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# Polytope of Type {4,12}

Atlas Canonical Name : {4,12}*192a
if this polytope has a name.
Group : SmallGroup(192,300)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 8, 48, 24
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,12,2} of size 384
{4,12,4} of size 768
{4,12,4} of size 768
{4,12,6} of size 1152
{4,12,6} of size 1152
{4,12,6} of size 1152
{4,12,3} of size 1152
{4,12,6} of size 1152
{4,12,10} of size 1920
Vertex Figure Of :
{2,4,12} of size 384
{4,4,12} of size 768
{6,4,12} of size 1152
{3,4,12} of size 1152
{10,4,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,12}*96a
3-fold quotients : {4,4}*64
4-fold quotients : {2,12}*48, {4,6}*48a
6-fold quotients : {4,4}*32
8-fold quotients : {2,6}*24
12-fold quotients : {2,4}*16, {4,2}*16
16-fold quotients : {2,3}*12
24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,24}*384a, {8,12}*384a, {4,12}*384a, {4,24}*384b, {8,12}*384b
3-fold covers : {4,36}*576a, {12,12}*576a, {12,12}*576b
4-fold covers : {8,24}*768a, {8,12}*768a, {8,24}*768b, {4,24}*768a, {8,24}*768c, {8,24}*768d, {16,12}*768a, {4,48}*768a, {16,12}*768b, {4,48}*768b, {4,12}*768a, {4,24}*768b, {8,12}*768b, {8,12}*768c, {8,24}*768e, {4,24}*768c, {4,24}*768d, {8,12}*768d, {8,24}*768f, {8,24}*768g, {8,24}*768h, {4,12}*768d
5-fold covers : {20,12}*960a, {4,60}*960a
6-fold covers : {8,36}*1152a, {4,72}*1152a, {12,24}*1152a, {12,24}*1152b, {24,12}*1152b, {24,12}*1152c, {4,36}*1152a, {4,72}*1152b, {8,36}*1152b, {12,12}*1152b, {12,24}*1152e, {24,12}*1152d, {24,12}*1152e, {12,12}*1152c, {12,24}*1152f
7-fold covers : {28,12}*1344a, {4,84}*1344a
9-fold covers : {4,108}*1728a, {12,36}*1728a, {12,36}*1728b, {36,12}*1728a, {12,12}*1728b, {12,12}*1728c, {12,12}*1728h, {4,12}*1728c, {4,12}*1728d, {12,12}*1728t
10-fold covers : {8,60}*1920a, {4,120}*1920a, {40,12}*1920a, {20,24}*1920a, {4,60}*1920a, {4,120}*1920b, {8,60}*1920b, {40,12}*1920b, {20,24}*1920b, {20,12}*1920a
Permutation Representation (GAP) :
```s0 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,22)
(11,23)(12,24);;
s1 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(13,19)(14,21)(15,20)(16,22)(17,24)(18,23);;
s2 := ( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,14)(16,17)(19,23)(20,22)(21,24);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*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(24)!( 1,13)( 2,14)( 3,15)( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)
(10,22)(11,23)(12,24);
s1 := Sym(24)!( 2, 3)( 5, 6)( 8, 9)(11,12)(13,19)(14,21)(15,20)(16,22)(17,24)
(18,23);
s2 := Sym(24)!( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,14)(16,17)(19,23)(20,22)
(21,24);
poly := sub<Sym(24)|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, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*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 >;

```
References : None.
to this polytope