Leírás
While Reuleaux polygons (planar convex figures whose boundary is formed by an odd number of circular arcs of the same radius, centered at the vertices of the polygon) possess constant width in two dimensions, their three-dimensional analogs, Reuleaux polyhedra, do not possess this property. Historically, Meissner bodies have served as the classical modification of the Reuleaux tetrahedron to achieve constant width in R^3. This work presents a new family of three-dimensional bodies of constant width, constructed by modifying Reuleaux polyhedra using elliptic edges instead of the classical circular arcs.
These bodies are constructed from previous results involving the projection of a body of constant width from R^4 to R^3; we present a method to construct these new edges. Utilizing the common orthogonal transversals to the opposite (conjugate) edges within an initial tetrahedral configuration, we define a three-dimensional elliptic skeleton. The new convex body is generated as the infinite intersection of closed unit balls centered at each point of this skeleton. The diameter of this elliptic set is strictly equal to 1. The resulting body possesses constant width, remaining visually almost indistinguishable from its corresponding Reuleaux polyhedron.