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# Polytope of Type {2,16,2}

Atlas Canonical Name : {2,16,2}*128
if this polytope has a name.
Group : SmallGroup(128,2140)
Rank : 4
Schlafli Type : {2,16,2}
Number of vertices, edges, etc : 2, 16, 16, 2
Order of s0s1s2s3 : 16
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,16,2,2} of size 256
{2,16,2,3} of size 384
{2,16,2,4} of size 512
{2,16,2,5} of size 640
{2,16,2,6} of size 768
{2,16,2,7} of size 896
{2,16,2,9} of size 1152
{2,16,2,10} of size 1280
{2,16,2,11} of size 1408
{2,16,2,13} of size 1664
{2,16,2,14} of size 1792
{2,16,2,15} of size 1920
Vertex Figure Of :
{2,2,16,2} of size 256
{3,2,16,2} of size 384
{4,2,16,2} of size 512
{5,2,16,2} of size 640
{6,2,16,2} of size 768
{7,2,16,2} of size 896
{9,2,16,2} of size 1152
{10,2,16,2} of size 1280
{11,2,16,2} of size 1408
{13,2,16,2} of size 1664
{14,2,16,2} of size 1792
{15,2,16,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,8,2}*64
4-fold quotients : {2,4,2}*32
8-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,16,4}*256a, {4,16,2}*256a, {2,32,2}*256
3-fold covers : {2,48,2}*384, {2,16,6}*384, {6,16,2}*384
4-fold covers : {2,16,4}*512a, {4,16,2}*512a, {2,16,8}*512c, {2,16,8}*512d, {8,16,2}*512c, {8,16,2}*512d, {4,16,4}*512a, {2,32,4}*512a, {4,32,2}*512a, {2,32,4}*512b, {4,32,2}*512b, {2,64,2}*512
5-fold covers : {2,80,2}*640, {2,16,10}*640, {10,16,2}*640
6-fold covers : {4,16,6}*768a, {6,16,4}*768a, {2,16,12}*768a, {12,16,2}*768a, {2,48,4}*768a, {4,48,2}*768a, {2,32,6}*768, {6,32,2}*768, {2,96,2}*768
7-fold covers : {2,112,2}*896, {2,16,14}*896, {14,16,2}*896
9-fold covers : {2,16,18}*1152, {18,16,2}*1152, {2,144,2}*1152, {6,16,6}*1152, {2,48,6}*1152a, {6,48,2}*1152a, {2,48,6}*1152b, {2,48,6}*1152c, {6,48,2}*1152b, {6,48,2}*1152c, {2,16,6}*1152, {6,16,2}*1152
10-fold covers : {4,16,10}*1280a, {10,16,4}*1280a, {2,16,20}*1280a, {20,16,2}*1280a, {2,80,4}*1280a, {4,80,2}*1280a, {2,32,10}*1280, {10,32,2}*1280, {2,160,2}*1280
11-fold covers : {2,16,22}*1408, {22,16,2}*1408, {2,176,2}*1408
13-fold covers : {2,16,26}*1664, {26,16,2}*1664, {2,208,2}*1664
14-fold covers : {4,16,14}*1792a, {14,16,4}*1792a, {2,16,28}*1792a, {28,16,2}*1792a, {2,112,4}*1792a, {4,112,2}*1792a, {2,32,14}*1792, {14,32,2}*1792, {2,224,2}*1792
15-fold covers : {2,16,30}*1920, {30,16,2}*1920, {2,240,2}*1920, {6,16,10}*1920, {10,16,6}*1920, {2,48,10}*1920, {10,48,2}*1920, {2,80,6}*1920, {6,80,2}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s3 := (19,20);;
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,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(20)!(1,2);
s1 := Sym(20)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);
s2 := Sym(20)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
s3 := Sym(20)!(19,20);
poly := sub<Sym(20)|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, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope