This painted and varnished paper object is the first in a series of models of convex polyhedra with regular faces constructed by Martin Berman. The faces are four regular triangles.

In 1970 Berman (1938-1984), a physicist at the Pittsburgh Energy Technology Center, constructed a set of models of regular-faced convex polyhedra. A polyhedron is said to be uniform if its faces are regular and its vertices are all alike (so that it has the same arrangement of polygons at each vertex). A polyhedron (uniform or not) is convex if a line segment joining any two of its points lies entirely on or inside it.

A polygon (convex or not) is regular if it is uniform and its faces are all alike. The ...