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# Polytope of Type {5,2,2,4}

Atlas Canonical Name : {5,2,2,4}*160
if this polytope has a name.
Group : SmallGroup(160,217)
Rank : 5
Schlafli Type : {5,2,2,4}
Number of vertices, edges, etc : 5, 5, 2, 4, 4
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{5,2,2,4,2} of size 320
{5,2,2,4,3} of size 480
{5,2,2,4,4} of size 640
{5,2,2,4,6} of size 960
{5,2,2,4,3} of size 960
{5,2,2,4,6} of size 960
{5,2,2,4,6} of size 960
{5,2,2,4,8} of size 1280
{5,2,2,4,8} of size 1280
{5,2,2,4,4} of size 1280
{5,2,2,4,9} of size 1440
{5,2,2,4,4} of size 1440
{5,2,2,4,6} of size 1440
{5,2,2,4,10} of size 1600
{5,2,2,4,12} of size 1920
{5,2,2,4,12} of size 1920
{5,2,2,4,12} of size 1920
{5,2,2,4,6} of size 1920
Vertex Figure Of :
{2,5,2,2,4} of size 320
{3,5,2,2,4} of size 960
{5,5,2,2,4} of size 960
{10,5,2,2,4} of size 1600
{4,5,2,2,4} of size 1920
{6,5,2,2,4} of size 1920
{3,5,2,2,4} of size 1920
{5,5,2,2,4} of size 1920
{6,5,2,2,4} of size 1920
{6,5,2,2,4} of size 1920
{10,5,2,2,4} of size 1920
{10,5,2,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,2,4,4}*320, {5,2,2,8}*320, {10,2,2,4}*320
3-fold covers : {5,2,2,12}*480, {5,2,6,4}*480a, {15,2,2,4}*480
4-fold covers : {5,2,4,8}*640a, {5,2,8,4}*640a, {5,2,4,8}*640b, {5,2,8,4}*640b, {5,2,4,4}*640, {5,2,2,16}*640, {20,2,2,4}*640, {10,2,4,4}*640, {10,4,2,4}*640, {10,2,2,8}*640
5-fold covers : {25,2,2,4}*800, {5,2,2,20}*800, {5,2,10,4}*800, {5,10,2,4}*800
6-fold covers : {5,2,4,12}*960a, {5,2,12,4}*960a, {5,2,2,24}*960, {5,2,6,8}*960, {15,2,4,4}*960, {15,2,2,8}*960, {10,2,2,12}*960, {10,2,6,4}*960a, {10,6,2,4}*960, {30,2,2,4}*960
7-fold covers : {5,2,2,28}*1120, {5,2,14,4}*1120, {35,2,2,4}*1120
8-fold covers : {5,2,4,8}*1280a, {5,2,8,4}*1280a, {5,2,8,8}*1280a, {5,2,8,8}*1280b, {5,2,8,8}*1280c, {5,2,8,8}*1280d, {5,2,4,16}*1280a, {5,2,16,4}*1280a, {5,2,4,16}*1280b, {5,2,16,4}*1280b, {5,2,4,4}*1280, {5,2,4,8}*1280b, {5,2,8,4}*1280b, {5,2,2,32}*1280, {10,4,4,4}*1280, {20,2,4,4}*1280, {20,4,2,4}*1280, {10,2,4,8}*1280a, {10,2,8,4}*1280a, {10,2,4,8}*1280b, {10,2,8,4}*1280b, {10,2,4,4}*1280, {10,4,2,8}*1280, {10,8,2,4}*1280, {20,2,2,8}*1280, {40,2,2,4}*1280, {10,2,2,16}*1280
9-fold covers : {5,2,2,36}*1440, {5,2,18,4}*1440a, {45,2,2,4}*1440, {5,2,6,12}*1440a, {5,2,6,12}*1440b, {5,2,6,12}*1440c, {15,2,2,12}*1440, {15,2,6,4}*1440a, {15,6,2,4}*1440, {5,2,6,4}*1440
10-fold covers : {25,2,4,4}*1600, {25,2,2,8}*1600, {50,2,2,4}*1600, {5,2,4,20}*1600, {5,2,20,4}*1600, {5,2,2,40}*1600, {5,2,10,8}*1600, {5,10,2,8}*1600, {5,10,4,4}*1600, {10,2,2,20}*1600, {10,2,10,4}*1600, {10,10,2,4}*1600a, {10,10,2,4}*1600c
11-fold covers : {5,2,2,44}*1760, {5,2,22,4}*1760, {55,2,2,4}*1760
12-fold covers : {15,2,4,8}*1920a, {15,2,8,4}*1920a, {5,2,8,12}*1920a, {5,2,12,8}*1920a, {5,2,4,24}*1920a, {5,2,24,4}*1920a, {15,2,4,8}*1920b, {15,2,8,4}*1920b, {5,2,8,12}*1920b, {5,2,12,8}*1920b, {5,2,4,24}*1920b, {5,2,24,4}*1920b, {15,2,4,4}*1920, {5,2,4,12}*1920a, {5,2,12,4}*1920a, {15,2,2,16}*1920, {5,2,6,16}*1920, {5,2,2,48}*1920, {30,2,4,4}*1920, {10,6,4,4}*1920, {10,2,4,12}*1920a, {10,2,12,4}*1920a, {30,4,2,4}*1920a, {60,2,2,4}*1920, {10,4,6,4}*1920a, {10,4,2,12}*1920, {10,12,2,4}*1920, {20,2,6,4}*1920a, {20,6,2,4}*1920a, {20,2,2,12}*1920, {30,2,2,8}*1920, {10,2,6,8}*1920, {10,6,2,8}*1920, {10,2,2,24}*1920, {5,2,4,12}*1920b, {5,2,6,4}*1920b, {5,2,6,12}*1920a, {15,6,2,4}*1920, {15,4,2,4}*1920
Permutation Representation (GAP) :
```s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
s3 := ( 9,10);;
s4 := ( 8, 9)(10,11);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(11)!(2,3)(4,5);
s1 := Sym(11)!(1,2)(3,4);
s2 := Sym(11)!(6,7);
s3 := Sym(11)!( 9,10);
s4 := Sym(11)!( 8, 9)(10,11);
poly := sub<Sym(11)|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, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope