A Hollow Octahedron Made of Rhombic Dodecahedra, with Variations

hOLLOW oCTAHEDRON mADE OF Rhombic Dodeca

The original polyhedral cluster I built using Stella 4d (available here) is above. Below is its 29th stellation.

hOLLOW oCTAHEDRON mADE OF Rhombic Dodeca 29th stellation

And the 30th stellation, as well:

hOLLOW oCTAHEDRON mADE OF Rhombic Dodeca 30th stellation

This is the original polyhedral cluster’s dual:

hOLLOW oCTAHEDRON mADE OF Rhombic Dodeca dual

The next image is a variant of the original polyhedral cluster, rendered with only its edges, but not faces or vertices, visible. I wish I could remember exactly how I made this variant, but I simply cannot recall the exact methods I used.

hollow octahedron variant

This is the dual of the polyhedron shown immediately above, rendered in the same manner:

hollow object made of cubes -- dual of hollow octahedron variantThis is a compound of the two dual polyhedra right before this sentence.

hollow octahedron variant compound of it and dual

2 thoughts on “A Hollow Octahedron Made of Rhombic Dodecahedra, with Variations

    • You cut half the cubes into six identical square-based pyramids. They then get stuck on the six faces of the remaining half of the cubes. You now have the set of rhombic dodecahedra — so, yes. Anything you can make of rhombic dodecahedra can be made of cubes.

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