A Spheroform with Tetrahedral Symmetry, also called Roberts' Body after Patrick Roberts discovery, is a body of constant width that lives in the same family as the two Meissner solids: constant width bodies of revolution and the Meissner polyhedra.

The basic construction is to start with a Reuleaux tetrahedron, then replace the edges with a cleverly constructed surface to form a solid of constant width.

You can read more about how this construct has connections to confocal quadrics in the paper Peabodies of Constant Width by Isaac Arelio, Luis Montejano, and Deborah Oliveros. The figure above, and the superimposed figure in the model picture, was taken from their paper.