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Monday, March 24, 2014

Day 210 - Rhombic Dodecahedron

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: http://www.thingiverse.com/thing:282499

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:

  1. 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.