This shows a regular pentagonal dodecahedron copied to 4 positions. The original dodecahedron, colored grey, is duplicated to each of the 4 colored ones, which all share the same center point. Scenes shows how this relates to 4 cubes copied to 4 positions from an original and more.

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Arrangement of 5 Dodecahedra

How this arrangement is generated can be understood by considering the Arrangement of 5 cubes shown in Scenes. The central grey cube can be seen as being rotated about each of its corner-to-corner axes by 60° to define, in succession, the yellow, red, blue, and green cubes. With the central original cube removed, these 4 make a symmetrical arrangement. Given that each cube can be circumscribed by a dodecahedron that shares the 8 corner vertices, the 5 dodecahedra can be seen as built around the cubes. By removing the original grey dodecahedron, we arrive at the arrangement of 4. It is possible, by a similar process, to copy the original dodecahedron by rotation about each of its corner-to-opposite corner axes to generate 10 copies. This can be seen Here

The symmetry of these arrangements is displayed in the convex hulls shown in Scenes.