Difference between conical meshes and circular meshes

hello friends

Recently, I’m studying Pottmann’s Architectural Geometry. Actually, although I’m very interested in this topic, it is difficult for me.
What is the difference between conical meshes and circular meshes and how are they drawn?

A conical mesh has faces around each vertex tangent to a common cone.
These are nice because they can be offset with a constant distance between parallel faces and no torsion in the beams. Here’s an example:

Circular meshes have the vertices of each face sharing a common circle. These also have an offset with torsion free beams, but at a constant distance between corresponding vertices.

I wrote some explanation of torsion free beam layouts here: