Move the central linkage to see the transitions withing the hyperbolic tesselation.
Here you can navigate a pentagon linkage within the hyperbolic tesselation.
The white region resembles a fundamental region with respect to translation and rotation of the linkage is shown.
Every instance of the pentagonal equilateral linkage corresponds to one point of the white region (or a suitable collection of points on the boundary, resembling the identification of the boundary edges).