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# Polytope of Type {4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12}*96c
if this polytope has a name.
Group : SmallGroup(96,187)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 4, 24, 12
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,12,2} of size 192
{4,12,4} of size 384
{4,12,4} of size 384
{4,12,4} of size 384
{4,12,6} of size 576
{4,12,6} of size 576
{4,12,8} of size 768
{4,12,4} of size 768
{4,12,4} of size 768
{4,12,10} of size 960
{4,12,12} of size 1152
{4,12,12} of size 1152
{4,12,14} of size 1344
{4,12,18} of size 1728
{4,12,6} of size 1728
{4,12,6} of size 1728
{4,12,6} of size 1728
{4,12,20} of size 1920
Vertex Figure Of :
{2,4,12} of size 192
{4,4,12} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6}*48c
4-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12}*192b
3-fold covers : {4,36}*288c
4-fold covers : {4,12}*384c, {4,12}*384d, {8,12}*384e, {8,12}*384f, {4,24}*384c, {4,24}*384d
5-fold covers : {4,60}*480c
6-fold covers : {4,36}*576b, {12,12}*576f, {12,12}*576g
7-fold covers : {4,84}*672c
8-fold covers : {8,12}*768g, {8,12}*768h, {4,24}*768g, {4,24}*768h, {8,24}*768i, {8,24}*768j, {8,24}*768k, {8,24}*768l, {4,12}*768b, {8,12}*768q, {8,12}*768r, {8,12}*768s, {4,24}*768i, {4,12}*768d, {8,12}*768t, {4,24}*768j, {8,12}*768u, {4,12}*768e, {4,24}*768k, {8,12}*768w, {4,12}*768f, {4,24}*768l, {4,48}*768c, {4,48}*768d
9-fold covers : {4,108}*864c, {12,12}*864o
10-fold covers : {20,12}*960b, {4,60}*960b
11-fold covers : {4,132}*1056c
12-fold covers : {4,36}*1152c, {4,36}*1152d, {8,36}*1152e, {8,36}*1152f, {4,72}*1152c, {4,72}*1152d, {24,12}*1152i, {24,12}*1152j, {24,12}*1152k, {24,12}*1152l, {12,24}*1152o, {12,24}*1152p, {12,24}*1152q, {12,24}*1152r, {12,12}*1152n, {12,12}*1152o
13-fold covers : {4,156}*1248c
14-fold covers : {28,12}*1344b, {4,84}*1344b
15-fold covers : {4,180}*1440c
17-fold covers : {4,204}*1632c
18-fold covers : {4,108}*1728b, {36,12}*1728c, {12,36}*1728e, {12,36}*1728f, {12,12}*1728k, {12,12}*1728l, {12,12}*1728w, {12,12}*1728ab
19-fold covers : {4,228}*1824c
20-fold covers : {4,60}*1920c, {40,12}*1920e, {40,12}*1920f, {20,24}*1920c, {20,24}*1920d, {20,12}*1920c, {4,60}*1920d, {8,60}*1920e, {8,60}*1920f, {4,120}*1920c, {4,120}*1920d
Permutation Representation (GAP) :
```s0 := ( 1,21)( 2,13)( 3,10)( 4,35)( 5,36)( 6, 7)( 8,27)( 9,28)(11,22)(12,23)
(14,19)(15,20)(16,47)(17,48)(18,46)(24,42)(25,44)(26,40)(29,45)(30,43)(31,41)
(32,39)(33,37)(34,38);;
s1 := ( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)
(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)
(42,45);;
s2 := ( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)(14,22)
(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)(33,41)
(38,44)(40,47)(45,46);;
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,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope