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# Polytope of Type {12,3}

Atlas Canonical Name : {12,3}*96
if this polytope has a name.
Group : SmallGroup(96,193)
Rank : 3
Schlafli Type : {12,3}
Number of vertices, edges, etc : 16, 24, 4
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{12,3,2} of size 192
{12,3,4} of size 768
{12,3,4} of size 768
Vertex Figure Of :
{2,12,3} of size 192
{4,12,3} of size 384
{3,12,3} of size 480
{6,12,3} of size 576
{4,12,3} of size 768
{4,12,3} of size 768
{8,12,3} of size 768
{4,12,3} of size 768
{4,12,3} of size 768
{6,12,3} of size 960
{10,12,3} of size 960
{12,12,3} of size 1152
{14,12,3} of size 1344
{3,12,3} of size 1440
{18,12,3} of size 1728
{20,12,3} of size 1920
{12,12,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,3}*48
4-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,6}*192b
3-fold covers : {12,3}*288
4-fold covers : {12,3}*384, {12,12}*384b, {12,6}*384, {12,12}*384c
5-fold covers : {12,15}*480
6-fold covers : {12,6}*576c, {12,6}*576d
7-fold covers : {12,21}*672
8-fold covers : {24,3}*768, {12,6}*768c, {12,6}*768d, {12,6}*768e, {24,6}*768, {12,24}*768a, {12,24}*768b, {12,12}*768a
9-fold covers : {12,9}*864, {12,3}*864
10-fold covers : {12,30}*960a, {60,6}*960b
11-fold covers : {12,33}*1056
12-fold covers : {12,3}*1152a, {12,12}*1152d, {12,12}*1152e, {12,12}*1152f, {12,6}*1152a, {12,6}*1152e, {12,12}*1152q, {12,3}*1152b
13-fold covers : {12,39}*1248
14-fold covers : {12,42}*1344a, {84,6}*1344b
15-fold covers : {12,15}*1440c
17-fold covers : {12,51}*1632
18-fold covers : {12,18}*1728a, {36,6}*1728c, {12,6}*1728c, {12,6}*1728d, {12,6}*1728g
19-fold covers : {12,57}*1824
20-fold covers : {12,15}*1920, {12,60}*1920a, {60,12}*1920a, {12,60}*1920b, {60,6}*1920, {12,30}*1920, {60,12}*1920d
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)(16,38)
(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)(36,48)
(39,40);;
s1 := ( 1, 9)( 2, 4)( 3,25)( 5,10)( 6,48)( 7,47)( 8,13)(11,42)(12,41)(14,26)
(15,46)(16,44)(17,36)(18,33)(19,32)(20,34)(21,30)(22,35)(23,31)(24,29)(27,40)
(28,39)(37,43)(38,45);;
s2 := ( 1,46)( 2,40)( 3,39)( 4,36)( 5,48)( 6,11)( 7,12)( 8,44)( 9,24)(10,42)
(13,21)(14,41)(15,29)(16,30)(17,27)(18,28)(19,31)(20,45)(22,34)(23,43)(25,33)
(26,47)(32,37)(35,38);;
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,
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope