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# Polytope of Type {12,4,2}

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

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

```

to this polytope