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# Polytope of Type {12,4}

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

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

```
References : None.
to this polytope