This is an arrangement of 10 cubes about a common center. The cubes are distributed so that there are no shared vertices. Scenes shows a convex hull, which is spheroidal with Octahedral symmetry.

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10 Cubes 80 vertices

Below is shown an arrangement of 4 cubes, distributed with no shared vertices. This can be seen as a precursor of the 10 cube arrangement. Scenes shows how a cube can be duplicated in a different orientation. Here, the original grey cube is copied into a position that is rotated about the z axis by 45°, to generate the yellow cube. Likewise, rotating the original cube about the x and y axes generates a red and a blue cube respectively. This same process can be reiterated, duplicating each of the generated cubes in 2 unique ways without any vertices coinciding, which is how the 10 cube model is constructed. In that model, the pale blue cube generates pale green, yellow, and pink cubes. Then, for example, the pale green cube generates a dark green and a grey cube, etc. Further rounds of duplication is possible.

4 cubes 32 vertices