# how to construct an hyperbolic (8,3) tiling

how can I construct an hyperbolic (8,3) tiling ( see https://en.wikipedia.org/wiki/Octagonal_tiling ) in the Poincare Disk model or Klein Disk model of hyperbolic geometry ?

or:

What are the hyperbolic lengths of all relevant distances (distance center - vertex, distance center midpoint of an edge , length of an edge ed)

the angle of a polygon = $2*asin(\frac{cos(\frac{\pi}{p})}{cosh(\frac{e}{2})})$
Since q=3, then that angle must be $\frac{2\pi}{3}$. You can solve the function $2*asin(\frac{cos(\frac{\pi}{p})}{cosh(\frac{e}{2})})=\frac{2\pi}{3}$ yourself, that's easy.
halfedgelength = $\frac{edgelength}{2}$
distance center - vertex = circumradius = $asinh(\frac{sinh(halfedgelength)}{sin(\frac{\pi}{p})})$
distance center - midpoint of an edge = inradius = $asinh(\frac{tanh(halfedgelength)}{tan(\frac{\pi}{p})})$