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# Polytope of Type {2,4,12}

Atlas Canonical Name : {2,4,12}*192a
if this polytope has a name.
Group : SmallGroup(192,1046)
Rank : 4
Schlafli Type : {2,4,12}
Number of vertices, edges, etc : 2, 4, 24, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,12,2} of size 384
{2,4,12,4} of size 768
{2,4,12,4} of size 768
{2,4,12,4} of size 768
{2,4,12,3} of size 768
{2,4,12,6} of size 1152
{2,4,12,6} of size 1152
{2,4,12,6} of size 1152
{2,4,12,3} of size 1152
{2,4,12,6} of size 1728
{2,4,12,6} of size 1728
{2,4,12,6} of size 1728
{2,4,12,10} of size 1920
Vertex Figure Of :
{2,2,4,12} of size 384
{3,2,4,12} of size 576
{4,2,4,12} of size 768
{5,2,4,12} of size 960
{6,2,4,12} of size 1152
{7,2,4,12} of size 1344
{9,2,4,12} of size 1728
{10,2,4,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,12}*96, {2,4,6}*96a
3-fold quotients : {2,4,4}*64
4-fold quotients : {2,2,6}*48
6-fold quotients : {2,2,4}*32, {2,4,2}*32
8-fold quotients : {2,2,3}*24
12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-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
3-fold covers : {2,4,36}*576a, {6,4,12}*576, {2,12,12}*576a, {2,12,12}*576b
4-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, {8,4,12}*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, {2,4,12}*768d
5-fold covers : {10,4,12}*960, {2,20,12}*960, {2,4,60}*960a
6-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
7-fold covers : {14,4,12}*1344, {2,28,12}*1344, {2,4,84}*1344a
9-fold covers : {2,4,108}*1728a, {18,4,12}*1728, {6,4,36}*1728, {6,12,12}*1728a, {2,12,36}*1728a, {2,12,36}*1728b, {2,36,12}*1728a, {2,12,12}*1728b, {2,12,12}*1728c, {6,12,12}*1728b, {6,12,12}*1728c, {6,12,12}*1728d, {2,12,12}*1728h, {6,12,12}*1728g, {6,4,12}*1728a, {2,4,12}*1728c, {2,4,12}*1728d, {2,12,12}*1728l
10-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
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 8)( 5,12)(10,17)(11,18)(13,21)(14,22);;
s2 := ( 3, 4)( 5, 9)( 6,11)( 7,10)( 8,16)(12,15)(13,20)(14,19)(17,26)(18,25)
(21,24)(22,23);;
s3 := ( 3, 6)( 4,13)( 5,10)( 8,21)( 9,19)(11,14)(12,17)(15,23)(16,25)(18,22);;
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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
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(26)!(1,2);
s1 := Sym(26)!( 4, 8)( 5,12)(10,17)(11,18)(13,21)(14,22);
s2 := Sym(26)!( 3, 4)( 5, 9)( 6,11)( 7,10)( 8,16)(12,15)(13,20)(14,19)(17,26)
(18,25)(21,24)(22,23);
s3 := Sym(26)!( 3, 6)( 4,13)( 5,10)( 8,21)( 9,19)(11,14)(12,17)(15,23)(16,25)
(18,22);
poly := sub<Sym(26)|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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, 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