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

space filling attempt with RCO and cubes and truncated 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.

space filling attempt with RCO and cubes and truncated cubes and octagonal prisms 2

The next step will be to add another layer of blue octagonal prisms.

space filling attempt with RCO and cubes and truncated cubes and octagonal prisms 3And now, more yellow cubes.

space filling attempt with RCO and cubes and truncated cubes and octagonal prisms 4This was an accidental discovery I made, just messing around with Stella 4d, a program you may try for yourself at http://www.software3d.com/Stella.php. The next cells added will be red truncated cubes.

space filling attempt with RCO and cubes and truncated cubes and octagonal prisms 5

Next up, I’ll add a set of pink rhombcuboctahedra.

space filling attempt with RCO and cubes and truncated cubes and octagonal prisms 6The next set of polyhedra added: some yellow cubes, and blue octagonal prisms.

space filling attempt with RCO and cubes and truncated cubes and octagonal prisms 7Now I’ll add more of the red truncated cubes.

space filling attempt with RCO and cubes and truncated cubes and octagonal prisms 8At this point, more yellow cubes are needed.

space filling attempt with RCO and cubes and truncated cubes and octagonal prisms 9The next polyhedra added will be pink rhombcuboctahedra.

space filling attempt with RCO and cubes and truncated cubes and octagonal prisms 10

And now, more of the blue octagonal prisms.

space filling attempt with RCO and cubes and truncated cubes and octagonal prisms 11

As long as this pattern is followed, this may be continued without limit, filling space, without leaving any gaps.

A Close-Packing of Space, Using Three Different Polyhedra

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A Close-Packing of Space, Using Three Different Polyhedra

This is like a tessellation, but in three dimensions, rather than two. The pattern can be repeated to fill all of space, using cubes (yellow), truncated octahedra (blue), and great rhombcuboctahedra, also known as truncated cuboctahedra (red).

Software credit: see www.software3d.com/stella.php to try or buy Stella 4d, the software I used to create this image.