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This is one of my most successful studies in 3 dimensionalizing the tradition Metatron's Cube design. 12 Spheres surround the central sphere creating a cubeoctahedron, and 12 more surround this to create a larger cubeoctahedron. If the centres of these 24 spheres were all connected to each other we would have the exact analog.
As the 2D design is known as Metatron's Cube it seems fitting that the 3D form should be called Metatron's Hypercube - especially as the secret of this form is the way it catches the shadows of higher dimensional shapes.
The 4 dimensional Metatron's Compass also available in our