4,120}*1920b, {10,8,12}*1920b, {10,4,24}*1920b, {2,40,12}*1920b, {2,20,24}*1920b, {2,4,60}*1920a, {10,4,12}*1920a, {2,20,12}*1920a, {8,2,60}*1920, {4,2,120}*1920, {8,10,12}*1920, {4,10,24}*1920, {40,2,12}*1920, {20,2,24}*1920, {2,2,240}*1920, {2,10,48}*1920, {10,2,48}*1920, {10,4,12}*1920b, {2,20,12}*1920b, {2,4,60}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(11,14)(12,13)(15,16);;
s3 := ( 5,11)( 6, 8)( 7,15)( 9,12)(10,13)(14,16);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(16)!(1,2);
s1 := Sym(16)!(3,4);
s2 := Sym(16)!( 6, 7)( 8, 9)(11,14)(12,13)(15,16);
s3 := Sym(16)!( 5,11)( 6, 8)( 7,15)( 9,12)(10,13)(14,16);
poly := sub<Sym(16)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope