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# Polytope of Type {24,2,6}

Atlas Canonical Name : {24,2,6}*576
if this polytope has a name.
Group : SmallGroup(576,6554)
Rank : 4
Schlafli Type : {24,2,6}
Number of vertices, edges, etc : 24, 24, 6, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{24,2,6,2} of size 1152
{24,2,6,3} of size 1728
Vertex Figure Of :
{2,24,2,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {24,2,3}*288, {12,2,6}*288
3-fold quotients : {24,2,2}*192, {8,2,6}*192
4-fold quotients : {12,2,3}*144, {6,2,6}*144
6-fold quotients : {8,2,3}*96, {12,2,2}*96, {4,2,6}*96
8-fold quotients : {3,2,6}*72, {6,2,3}*72
9-fold quotients : {8,2,2}*64
12-fold quotients : {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
16-fold quotients : {3,2,3}*36
18-fold quotients : {4,2,2}*32
24-fold quotients : {2,2,3}*24, {3,2,2}*24
36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,4,6}*1152a, {24,2,12}*1152, {48,2,6}*1152
3-fold covers : {72,2,6}*1728, {24,2,18}*1728, {24,6,6}*1728a, {24,6,6}*1728b, {24,6,6}*1728d, {24,6,6}*1728e
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(19,22)(20,21)
(23,24);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,23)(17,20)
(18,21)(22,24);;
s2 := (27,28)(29,30);;
s3 := (25,29)(26,27)(28,30);;
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*s2*s3*s2*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*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(30)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,15)(13,17)(14,16)(19,22)
(20,21)(23,24);
s1 := Sym(30)!( 1, 7)( 2, 4)( 3,13)( 5, 8)( 6,10)( 9,19)(11,14)(12,16)(15,23)
(17,20)(18,21)(22,24);
s2 := Sym(30)!(27,28)(29,30);
s3 := Sym(30)!(25,29)(26,27)(28,30);
poly := sub<Sym(30)|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*s2*s3*s2*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*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