Hanner polytope [SEP] discoverer or inventor
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
be isomorphic to each other. For instance, in the octahedral prism, two of the facets are octahedra, and the other eight facets are triangular prisms. Dually, in every Hanner polytope, every two opposite vertices touch disjoint sets of facets, and together touch all of the facets of the polytope.
Properties Mahler volume.
The Mahler volume of a Hanner polytope (the product of its volume and the volume of its polar dual) is the same as for a cube or cross polytope. If the Mahler conjecture is