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# Polytope of Type {12,4,2}

Atlas Canonical Name : {12,4,2}*192a
if this polytope has a name.
Group : SmallGroup(192,1046)
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
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
{3,12,4,2} of size 768
{6,12,4,2} of size 1152
{6,12,4,2} of size 1152
{6,12,4,2} of size 1152
{3,12,4,2} of size 1152
{6,12,4,2} of size 1728
{6,12,4,2} of size 1728
{6,12,4,2} of size 1728
{10,12,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,2,2}*96, {6,4,2}*96a
3-fold quotients : {4,4,2}*64
4-fold quotients : {6,2,2}*48
6-fold quotients : {2,4,2}*32, {4,2,2}*32
8-fold quotients : {3,2,2}*24
12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,4,4}*384, {24,4,2}*384a, {12,4,2}*384a, {24,4,2}*384b, {12,8,2}*384a, {12,8,2}*384b
3-fold covers : {36,4,2}*576a, {12,4,6}*576, {12,12,2}*576a, {12,12,2}*576c
4-fold covers : {12,8,2}*768a, {24,4,2}*768a, {24,8,2}*768a, {24,8,2}*768b, {24,8,2}*768c, {24,8,2}*768d, {12,4,8}*768a, {24,4,4}*768a, {12,4,8}*768b, {24,4,4}*768b, {12,8,4}*768a, {12,4,4}*768a, {12,4,4}*768b, {12,8,4}*768b, {12,8,4}*768c, {12,8,4}*768d, {12,16,2}*768a, {48,4,2}*768a, {12,16,2}*768b, {48,4,2}*768b, {12,4,2}*768a, {24,4,2}*768b, {12,8,2}*768b, {12,4,2}*768d
5-fold covers : {12,4,10}*960, {12,20,2}*960, {60,4,2}*960a
6-fold covers : {36,4,4}*1152, {12,12,4}*1152b, {12,12,4}*1152c, {12,4,12}*1152, {36,8,2}*1152a, {72,4,2}*1152a, {12,8,6}*1152a, {24,4,6}*1152a, {12,24,2}*1152a, {24,12,2}*1152a, {24,12,2}*1152b, {12,24,2}*1152c, {36,8,2}*1152b, {72,4,2}*1152b, {12,8,6}*1152b, {24,4,6}*1152b, {12,24,2}*1152d, {24,12,2}*1152d, {24,12,2}*1152e, {12,24,2}*1152f, {36,4,2}*1152a, {12,4,6}*1152a, {12,12,2}*1152a, {12,12,2}*1152c
7-fold covers : {12,4,14}*1344, {12,28,2}*1344, {84,4,2}*1344a
9-fold covers : {108,4,2}*1728a, {12,4,18}*1728, {36,4,6}*1728, {12,12,6}*1728a, {12,36,2}*1728a, {36,12,2}*1728a, {36,12,2}*1728b, {12,12,2}*1728a, {12,12,2}*1728c, {12,12,6}*1728b, {12,12,6}*1728d, {12,12,6}*1728f, {12,12,2}*1728h, {12,12,6}*1728g, {12,4,6}*1728a, {12,4,2}*1728c, {12,4,2}*1728d, {12,12,2}*1728k
10-fold covers : {60,4,4}*1920, {12,20,4}*1920, {12,4,20}*1920, {60,8,2}*1920a, {120,4,2}*1920a, {12,8,10}*1920a, {24,4,10}*1920a, {12,40,2}*1920a, {24,20,2}*1920a, {60,8,2}*1920b, {120,4,2}*1920b, {12,8,10}*1920b, {24,4,10}*1920b, {12,40,2}*1920b, {24,20,2}*1920b, {60,4,2}*1920a, {12,4,10}*1920a, {12,20,2}*1920a
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 6,10)( 8,12)( 9,11)(15,20)(16,19)(17,18)(21,22)(23,24);;
s1 := ( 1, 8)( 2, 4)( 3,17)( 5, 9)( 6,23)( 7,11)(10,21)(12,18)(13,19)(14,15)
(16,24)(20,22);;
s2 := ( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);;
s3 := (25,26);;
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
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(26)!( 2, 3)( 4, 5)( 6,10)( 8,12)( 9,11)(15,20)(16,19)(17,18)(21,22)
(23,24);
s1 := Sym(26)!( 1, 8)( 2, 4)( 3,17)( 5, 9)( 6,23)( 7,11)(10,21)(12,18)(13,19)
(14,15)(16,24)(20,22);
s2 := Sym(26)!( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);
s3 := Sym(26)!(25,26);
poly := sub<Sym(26)|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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, 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