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# Polytope of Type {8,12}

Atlas Canonical Name : {8,12}*192b
if this polytope has a name.
Group : SmallGroup(192,381)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 8, 48, 12
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,12,2} of size 384
{8,12,4} of size 768
{8,12,4} of size 768
{8,12,6} of size 1152
{8,12,6} of size 1152
{8,12,6} of size 1152
{8,12,10} of size 1920
Vertex Figure Of :
{2,8,12} of size 384
{4,8,12} of size 768
{4,8,12} of size 768
{6,8,12} of size 1152
{10,8,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,12}*96a
3-fold quotients : {8,4}*64b
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 : {8,24}*384a, {8,12}*384a, {8,24}*384c
3-fold covers : {8,36}*576b, {24,12}*576a, {24,12}*576e
4-fold covers : {8,24}*768a, {8,12}*768a, {8,24}*768c, {16,12}*768a, {16,12}*768b, {16,24}*768a, {16,24}*768b, {8,48}*768c, {8,48}*768e, {8,12}*768w
5-fold covers : {40,12}*960b, {8,60}*960b
6-fold covers : {8,36}*1152a, {24,12}*1152b, {24,12}*1152c, {8,72}*1152b, {24,24}*1152a, {24,24}*1152i, {8,72}*1152d, {24,24}*1152j, {24,24}*1152k
7-fold covers : {56,12}*1344b, {8,84}*1344b
9-fold covers : {8,108}*1728b, {24,36}*1728a, {24,12}*1728a, {72,12}*1728c, {24,36}*1728d, {24,12}*1728f, {24,12}*1728p, {8,12}*1728f, {8,12}*1728h, {24,12}*1728w
10-fold covers : {8,60}*1920a, {40,12}*1920a, {8,120}*1920b, {40,24}*1920b, {8,120}*1920d, {40,24}*1920d
Permutation Representation (GAP) :
```s0 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5,17)( 6,18)( 7,22)( 8,23)( 9,24)(10,19)
(11,20)(12,21);;
s1 := ( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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)( 7,22)( 8,23)( 9,24)
(10,19)(11,20)(12,21);
s1 := Sym(24)!( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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