# Polytope of Type {4,10,2,3}

Atlas Canonical Name : {4,10,2,3}*480
if this polytope has a name.
Group : SmallGroup(480,1097)
Rank : 5
Schlafli Type : {4,10,2,3}
Number of vertices, edges, etc : 4, 20, 10, 3, 3
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,10,2,3,2} of size 960
{4,10,2,3,3} of size 1920
{4,10,2,3,4} of size 1920
Vertex Figure Of :
{2,4,10,2,3} of size 960
{4,4,10,2,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,10,2,3}*240
4-fold quotients : {2,5,2,3}*120
5-fold quotients : {4,2,2,3}*96
10-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,20,2,3}*960, {8,10,2,3}*960, {4,10,2,6}*960
3-fold covers : {4,10,2,9}*1440, {12,10,2,3}*1440, {4,10,6,3}*1440, {4,30,2,3}*1440a
4-fold covers : {8,20,2,3}*1920a, {4,40,2,3}*1920a, {8,20,2,3}*1920b, {4,40,2,3}*1920b, {4,20,2,3}*1920, {16,10,2,3}*1920, {4,20,2,6}*1920, {4,10,4,6}*1920, {4,10,2,12}*1920, {8,10,2,6}*1920, {4,10,4,3}*1920
Permutation Representation (GAP) :
```s0 := ( 2, 5)( 6,11)( 7,12)(13,17)(14,18);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,16)(12,15)(17,20)(18,19);;
s2 := ( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)(10,15)(12,17)(16,19);;
s3 := (22,23);;
s4 := (21,22);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, 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(23)!( 2, 5)( 6,11)( 7,12)(13,17)(14,18);
s1 := Sym(23)!( 1, 2)( 3, 7)( 4, 6)( 5,10)( 8,14)( 9,13)(11,16)(12,15)(17,20)
(18,19);
s2 := Sym(23)!( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7,13)(10,15)(12,17)(16,19);
s3 := Sym(23)!(22,23);
s4 := Sym(23)!(21,22);
poly := sub<Sym(23)|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, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope