Polytope of Type {13,2} with group SmallGroup(52,4) - Atlas of Small Regular Polytopes

Overview

Group: SmallGroup(52,4)
Rank: 3
Schläfli Type: {13,2}
Vertices, edges, …: 13, 13, 2
Order of s₀s₁s₂: 26
Order of s₀s₁s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

2-fold

{26,2}*104

3-fold

{39,2}*156

4-fold

5-fold

{65,2}*260

6-fold

7-fold

{91,2}*364

8-fold

9-fold

10-fold

11-fold

{143,2}*572

12-fold

13-fold

14-fold

15-fold

{195,2}*780

16-fold

17-fold

{221,2}*884

18-fold

19-fold

{247,2}*988

20-fold

21-fold

{273,2}*1092

22-fold

23-fold

{299,2}*1196

24-fold

25-fold

26-fold

27-fold

28-fold

29-fold

{377,2}*1508

30-fold

31-fold

{403,2}*1612

32-fold

33-fold

{429,2}*1716

34-fold

35-fold

{455,2}*1820

36-fold

37-fold

{481,2}*1924

38-fold

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := (14,15);;
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, 
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(15)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(15)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(15)!(14,15);
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*s2*s0*s2, s1*s2*s1*s2, 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 >;