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# Polytope of Type {2,12,4}

Atlas Canonical Name : {2,12,4}*192c
if this polytope has a name.
Group : SmallGroup(192,1470)
Rank : 4
Schlafli Type : {2,12,4}
Number of vertices, edges, etc : 2, 12, 24, 4
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,12,4,2} of size 384
Vertex Figure Of :
{2,2,12,4} of size 384
{3,2,12,4} of size 576
{4,2,12,4} of size 768
{5,2,12,4} of size 960
{6,2,12,4} of size 1152
{7,2,12,4} of size 1344
{9,2,12,4} of size 1728
{10,2,12,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6,4}*96c
4-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,4}*384c, {2,12,4}*384b
3-fold covers : {2,36,4}*576c, {6,12,4}*576e, {6,12,4}*576g
4-fold covers : {2,12,4}*768c, {8,12,4}*768d, {4,12,4}*768e, {2,12,4}*768d, {2,12,8}*768e, {2,12,8}*768f, {2,24,4}*768c, {2,24,4}*768d, {4,12,4}*768p
5-fold covers : {10,12,4}*960c, {2,60,4}*960c
6-fold covers : {4,36,4}*1152c, {2,36,4}*1152b, {12,12,4}*1152e, {12,12,4}*1152g, {6,12,4}*1152e, {6,12,4}*1152f, {2,12,12}*1152d, {2,12,12}*1152e
7-fold covers : {14,12,4}*1344c, {2,84,4}*1344c
9-fold covers : {2,108,4}*1728c, {18,12,4}*1728d, {6,36,4}*1728d, {6,36,4}*1728f, {6,12,4}*1728e, {6,12,4}*1728g, {6,12,4}*1728m, {2,12,12}*1728n
10-fold covers : {20,12,4}*1920c, {4,60,4}*1920c, {10,12,4}*1920b, {2,12,20}*1920b, {2,60,4}*1920b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,18)(10,14)(11,13)(12,26)(15,31)(16,34)(17,19)(20,36)
(21,22)(23,39)(24,42)(25,32)(27,30)(28,46)(29,43)(33,45)(37,48)(38,40)(41,50)
(44,47);;
s2 := ( 3,10)( 4, 6)( 5,21)( 7,11)( 8,45)( 9,13)(12,36)(14,22)(15,50)(16,44)
(17,28)(18,27)(19,31)(20,25)(23,46)(24,35)(26,40)(29,49)(30,41)(32,39)(33,38)
(34,43)(37,47)(42,48);;
s3 := ( 3,49)( 4,47)( 5,44)( 6,50)( 7,41)( 8,39)( 9,35)(10,46)(11,33)(12,26)
(13,45)(14,28)(15,31)(16,40)(17,48)(18,23)(19,37)(20,22)(21,36)(24,32)(25,42)
(27,29)(30,43)(34,38);;
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*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1 ];;
poly := F / rels;;

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

```

to this polytope