Hanner polytope [SEP] time of discovery
Hanner polytope
In geometry, a Hanner polytope is a convex polytope constructed recursively by Cartesian product and polar dual operations. Hanner polytopes are named after Olof Hanner, who introduced them in 1956.
Construction.
The Hanner polytopes are constructed recursively by the following rules:
- A line segment is a one-dimensional Hanner polytope
- The Cartesian product of every two Hanner polytopes is another Hanner polytope, whose dimension is the sum of the dimensions of the two given polytopes
- The dual of a Hanner polytope
that all centrally symmetric polytopes have at least 3 nonempty faces.
Properties Pairs of opposite facets and vertices.
In a Hanner polytope, every two opposite facets are disjoint, and together include all of the vertices of the polytope, so that the convex hull of the two facets is the whole polytope. As a simple consequence of this fact, all facets of a Hanner polytope have the same number of vertices as each other (half the number of vertices of the whole polytope). However, the facets may not all