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

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. The majority of these things are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
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2 Responses to A Hollow Octahedron Made of Rhombic Dodecahedra, with Variations

  1. teachezwell says:

    It’s almost hypnotic! Is this a “real” shape? Like could you make this with cubes?

    Liked by 1 person

    • 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.

      Like

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