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# Polytope of Type {4,40}

Atlas Canonical Name : {4,40}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240580)
Rank : 3
Schlafli Type : {4,40}
Number of vertices, edges, etc : 24, 480, 240
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 : {4,20}*960c
4-fold quotients : {4,10}*480c
8-fold quotients : {4,5}*240, {4,10}*240a, {4,10}*240b
16-fold quotients : {4,5}*120
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 := ( 3, 5)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)
(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);;
s1 := ( 2, 3)( 4, 5)( 6,22)( 7,23)( 8,25)( 9,24)(10,27)(11,26)(12,28)(13,29)
(14,32)(15,33)(16,30)(17,31)(18,37)(19,36)(20,35)(21,34);;
s2 := ( 1, 2)( 3, 5)( 6,18)( 7,19)( 8,21)( 9,20)(10,14)(11,15)(12,17)(13,16)
(22,34)(23,35)(24,37)(25,36)(26,30)(27,31)(28,33)(29,32);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s2*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(37)!( 3, 5)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)
(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);
s1 := Sym(37)!( 2, 3)( 4, 5)( 6,22)( 7,23)( 8,25)( 9,24)(10,27)(11,26)(12,28)
(13,29)(14,32)(15,33)(16,30)(17,31)(18,37)(19,36)(20,35)(21,34);
s2 := Sym(37)!( 1, 2)( 3, 5)( 6,18)( 7,19)( 8,21)( 9,20)(10,14)(11,15)(12,17)
(13,16)(22,34)(23,35)(24,37)(25,36)(26,30)(27,31)(28,33)(29,32);
poly := sub<Sym(37)|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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s2*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0 >;

```
References : None.
to this polytope