What is a "Gaussian sphere" and how it can be create?

Question

I read an article by Joseph O'Rourke. It is about an algorithm for finding a minimum bounding box in three-dimensional this article.

He said there:

The Gaussian sphere is dual of the convex polyhedron.

and also:

Gaussian sphere partitions the surface of the unit sphere to into the convex region, one for each vertex of the convex polyhedron, such that if n is a unit vector from the origin whose tip lies in the convex region then the plane through the convex region with normal n is a supporting plane for the polyhedron.

My questions are:

What is a "Gaussian sphere"

Which algorithm helps to create it?

I search on the net but gained nothing.

Any tip that makes a way to know it, makes me happy.

Answer 1

Here is Fig.2.1 from that paper.

Each vertex on the polyhedron maps to a face on the sphere, each of which is a convex geodesic polygon, geodesic in the sense that the edges are subarcs of great circles. Each face of the polyhedron maps to a vertex on the sphere. And each edge $v_1 v_2$ on the polyhedron maps to an edge on the sphere shared between the two regions corresponding to $v_1$ and $v_2$.