# Polytope of Type {6,4,10,2}

Atlas Canonical Name : {6,4,10,2}*960
if this polytope has a name.
Group : SmallGroup(960,11219)
Rank : 5
Schlafli Type : {6,4,10,2}
Number of vertices, edges, etc : 6, 12, 20, 10, 2
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,4,10,2,2} of size 1920
Vertex Figure Of :
{2,6,4,10,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,2,10,2}*480
3-fold quotients : {2,4,10,2}*320
4-fold quotients : {3,2,10,2}*240, {6,2,5,2}*240
5-fold quotients : {6,4,2,2}*192a
6-fold quotients : {2,2,10,2}*160
8-fold quotients : {3,2,5,2}*120
10-fold quotients : {6,2,2,2}*96
12-fold quotients : {2,2,5,2}*80
15-fold quotients : {2,4,2,2}*64
20-fold quotients : {3,2,2,2}*48
30-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,4,10,2}*1920, {6,4,20,2}*1920, {6,4,10,4}*1920, {6,8,10,2}*1920
Permutation Representation (GAP) :
```s0 := ( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(21,26)(22,27)(23,28)(24,29)(25,30)
(36,41)(37,42)(38,43)(39,44)(40,45)(51,56)(52,57)(53,58)(54,59)(55,60);;
s1 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(16,21)(17,22)(18,23)(19,24)(20,25)
(31,51)(32,52)(33,53)(34,54)(35,55)(36,46)(37,47)(38,48)(39,49)(40,50)(41,56)
(42,57)(43,58)(44,59)(45,60);;
s2 := ( 1,31)( 2,35)( 3,34)( 4,33)( 5,32)( 6,36)( 7,40)( 8,39)( 9,38)(10,37)
(11,41)(12,45)(13,44)(14,43)(15,42)(16,46)(17,50)(18,49)(19,48)(20,47)(21,51)
(22,55)(23,54)(24,53)(25,52)(26,56)(27,60)(28,59)(29,58)(30,57);;
s3 := ( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)(23,25)
(26,27)(28,30)(31,32)(33,35)(36,37)(38,40)(41,42)(43,45)(46,47)(48,50)(51,52)
(53,55)(56,57)(58,60);;
s4 := (61,62);;
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, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(62)!( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(21,26)(22,27)(23,28)(24,29)
(25,30)(36,41)(37,42)(38,43)(39,44)(40,45)(51,56)(52,57)(53,58)(54,59)(55,60);
s1 := Sym(62)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(16,21)(17,22)(18,23)(19,24)
(20,25)(31,51)(32,52)(33,53)(34,54)(35,55)(36,46)(37,47)(38,48)(39,49)(40,50)
(41,56)(42,57)(43,58)(44,59)(45,60);
s2 := Sym(62)!( 1,31)( 2,35)( 3,34)( 4,33)( 5,32)( 6,36)( 7,40)( 8,39)( 9,38)
(10,37)(11,41)(12,45)(13,44)(14,43)(15,42)(16,46)(17,50)(18,49)(19,48)(20,47)
(21,51)(22,55)(23,54)(24,53)(25,52)(26,56)(27,60)(28,59)(29,58)(30,57);
s3 := Sym(62)!( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)
(23,25)(26,27)(28,30)(31,32)(33,35)(36,37)(38,40)(41,42)(43,45)(46,47)(48,50)
(51,52)(53,55)(56,57)(58,60);
s4 := Sym(62)!(61,62);
poly := sub<Sym(62)|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, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope