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# Polytope of Type {12,4}

Atlas Canonical Name : {12,4}*192c
if this polytope has a name.
Group : SmallGroup(192,1472)
Rank : 3
Schlafli Type : {12,4}
Number of vertices, edges, etc : 24, 48, 8
Order of s0s1s2 : 6
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{12,4,2} of size 384
{12,4,4} of size 768
{12,4,6} of size 1152
{12,4,10} of size 1920
Vertex Figure Of :
{2,12,4} of size 384
{3,12,4} of size 768
{3,12,4} of size 768
{4,12,4} of size 768
{4,12,4} of size 768
{4,12,4} of size 768
{6,12,4} of size 1152
{6,12,4} of size 1152
{10,12,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,4}*96
4-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
8-fold quotients : {3,4}*24, {6,2}*24
16-fold quotients : {3,2}*12
24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,4}*384d, {12,8}*384g, {12,8}*384h, {24,4}*384e, {24,4}*384f
3-fold covers : {36,4}*576c, {12,12}*576h, {12,12}*576j
4-fold covers : {24,8}*768m, {24,8}*768n, {24,8}*768o, {24,8}*768p, {12,4}*768c, {12,8}*768s, {24,4}*768i, {12,4}*768d, {12,8}*768t, {24,4}*768j, {12,8}*768u, {12,4}*768e, {24,4}*768k, {12,8}*768v, {12,8}*768w, {12,4}*768f, {24,4}*768l, {12,8}*768x
5-fold covers : {12,20}*960c, {60,4}*960c
6-fold covers : {36,4}*1152d, {36,8}*1152g, {36,8}*1152h, {72,4}*1152e, {72,4}*1152f, {12,24}*1152m, {12,24}*1152n, {24,12}*1152s, {24,12}*1152t, {12,12}*1152k, {12,12}*1152m, {12,24}*1152u, {12,24}*1152v, {24,12}*1152w, {24,12}*1152x
7-fold covers : {12,28}*1344c, {84,4}*1344c
9-fold covers : {108,4}*1728c, {12,36}*1728d, {36,12}*1728g, {12,12}*1728m, {36,12}*1728h, {12,12}*1728o, {12,12}*1728x, {12,4}*1728e
10-fold covers : {12,20}*1920c, {12,40}*1920g, {12,40}*1920h, {24,20}*1920e, {24,20}*1920f, {60,4}*1920d, {60,8}*1920g, {60,8}*1920h, {120,4}*1920e, {120,4}*1920f
Permutation Representation (GAP) :
```s0 := ( 1, 5)( 2, 6)( 7,12)( 8,11)( 9,10);;
s1 := ( 1, 7)( 2, 8)( 3,11)( 4,12)( 5, 9)( 6,10);;
s2 := ( 3, 4)( 7, 8)(11,12);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(12)!( 1, 5)( 2, 6)( 7,12)( 8,11)( 9,10);
s1 := Sym(12)!( 1, 7)( 2, 8)( 3,11)( 4,12)( 5, 9)( 6,10);
s2 := Sym(12)!( 3, 4)( 7, 8)(11,12);
poly := sub<Sym(12)|s0,s1,s2>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

```
References : None.
to this polytope