manifolds.Sphere: Make relation to simplicial spheres more concrete

[mkoeppe]

The example manifolds.Sphere defines a method minimal_triangulation, which returns a simplicial sphere (the boundary of the (n+1)-simplex) as an abstract simplicial complex.

We propose to make the relationship between the two objects more concrete by introducing intermediate objects and maps as follows.

Define a geometric realization of the simplicial complex as the polyhedral complex that is the boundary of a geometric (n+1)-simplex (or of any full-dimensional polyhedron).

Define the face_manifold_poset (#31660) of the polyhedron. The poset elements are images of embedded submanifolds (and subsets) of the Euclidean space.

Let c be a point in the interior of the polyhedron.

Define the differentiable map sending Eⁿ⁺¹ \ c to Eⁿ⁺¹ \ 0, defined in Cartesian coordinates as x ⟼ (x-c)/|x-c|. It pulls back to differentiable maps on the embedded submanifolds, defining differentiable embeddings into the sphere; and to a continuous map on their union, defining a continuous embedding into the sphere.