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

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

```

to this polytope