# Polytope of Type {3,12}

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

```
References : None.
to this polytope