Mutually Equidistant Spheres that Intersect

TL;DR

This paper calculates the mean width of a Reuleaux tetrahedron, a shape formed by intersecting four unit spheres in three-dimensional space, expanding understanding of its geometric properties.

Contribution

It introduces the first calculation of the mean width for the Reuleaux tetrahedron, complementing known volume and surface area data.

Findings

Mean width of the Reuleaux tetrahedron is computed.

Provides new geometric insight into intersecting sphere shapes.

Enhances understanding of Reuleaux tetrahedron properties.

Abstract

The setting for this brief paper is R^3. Distance between two spheres is understood as distance delta between spherical centers. For instance, a Reuleaux tetrahedron T is the intersection of four unit balls satisfying delta=1 pairwise. Volume and surface area of T are already well-known; our humble contribution is to calculate the mean width of T.