Fibonacci group

Definition
The Fibonacci group $$F(2,m)$$ is defined as the group with the following presentation:

$$\{ x_1, x_2, \dots, x_m | x_ix_{i+1} = x_{i+2}\}$$

where the indexes are reduced modulo $$m$$.

Particular cases
The only cases where $$F(2,m)$$ is finite are $$m = 1,2,3,4,5,7$$: