A Space-Filling Pair of Polyhedra: The Cuboctahedron and the Octahedron

A Space-Filling Pair of Polyhedra:  The Cuboctahedron and the Octahedron

There are only a few polyhedra which can fill space without leaving gaps, without “help” from a second polyhedron. This filling of space is the three-dimensional version of tessellating a plane. Among those that can do this are the cube, the truncated octahedron, and the rhombic dodecahedron.

If multiple polyhedra are allowed in a space-filling pattern, this opens new possibilities. Here is one: the filling of space by cuboctahedra and octahedra. There are others, and they are likely to appear as future blog-posts here.

Software credit: I made this virtual model using Stella 4d, polyhedral-manipulation software you can buy, or try as a free trial download, at http://www.software3d.com/Stella.php.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which 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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One Response to A Space-Filling Pair of Polyhedra: The Cuboctahedron and the Octahedron

  1. Tom R says:

    This is a rectified cubic honeycomb, r{4,3,4}. New vertices are inserted mid-edge to the cubic honeycomb. Cubic cells are cut down to cuboctahedra and new octahedral cells are added where the original vertices were.
    https://en.wikipedia.org/wiki/Rectified_cubic_honeycomb

    Like

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