# Polytope of Type {10,10,4}

Atlas Canonical Name : {10,10,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240595)
Rank : 4
Schlafli Type : {10,10,4}
Number of vertices, edges, etc : 24, 120, 48, 4
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,10,4}*960, {10,10,4}*960a, {10,10,4}*960b, {10,10,2}*960
4-fold quotients : {5,10,4}*480, {5,10,2}*480, {10,5,2}*480, {10,10,2}*480a, {10,10,2}*480b, {10,10,2}*480c, {10,10,2}*480d
8-fold quotients : {5,5,2}*240, {5,10,2}*240a, {5,10,2}*240b, {10,5,2}*240a, {10,5,2}*240b
16-fold quotients : {5,5,2}*120
60-fold quotients : {2,2,4}*32
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1, 7)( 2, 4)( 3,16)( 5,10)( 6,11)( 8, 9)(12,13)(14,15)(18,21)(19,20);;
s1 := ( 1,16)( 2, 9)( 3, 7)( 4, 8)( 5,11)( 6,10)(12,15)(13,14)(17,21)(18,20);;
s2 := ( 1, 6)( 2,14)( 3, 5)( 4,15)( 7,11)( 8,12)( 9,13)(10,16)(18,19)(20,21);;
s3 := ( 1,15)( 2, 9)( 3,13)( 4, 8)( 5,11)( 6,10)( 7,14)(12,16);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope