# Polytope of Type {10,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,40}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240561)
Rank : 3
Schlafli Type : {10,40}
Number of vertices, edges, etc : 24, 480, 96
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {10,40}*960a, {10,40}*960b, {10,20}*960a
4-fold quotients : {10,20}*480a, {10,20}*480b, {10,10}*480
8-fold quotients : {5,10}*240, {10,5}*240, {10,10}*240a, {10,10}*240b, {10,10}*240c, {10,10}*240d
16-fold quotients : {5,5}*120, {5,10}*120a, {5,10}*120b, {10,5}*120a, {10,5}*120b
32-fold quotients : {5,5}*60
60-fold quotients : {2,8}*32
120-fold quotients : {2,4}*16
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(18,21)(19,20);;
s1 := ( 1,11)( 2, 9)( 3,15)( 4,13)( 5, 7)( 6,16)( 8,14)(10,12)(17,20)(19,21);;
s2 := ( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(18,19)(20,21);;
poly := Group([s0,s1,s2]);;

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

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

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

```
References : None.
to this polytope