Polytope of Type {11,2} with group SmallGroup(44,3) - Atlas of Small Regular Polytopes

Overview

Group: SmallGroup(44,3)
Rank: 3
Schläfli Type: {11,2}
Vertices, edges, …: 11, 11, 2
Order of s₀s₁s₂: 22
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

{22,2}*88

3-fold

{33,2}*132

4-fold

5-fold

{55,2}*220

6-fold

7-fold

{77,2}*308

8-fold

9-fold

10-fold

11-fold

12-fold

13-fold

{143,2}*572

14-fold

15-fold

{165,2}*660

16-fold

17-fold

{187,2}*748

18-fold

19-fold

{209,2}*836

20-fold

21-fold

{231,2}*924

22-fold

23-fold

{253,2}*1012

24-fold

25-fold

26-fold

27-fold

28-fold

29-fold

{319,2}*1276

30-fold

31-fold

{341,2}*1364

32-fold

33-fold

34-fold

35-fold

{385,2}*1540

36-fold

37-fold

{407,2}*1628

38-fold

39-fold

{429,2}*1716

40-fold

41-fold

{451,2}*1804

42-fold

43-fold

{473,2}*1892

44-fold

45-fold

Representations

Permutation Representation (GAP)

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s2 := (12,13);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma)

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