Henry Segerman (Vertex-augmented tetrahedron)

106-108-4 Topological Polyhedron, 3D-printed nylon

[4 F, 108 E, 106 V] This sculpture illustrates a subdivision of a sphere into four parts. With the correct interpretation of what vertices, edges, and faces are, we can think of this as a “topological” polyhedron where each part of the subdivision is a face with 54 sides. Most of the vertices have only two faces next to them – this would be strange for a geometric polyhedron but is no problem for a topological polyhedron. Euler’s formula still applies here, since 106 – 108 + 4 = 2.