Tag Archives: space-filling

Octahedra and Truncated Cubes Can Fill Space Without Leaving Any Gaps

I created this using Stella 4d, which you can try for free right here. It’s much like a tessellation, but in three dimensions instead of two.

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Space-Filling Truncated Octahedra in a Rhombic Dodecahedral Cluster

The truncated octahedron is well-known as the only Archimedean solid which can fill space, by itself, without leaving any gaps. The cluster below shows this, and has the overall shape of a rhombic dodecahedron. It’s easier to see the rhombic … Continue reading

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A Space-Filling Lattice of Truncated Octahedra

Truncated octahedra are among the special polyhedra which can fill space without leaving any gaps. There are others, as well. This image was created using Stella 4d, software you may try, for yourself, right here. There is a free “try it … Continue reading

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A Space-Filling Arrangement of Polyhedra Using Truncated Cubes, Rhombcuboctahedra, Cubes, and Octagonal Prisms

This image above has only one polyhedron-type hidden from view, in the center:  a red truncated cube. Next, more of this pattern I just found will be added. The next step will be to add another layer of blue octagonal … Continue reading

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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, … Continue reading

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