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# Polytope of Type {4,12,2}

Atlas Canonical Name : {4,12,2}*192b
if this polytope has a name.
Group : SmallGroup(192,1470)
Rank : 4
Schlafli Type : {4,12,2}
Number of vertices, edges, etc : 4, 24, 12, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,12,2,2} of size 384
{4,12,2,3} of size 576
{4,12,2,4} of size 768
{4,12,2,5} of size 960
{4,12,2,6} of size 1152
{4,12,2,7} of size 1344
{4,12,2,9} of size 1728
{4,12,2,10} of size 1920
Vertex Figure Of :
{2,4,12,2} of size 384
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6,2}*96c
4-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,4}*384d, {4,24,2}*384c, {4,24,2}*384d, {4,12,2}*384b
3-fold covers : {4,36,2}*576b, {4,12,6}*576d, {4,12,6}*576e
4-fold covers : {4,12,2}*768b, {4,24,4}*768g, {4,24,4}*768h, {4,12,4}*768d, {4,24,4}*768k, {4,24,4}*768l, {4,12,8}*768c, {4,12,8}*768e, {4,48,2}*768c, {4,48,2}*768d, {4,12,4}*768f, {4,12,2}*768d, {8,12,2}*768e, {8,12,2}*768f, {4,24,2}*768c, {4,24,2}*768d, {4,12,4}*768m
5-fold covers : {4,12,10}*960b, {4,60,2}*960b
6-fold covers : {4,36,4}*1152d, {4,72,2}*1152c, {4,72,2}*1152d, {4,36,2}*1152b, {4,24,6}*1152g, {4,24,6}*1152h, {4,24,6}*1152i, {4,24,6}*1152j, {4,12,12}*1152d, {4,12,12}*1152e, {4,12,6}*1152e, {4,12,6}*1152f, {12,12,2}*1152f, {12,12,2}*1152g
7-fold covers : {4,12,14}*1344b, {4,84,2}*1344b
9-fold covers : {4,108,2}*1728b, {4,12,18}*1728c, {4,36,6}*1728c, {4,36,6}*1728d, {4,12,6}*1728d, {4,12,6}*1728e, {4,12,6}*1728l, {4,12,6}*1728r
10-fold covers : {4,24,10}*1920c, {4,24,10}*1920d, {4,12,20}*1920b, {4,60,4}*1920d, {4,120,2}*1920c, {4,120,2}*1920d, {4,12,10}*1920b, {20,12,2}*1920b, {4,60,2}*1920b
Permutation Representation (GAP) :
```s0 := ( 1, 6)( 2,10)( 3,13)( 4,14)( 5,15)( 7,21)( 8,22)( 9,23)(11,27)(12,28)
(16,33)(17,34)(18,32)(19,35)(20,36)(24,45)(25,43)(26,41)(29,42)(30,44)(31,40)
(37,47)(38,48)(39,46);;
s1 := ( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)
(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)
(42,45);;
s2 := ( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)(14,22)
(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)(33,41)
(38,44)(40,47)(45,46);;
s3 := (49,50);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1,
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(50)!( 1, 6)( 2,10)( 3,13)( 4,14)( 5,15)( 7,21)( 8,22)( 9,23)(11,27)
(12,28)(16,33)(17,34)(18,32)(19,35)(20,36)(24,45)(25,43)(26,41)(29,42)(30,44)
(31,40)(37,47)(38,48)(39,46);
s1 := Sym(50)!( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)
(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)
(39,48)(42,45);
s2 := Sym(50)!( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)
(14,22)(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)
(33,41)(38,44)(40,47)(45,46);
s3 := Sym(50)!(49,50);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, 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