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# Polytope of Type {2,3,8}

Atlas Canonical Name : {2,3,8}*192
if this polytope has a name.
Group : SmallGroup(192,1481)
Rank : 4
Schlafli Type : {2,3,8}
Number of vertices, edges, etc : 2, 6, 24, 16
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,3,8,2} of size 384
{2,3,8,4} of size 768
{2,3,8,6} of size 1152
{2,3,8,10} of size 1920
Vertex Figure Of :
{2,2,3,8} of size 384
{3,2,3,8} of size 576
{4,2,3,8} of size 768
{5,2,3,8} of size 960
{6,2,3,8} of size 1152
{7,2,3,8} of size 1344
{9,2,3,8} of size 1728
{10,2,3,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3,4}*96
4-fold quotients : {2,3,4}*48
8-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,6,8}*384b
3-fold covers : {2,9,8}*576, {2,3,24}*576, {6,3,8}*576
4-fold covers : {2,3,8}*768, {2,12,8}*768e, {2,6,8}*768f, {2,12,8}*768h, {4,6,8}*768c, {4,3,8}*768b
5-fold covers : {2,15,8}*960
6-fold covers : {2,18,8}*1152b, {2,6,24}*1152b, {6,6,8}*1152b, {6,6,8}*1152c, {2,6,24}*1152e
7-fold covers : {2,21,8}*1344
9-fold covers : {2,27,8}*1728, {2,9,24}*1728, {2,3,24}*1728, {6,9,8}*1728, {6,3,8}*1728, {6,3,24}*1728
10-fold covers : {10,6,8}*1920a, {2,6,40}*1920c, {2,30,8}*1920b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)(18,40)
(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)(38,50)
(41,42);;
s2 := ( 3, 6)( 4,15)( 5,11)( 8,44)( 9,43)(10,27)(12,16)(13,49)(14,50)(17,42)
(18,41)(19,26)(20,23)(21,22)(24,25)(29,46)(30,48)(31,35)(32,38)(33,34)(36,37)
(39,40);;
s3 := ( 3,46)( 4,42)( 5,41)( 6,49)( 7,35)( 8,36)( 9,33)(10,48)(11,44)(12,26)
(13,24)(14,21)(15,43)(16,23)(17,37)(18,34)(19,47)(20,45)(22,29)(25,30)(27,50)
(28,38)(31,40)(32,39);;
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*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)
(18,40)(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)
(38,50)(41,42);
s2 := Sym(50)!( 3, 6)( 4,15)( 5,11)( 8,44)( 9,43)(10,27)(12,16)(13,49)(14,50)
(17,42)(18,41)(19,26)(20,23)(21,22)(24,25)(29,46)(30,48)(31,35)(32,38)(33,34)
(36,37)(39,40);
s3 := Sym(50)!( 3,46)( 4,42)( 5,41)( 6,49)( 7,35)( 8,36)( 9,33)(10,48)(11,44)
(12,26)(13,24)(14,21)(15,43)(16,23)(17,37)(18,34)(19,47)(20,45)(22,29)(25,30)
(27,50)(28,38)(31,40)(32,39);
poly := sub<Sym(50)|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*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 >;

```

to this polytope