Hyperbolic Regular Polygons: Construction and Visualization

Question

I am working on visualising a polygon in a hyperbolic space using a HyperbolicRegularPolygon class in SageMath, which constructs regular polygons in the hyperbolic plane. The construction algorithm involves several steps:

Algorithm: URL

1. Compute the rotation angle beta and other initial variables.
2. Calculate the radius r of the circumscribed circle using the cosine theorem.
3. Find the initial point z_0 on the imaginary axis.
4. Determine the scale and displacement needed to move the center of the polygon to the imaginary part of the given center.
5. Compute the vertices of the polygon in the given center (d_z_k), vertices with Re(z) > 0 (z_k), and vertices with Re(z) < 0 (r_z_k).
6. Initialize the HyperbolicPolygon object with the computed vertices and options.

Questions

I have two questions regarding this construction:

1. What's I*(e**r).n(digits=8) at L132 doing?

2. I'm thinking to scale this to construct a quadrilateral given four (possibly different) angles in a form of $\pi / k$ for $k \in \mathbb{Z}$. Are there any academic or authoritative references that describe this construction algorithm for hyperbolic regular polygons?

I would appreciate any insights or references on this topic. Thank you.