Geometric Model by A. Harry Wheeler, Moebius Polyhedron (Polyhedron of Musical Chords)

This plastic model is in roughly the shape of a ring or torus. All the faces are triangles,twelve yellow and twelve white, with the colors alternating. The surface has thirty-six edges and twelve vertices. This would give an Euler characteristic of vertices minus edges plus faces equal to 12 – 36 + 24 = 0. This is appropriate for a surface with one hole. Four of the white triangles are numbered. Face 1 is on the side along with Wheeler’s 739 model number, 2 is a congruent white triangle on the left side, 3 is a white triangle on the bottom of the back, and 4 is a triangle on the bottom of the right side.