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# Polytope of Type {2,39}

Atlas Canonical Name : {2,39}*156
if this polytope has a name.
Group : SmallGroup(156,17)
Rank : 3
Schlafli Type : {2,39}
Number of vertices, edges, etc : 2, 39, 39
Order of s0s1s2 : 78
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,39,2} of size 312
{2,39,4} of size 624
{2,39,6} of size 936
{2,39,6} of size 1248
{2,39,4} of size 1248
Vertex Figure Of :
{2,2,39} of size 312
{3,2,39} of size 468
{4,2,39} of size 624
{5,2,39} of size 780
{6,2,39} of size 936
{7,2,39} of size 1092
{8,2,39} of size 1248
{9,2,39} of size 1404
{10,2,39} of size 1560
{11,2,39} of size 1716
{12,2,39} of size 1872
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,13}*52
13-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,78}*312
3-fold covers : {2,117}*468, {6,39}*468
4-fold covers : {2,156}*624, {4,78}*624a, {4,39}*624
5-fold covers : {2,195}*780
6-fold covers : {2,234}*936, {6,78}*936b, {6,78}*936c
7-fold covers : {2,273}*1092
8-fold covers : {4,156}*1248a, {2,312}*1248, {8,78}*1248, {8,39}*1248, {4,78}*1248
9-fold covers : {2,351}*1404, {6,117}*1404, {6,39}*1404
10-fold covers : {10,78}*1560, {2,390}*1560
11-fold covers : {2,429}*1716
12-fold covers : {2,468}*1872, {4,234}*1872a, {4,117}*1872, {12,78}*1872b, {6,156}*1872b, {6,156}*1872c, {12,78}*1872c, {12,39}*1872, {6,39}*1872
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 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);;
s2 := ( 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);;
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*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(41)!(1,2);
s1 := Sym(41)!( 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);
s2 := Sym(41)!( 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);
poly := sub<Sym(41)|s0,s1,s2>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope