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

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.

• @user64742 I know the Gaussian surface and I know the Gaussian sphere by a point charge. It is not what I want and what the article said.
– ALIN
Aug 20, 2020 at 6:36

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 $$v_2$$.