# Polytope of Type {3,2,2,24}

Atlas Canonical Name : {3,2,2,24}*576
if this polytope has a name.
Group : SmallGroup(576,6554)
Rank : 5
Schlafli Type : {3,2,2,24}
Number of vertices, edges, etc : 3, 3, 2, 24, 24
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,2,2,24,2} of size 1152
Vertex Figure Of :
{2,3,2,2,24} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,2,12}*288
3-fold quotients : {3,2,2,8}*192
4-fold quotients : {3,2,2,6}*144
6-fold quotients : {3,2,2,4}*96
8-fold quotients : {3,2,2,3}*72
12-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,2,4,24}*1152a, {3,2,2,48}*1152, {6,2,2,24}*1152
3-fold covers : {3,2,2,72}*1728, {9,2,2,24}*1728, {3,2,6,24}*1728a, {3,2,6,24}*1728b, {3,6,2,24}*1728
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 7, 8)( 9,10)(11,14)(12,16)(13,15)(17,20)(18,22)(19,21)(24,27)(25,26)
(28,29);;
s4 := ( 6,12)( 7, 9)( 8,18)(10,13)(11,15)(14,24)(16,19)(17,21)(20,28)(22,25)
(23,26)(27,29);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(29)!(2,3);
s1 := Sym(29)!(1,2);
s2 := Sym(29)!(4,5);
s3 := Sym(29)!( 7, 8)( 9,10)(11,14)(12,16)(13,15)(17,20)(18,22)(19,21)(24,27)
(25,26)(28,29);
s4 := Sym(29)!( 6,12)( 7, 9)( 8,18)(10,13)(11,15)(14,24)(16,19)(17,21)(20,28)
(22,25)(23,26)(27,29);
poly := sub<Sym(29)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope