There are a number of attractive polyhedron compounds involving four cubes, several of which are illustrated above. The first (left figures),
also known as Bakos' compound, has the symmetry of the cube
and arises by joining four cubes such that each axis falls along the axis of one of the other cubes
(Bakos 1959; Holden 1991, p. 35). In particular, let the first cube consists of a cube in standard position be rotated by radians around the -axis, then the other three cubes are obtained by rotating
around the -axis (z-axis) by , , and radians, respectively.

For the first compound, the common solid is a small triakis octahedron and the convex hull is a chamfered cube. For the second, the common solid is
a chamfered cube and the convex
hull has the connectivity of a hexagon-augmented truncated octahedron. The common
solid of the third compound is an elongated 8-dipyramid. The common solid of the
fourth compound is a 12-dipyramid and the convex hull
is an elongated 12-dipyramid. For the fifth compound, the interior and convex
hull are (different) 16-prisms.

The net of the first cube 4-compound (Bakos' compound) is illustrated above for cubes with unit edges lengths. The indicated lengths are given by

(1)

(2)

(3)

(4)

(5)

(6)

The surface area of the hull of the first compound is