This green translucent plastic model is an immersion of a Moebius band into three-dimensional space. That is, the surface passes through itself along certain lines. The model is dissected into three triangles and three four-sided figures (quadrilaterals). The triangles have angles of 36, 72, and 72 degrees. The pass-through lines of the immersion meet the triangles only at their vertices. The quadrilaterals are in the shape of isosceles trapezoids, and the diagonals of the trapezoids are the pass-through lines of the immersion.
Wheeler described this model as: "six planes of the heptahedron forming an element to be repeated to form one-sided polyhedra." He stated that it has six vertices, twelve edges, and six faces, for an Euler characteristic of e -k +f = 0. He assigned the model number 708 or M67.
Compare 1979.0102.416 (which has a full discussion of the surface), 1979.0102.197, 1979.0102.198, 1979.0102.199, 1079.0102.200, and MA.304723.718.
Reference:
A.H. Wheeler, Catalog of Models, A. H. Wheeler Papers, Mathematics Collections, National Museum of American History.