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# Polytope of Type {2,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12}*384a
if this polytope has a name.
Group : SmallGroup(384,11260)
Rank : 4
Schlafli Type : {2,4,12}
Number of vertices, edges, etc : 2, 8, 48, 24
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 768
Vertex Figure Of :
{2,2,4,12} of size 768
{3,2,4,12} of size 1152
{5,2,4,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,12}*192a
3-fold quotients : {2,4,4}*128
4-fold quotients : {2,2,12}*96, {2,4,6}*96a
6-fold quotients : {2,4,4}*64
8-fold quotients : {2,2,6}*48
12-fold quotients : {2,2,4}*32, {2,4,2}*32
16-fold quotients : {2,2,3}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,8,12}*768a, {2,4,24}*768a, {4,4,12}*768b, {2,4,12}*768a, {2,4,24}*768b, {2,8,12}*768b
3-fold covers : {2,4,36}*1152a, {6,4,12}*1152a, {2,12,12}*1152a, {2,12,12}*1152b
5-fold covers : {2,4,60}*1920a, {10,4,12}*1920a, {2,20,12}*1920a
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,24)
(13,25)(14,26);;
s2 := ( 4, 5)( 7, 8)(10,11)(13,14)(15,21)(16,23)(17,22)(18,24)(19,26)(20,25);;
s3 := ( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,16)(18,19)(21,25)(22,24)(23,26);;
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, s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*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)!( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)
(12,24)(13,25)(14,26);
s2 := Sym(26)!( 4, 5)( 7, 8)(10,11)(13,14)(15,21)(16,23)(17,22)(18,24)(19,26)
(20,25);
s3 := Sym(26)!( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,16)(18,19)(21,25)(22,24)
(23,26);
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,
s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*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