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# Polytope of Type {46}

Atlas Canonical Name : {46}*92
Also Known As : 46-gon, {46}. if this polytope has another name.
Group : SmallGroup(92,3)
Rank : 2
Schlafli Type : {46}
Number of vertices, edges, etc : 46, 46
Order of s0s1 : 46
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{46,2} of size 184
{46,4} of size 368
{46,6} of size 552
{46,8} of size 736
{46,10} of size 920
{46,12} of size 1104
{46,14} of size 1288
{46,16} of size 1472
{46,18} of size 1656
{46,20} of size 1840
Vertex Figure Of :
{2,46} of size 184
{4,46} of size 368
{6,46} of size 552
{8,46} of size 736
{10,46} of size 920
{12,46} of size 1104
{14,46} of size 1288
{16,46} of size 1472
{18,46} of size 1656
{20,46} of size 1840
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {23}*46
23-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {92}*184
3-fold covers : {138}*276
4-fold covers : {184}*368
5-fold covers : {230}*460
6-fold covers : {276}*552
7-fold covers : {322}*644
8-fold covers : {368}*736
9-fold covers : {414}*828
10-fold covers : {460}*920
11-fold covers : {506}*1012
12-fold covers : {552}*1104
13-fold covers : {598}*1196
14-fold covers : {644}*1288
15-fold covers : {690}*1380
16-fold covers : {736}*1472
17-fold covers : {782}*1564
18-fold covers : {828}*1656
19-fold covers : {874}*1748
20-fold covers : {920}*1840
21-fold covers : {966}*1932
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)
(45,46);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)
(20,25)(22,23)(24,29)(26,27)(28,33)(30,31)(32,37)(34,35)(36,41)(38,39)(40,45)
(42,43)(44,46);;
poly := Group([s0,s1]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope