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

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

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

```

to this polytope