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