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