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The convex hull of these 24 elements in 4-dimensional space form a convex regular 4-polytope called the 24-cell.
For example, Chan's algorithm can compute the convex hull of a set of points in O(n log h) time, where n is the number of points in the input and h is the number of points in the resulting convex hull, a subset of the input points.
It is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the other circle.
When such a triangulation exists it is a special case of the Delaunay triangulation, and consists of the union of the Gabriel graph and convex hull.
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Thus, a circle having that edge as diameter must be empty of vertices, so the Pitteway triangulation consists of the Gabriel graph together with the convex hull of the point set.