An image to help with Spherical Layers

This relates to the previous post, Spherical Layers.

Each new colour is a new layer.

Of course this is just about layering circles, but the concept of circular layers applies also to spherical layers.  Imagine an incrementally larger circle and how many circles can fit into that circle, or an incrementally larger sphere and how many spheres can fit into that sphere.  As your circle or sphere gets larger, the resultant approximation of the layers gets closer and closer to a circle or a sphere.  In between approximations of circles or spheres, you do get approximations of hexagons or dodecahedrons (which in themselves could be thought of as rough approximations of circles and spheres).

Note that the red and light green layers are also approximations of a dodecagon.  Note also that, when considering polygons, the best approximation of a circle is a regular ∞-gon (or apeirogon), but do note that a circle doesn't have sides per se, it has one curved side (singular, not plural) and is not a polygon.