Geometric Model by A. Harry Wheeler, Cube Transformable into Four Regular Octahedra and a Faceted Cubeoctahedron, Dissected Polyhedron

This paper model comes in a paper box folded in the shape of a cube. Inside the box, arranged in the shape of a cube, are a faceted cuboctahedron, six square pyramids that fit in the facets of the cuboctahedron and eight triangular pyramids that fit over the triangular faces of the cuboctahedron. The pieces separate into the faceted cubocatahedron, four square pyramids, a square pyramid hinged to four triangular pyramids, and another square pyramid hinged to another four triangular pyramids. The four square pyramids can be arranged as two octahedra, as can both of the sets of hinged pieces. Hence the pieces of the model can be arranged either as a cube or as four regular octahedra and a faceted cuboctahedron (this form of faceted cubocatahedraon is called by Wenninger an octahemioctahedron).

Wheeler numbered this model 763.

Compare MA.304723.294 (larger paper model), MA.304723.296 (middle-sized paper model), MA.304273.306 (smallest paper model), and MA.304723.132.

There is a drawing in 1979.3002.42 for a "cube with four removable octahedra." It is dated March 12, 1938. This is quite possibly for the plastic version of the model.

Reference:

Magnus J. Wenninger, Polyhedron Models, Cambridge: Cambridge University Press, 1971, p. 103.

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