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

Atlas Canonical Name : {2,4,2,4}*128
if this polytope has a name.
Group : SmallGroup(128,2194)
Rank : 5
Schlafli Type : {2,4,2,4}
Number of vertices, edges, etc : 2, 4, 4, 4, 4
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,2,4,2} of size 256
{2,4,2,4,3} of size 384
{2,4,2,4,4} of size 512
{2,4,2,4,6} of size 768
{2,4,2,4,3} of size 768
{2,4,2,4,6} of size 768
{2,4,2,4,6} of size 768
{2,4,2,4,4} of size 1152
{2,4,2,4,6} of size 1152
{2,4,2,4,9} of size 1152
{2,4,2,4,10} of size 1280
{2,4,2,4,14} of size 1792
{2,4,2,4,15} of size 1920
{2,4,2,4,5} of size 1920
{2,4,2,4,6} of size 1920
Vertex Figure Of :
{2,2,4,2,4} of size 256
{3,2,4,2,4} of size 384
{5,2,4,2,4} of size 640
{6,2,4,2,4} of size 768
{7,2,4,2,4} of size 896
{9,2,4,2,4} of size 1152
{10,2,4,2,4} of size 1280
{11,2,4,2,4} of size 1408
{13,2,4,2,4} of size 1664
{14,2,4,2,4} of size 1792
{15,2,4,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
4-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,4,4,4}*256, {4,4,2,4}*256, {2,4,2,8}*256, {2,8,2,4}*256
3-fold covers : {2,4,2,12}*384, {2,12,2,4}*384, {2,4,6,4}*384a, {6,4,2,4}*384a
4-fold covers : {4,4,4,4}*512, {2,8,2,8}*512, {2,4,8,4}*512a, {2,4,8,4}*512b, {2,4,8,4}*512c, {2,4,8,4}*512d, {2,4,4,8}*512a, {2,8,4,4}*512a, {2,4,4,8}*512b, {2,8,4,4}*512b, {2,4,4,4}*512a, {2,4,4,4}*512b, {2,4,2,16}*512, {2,16,2,4}*512
5-fold covers : {2,4,2,20}*640, {2,20,2,4}*640, {2,4,10,4}*640, {10,4,2,4}*640
6-fold covers : {6,4,4,4}*768, {2,4,4,12}*768, {2,12,4,4}*768, {2,4,12,4}*768a, {4,4,6,4}*768a, {4,4,2,12}*768, {4,12,2,4}*768a, {12,4,2,4}*768a, {6,4,2,8}*768a, {6,8,2,4}*768, {2,4,6,8}*768a, {2,8,6,4}*768a, {2,8,2,12}*768, {2,12,2,8}*768, {2,4,2,24}*768, {2,24,2,4}*768
7-fold covers : {2,4,2,28}*896, {2,28,2,4}*896, {2,4,14,4}*896, {14,4,2,4}*896
9-fold covers : {18,4,2,4}*1152a, {2,4,18,4}*1152a, {2,4,2,36}*1152, {2,36,2,4}*1152, {6,4,6,4}*1152a, {6,12,2,4}*1152a, {6,4,2,12}*1152a, {6,12,2,4}*1152b, {6,12,2,4}*1152c, {2,4,6,12}*1152a, {2,12,6,4}*1152a, {2,4,6,12}*1152b, {2,12,6,4}*1152b, {2,4,6,12}*1152c, {2,12,6,4}*1152c, {2,12,2,12}*1152, {2,4,6,4}*1152a, {2,4,6,4}*1152b, {6,4,2,4}*1152
10-fold covers : {10,4,4,4}*1280, {2,4,4,20}*1280, {2,20,4,4}*1280, {2,4,20,4}*1280, {4,4,10,4}*1280, {4,4,2,20}*1280, {4,20,2,4}*1280, {20,4,2,4}*1280, {10,4,2,8}*1280, {10,8,2,4}*1280, {2,4,10,8}*1280, {2,8,10,4}*1280, {2,8,2,20}*1280, {2,20,2,8}*1280, {2,4,2,40}*1280, {2,40,2,4}*1280
11-fold covers : {22,4,2,4}*1408, {2,4,22,4}*1408, {2,4,2,44}*1408, {2,44,2,4}*1408
13-fold covers : {26,4,2,4}*1664, {2,4,26,4}*1664, {2,4,2,52}*1664, {2,52,2,4}*1664
14-fold covers : {14,4,4,4}*1792, {2,4,4,28}*1792, {2,28,4,4}*1792, {2,4,28,4}*1792, {4,4,14,4}*1792, {4,4,2,28}*1792, {4,28,2,4}*1792, {28,4,2,4}*1792, {14,4,2,8}*1792, {14,8,2,4}*1792, {2,4,14,8}*1792, {2,8,14,4}*1792, {2,8,2,28}*1792, {2,28,2,8}*1792, {2,4,2,56}*1792, {2,56,2,4}*1792
15-fold covers : {30,4,2,4}*1920a, {2,4,30,4}*1920a, {2,4,2,60}*1920, {2,60,2,4}*1920, {10,4,6,4}*1920a, {6,4,10,4}*1920, {10,4,2,12}*1920, {10,12,2,4}*1920, {6,4,2,20}*1920a, {6,20,2,4}*1920a, {2,4,10,12}*1920, {2,12,10,4}*1920, {2,4,6,20}*1920a, {2,20,6,4}*1920a, {2,12,2,20}*1920, {2,20,2,12}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4)(5,6);;
s3 := (8,9);;
s4 := ( 7, 8)( 9,10);;
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,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

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

```

to this polytope