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The solid common to both the cube and octahedron (left figure) in a
cube-octahedron compound is a cuboctahedron (right figure; Ball and Coxeter
1987). |
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The cuboctahedron can be inscribed in the rhombic dodecahedron (left
figure; Steinhaus 1999, p. 206). The centers of the square faces determine
an octahedron (right figure; Ball and Coxeter 1987, p. 143). |
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Wenninger (1989) lists four of the possible stellations of the cuboctahedron:
the cube-octahedron compound, a truncated form of the stella octangula,
a sort of compound of six intersecting square pyramids, and an attractive
concave solid formed of rhombi meeting four at a time.
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each sphere is surrounded by 12 other spheres. Taking a collection
of 13 such spheres gives the cluster illustrated above. Connecting the
centers of the external 12 spheres gives a cuboctahedron (Steinhaus 1999,
pp. 203-207).
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