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The solid formed by the faces having the edges of the stella octangula (left figure) as polygon diagonals is a cube (right figure; Ball and Coxeter 1987). Affixing a square pyramid of height 1/2 on each face of a cube having unit edge length results in a rhombic dodecahedron (Br?ckner 1900, p. 130; Steinhaus 1999, p. 185). Since its eight faces are mutually perpendicular or parallel, the cube cannot be stellated. The cube can be constructed by cumulation of a unit edge-length tetrahedron by...
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