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# Polytope of Type {2,6,20}

Atlas Canonical Name : {2,6,20}*480a
if this polytope has a name.
Group : SmallGroup(480,1088)
Rank : 4
Schlafli Type : {2,6,20}
Number of vertices, edges, etc : 2, 6, 60, 20
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,20,2} of size 960
{2,6,20,4} of size 1920
Vertex Figure Of :
{2,2,6,20} of size 960
{3,2,6,20} of size 1440
{4,2,6,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,10}*240
3-fold quotients : {2,2,20}*160
5-fold quotients : {2,6,4}*96a
6-fold quotients : {2,2,10}*80
10-fold quotients : {2,6,2}*48
12-fold quotients : {2,2,5}*40
15-fold quotients : {2,2,4}*32
20-fold quotients : {2,3,2}*24
30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,6,20}*960a, {2,6,40}*960, {2,12,20}*960
3-fold covers : {2,18,20}*1440a, {6,6,20}*1440a, {6,6,20}*1440b, {2,6,60}*1440a, {2,6,60}*1440b
4-fold covers : {4,12,20}*1920a, {2,12,40}*1920a, {2,24,20}*1920a, {2,12,40}*1920b, {2,24,20}*1920b, {2,12,20}*1920a, {8,6,20}*1920, {4,6,40}*1920a, {2,6,80}*1920, {4,6,20}*1920a, {2,6,20}*1920a
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 8,13)( 9,14)(10,15)(11,16)(12,17)(23,28)(24,29)(25,30)(26,31)(27,32)
(38,43)(39,44)(40,45)(41,46)(42,47)(53,58)(54,59)(55,60)(56,61)(57,62);;
s2 := ( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(14,17)(15,16)(18,23)(19,27)(20,26)
(21,25)(22,24)(29,32)(30,31)(33,53)(34,57)(35,56)(36,55)(37,54)(38,48)(39,52)
(40,51)(41,50)(42,49)(43,58)(44,62)(45,61)(46,60)(47,59);;
s3 := ( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,39)( 9,38)(10,42)(11,41)(12,40)
(13,44)(14,43)(15,47)(16,46)(17,45)(18,49)(19,48)(20,52)(21,51)(22,50)(23,54)
(24,53)(25,57)(26,56)(27,55)(28,59)(29,58)(30,62)(31,61)(32,60);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)!(1,2);
s1 := Sym(62)!( 8,13)( 9,14)(10,15)(11,16)(12,17)(23,28)(24,29)(25,30)(26,31)
(27,32)(38,43)(39,44)(40,45)(41,46)(42,47)(53,58)(54,59)(55,60)(56,61)(57,62);
s2 := Sym(62)!( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(14,17)(15,16)(18,23)(19,27)
(20,26)(21,25)(22,24)(29,32)(30,31)(33,53)(34,57)(35,56)(36,55)(37,54)(38,48)
(39,52)(40,51)(41,50)(42,49)(43,58)(44,62)(45,61)(46,60)(47,59);
s3 := Sym(62)!( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,39)( 9,38)(10,42)(11,41)
(12,40)(13,44)(14,43)(15,47)(16,46)(17,45)(18,49)(19,48)(20,52)(21,51)(22,50)
(23,54)(24,53)(25,57)(26,56)(27,55)(28,59)(29,58)(30,62)(31,61)(32,60);
poly := sub<Sym(62)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope