Day 210 – Rhombic Dodecahedron

Day 210 – Rhombic Dodecahedron

Day 210 – Rhombic Dodecahedron 150 150 mathgrrl

We’re almost at the end of the Catalan series! Today we printed our eleventh, the Rhombic Dodecahedron, dual of the Cuboctahedron (which we also constructed with printed snap-tiles on Day 87).

Thingiverse link:

Settings: MakerWare .3mm/low with custom reduced-support slicing profile, on a Replicator 2.

Technical notes, tessellation flavor: The Rhombic Dodecahedron has a very interesting property: it fills space. What I mean by that is that you can stack them up to pack together perfectly, with no open spaces between.  This is a pretty rare property: the only Platonic solid that fills space is the cube; the only Archimedean solid that fills space is the Truncated Octahedron; and the only Catalan solid that fills space is the Rhombic Dodecahedron.

For more information see “Simplicity is not Simple: Tesselations and Modular Architecture“, the cover article for Math Horizons about Gregg Fleishman‘s space-filling housing units that I wrote with Eugenie Hunsicker of Loughborough University in 2002.  Twelve years later I can now finally stack up a handful of Rhombic Dodecahedra and see for myself!

1 Comment
  • Very nice model. I've been looking for a nice 4D cube. This is a 3D outline of a 4D cube. To finish the 4D cube, the 3-way corners need to be connected through the center point of the model.
    More correctly, to make a near-side model, the center point should be connected to 4 of the 3-way corners.
    Unfortunately, I'm not very good with math or modelling.

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