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# Polytope of Type {2,13}

Atlas Canonical Name : {2,13}*52
if this polytope has a name.
Group : SmallGroup(52,4)
Rank : 3
Schlafli Type : {2,13}
Number of vertices, edges, etc : 2, 13, 13
Order of s0s1s2 : 26
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,13,2} of size 104
{2,13,26} of size 1352
Vertex Figure Of :
{2,2,13} of size 104
{3,2,13} of size 156
{4,2,13} of size 208
{5,2,13} of size 260
{6,2,13} of size 312
{7,2,13} of size 364
{8,2,13} of size 416
{9,2,13} of size 468
{10,2,13} of size 520
{11,2,13} of size 572
{12,2,13} of size 624
{13,2,13} of size 676
{14,2,13} of size 728
{15,2,13} of size 780
{16,2,13} of size 832
{17,2,13} of size 884
{18,2,13} of size 936
{19,2,13} of size 988
{20,2,13} of size 1040
{21,2,13} of size 1092
{22,2,13} of size 1144
{23,2,13} of size 1196
{24,2,13} of size 1248
{25,2,13} of size 1300
{26,2,13} of size 1352
{27,2,13} of size 1404
{28,2,13} of size 1456
{29,2,13} of size 1508
{30,2,13} of size 1560
{31,2,13} of size 1612
{32,2,13} of size 1664
{33,2,13} of size 1716
{34,2,13} of size 1768
{35,2,13} of size 1820
{36,2,13} of size 1872
{37,2,13} of size 1924
{38,2,13} of size 1976
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,26}*104
3-fold covers : {2,39}*156
4-fold covers : {2,52}*208, {4,26}*208
5-fold covers : {2,65}*260
6-fold covers : {6,26}*312, {2,78}*312
7-fold covers : {2,91}*364
8-fold covers : {4,52}*416, {2,104}*416, {8,26}*416
9-fold covers : {2,117}*468, {6,39}*468
10-fold covers : {10,26}*520, {2,130}*520
11-fold covers : {2,143}*572
12-fold covers : {12,26}*624, {6,52}*624a, {2,156}*624, {4,78}*624a, {6,39}*624, {4,39}*624
13-fold covers : {2,169}*676, {26,13}*676
14-fold covers : {14,26}*728, {2,182}*728
15-fold covers : {2,195}*780
16-fold covers : {4,104}*832a, {4,52}*832, {4,104}*832b, {8,52}*832a, {8,52}*832b, {2,208}*832, {16,26}*832
17-fold covers : {2,221}*884
18-fold covers : {18,26}*936, {2,234}*936, {6,78}*936a, {6,78}*936b, {6,78}*936c
19-fold covers : {2,247}*988
20-fold covers : {20,26}*1040, {10,52}*1040, {2,260}*1040, {4,130}*1040
21-fold covers : {2,273}*1092
22-fold covers : {22,26}*1144, {2,286}*1144
23-fold covers : {2,299}*1196
24-fold covers : {24,26}*1248, {6,104}*1248, {12,52}*1248, {4,156}*1248a, {2,312}*1248, {8,78}*1248, {12,39}*1248, {8,39}*1248, {6,52}*1248, {6,78}*1248, {4,78}*1248
25-fold covers : {2,325}*1300, {10,65}*1300
26-fold covers : {2,338}*1352, {26,26}*1352a, {26,26}*1352b
27-fold covers : {2,351}*1404, {6,117}*1404, {6,39}*1404
28-fold covers : {28,26}*1456, {14,52}*1456, {2,364}*1456, {4,182}*1456
29-fold covers : {2,377}*1508
30-fold covers : {30,26}*1560, {10,78}*1560, {6,130}*1560, {2,390}*1560
31-fold covers : {2,403}*1612
32-fold covers : {8,52}*1664a, {4,104}*1664a, {8,104}*1664a, {8,104}*1664b, {8,104}*1664c, {8,104}*1664d, {16,52}*1664a, {4,208}*1664a, {16,52}*1664b, {4,208}*1664b, {4,52}*1664, {4,104}*1664b, {8,52}*1664b, {32,26}*1664, {2,416}*1664
33-fold covers : {2,429}*1716
34-fold covers : {34,26}*1768, {2,442}*1768
35-fold covers : {2,455}*1820
36-fold covers : {36,26}*1872, {18,52}*1872a, {2,468}*1872, {4,234}*1872a, {4,117}*1872, {6,156}*1872a, {12,78}*1872a, {12,78}*1872b, {6,156}*1872b, {6,156}*1872c, {12,78}*1872c, {4,52}*1872, {4,78}*1872, {12,39}*1872, {6,39}*1872, {6,52}*1872
37-fold covers : {2,481}*1924
38-fold covers : {38,26}*1976, {2,494}*1976
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
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 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(15)!(1,2);
s1 := Sym(15)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s2 := Sym(15)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
poly := sub<Sym(15)|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 >;

```

to this polytope