Three Archimedean Solids Which Fill Space Together: The Great Rhombcuboctahedron, the Truncated Tetrahedron, and the Truncated Cube

To start building this space-filling honeycomb of three Archimedean solids, I begin with a great rhombcuboctahedron. This polyhedron is also called the great rhombicuboctahedron, as well as the truncated cuboctahedron.

Trunc Cubocta honeycomb core

Next, I augment the hexagonal faces with truncated tetrahedra.

Trunc Cubocta honeycomb core plus 1.gif

The next polyhedra to be added are truncated cubes.

Trunc Cubocta honeycomb core plus 2

Now it’s time for another layer of great rhombcuboctahedra.

Trunc Cubocta honeycomb core plus 3

Now more truncated tetrahedra are added.

Trunc Cubocta honeycomb core plus 4

Now it’s time for a few more great rhombcuboctahedra.

Trunc Cubocta honeycomb core plus 5

Next come more truncated cubes.

Trunc Cubocta honeycomb core plus 6

More great rhombcuboctahedra come next.

Trunc Cubocta honeycomb core plus 7

More augmentations using these three Archimedean solids can be continued, in this manner, indefinitely. The images above were created with Stella 4d: Polyhedron Navigator, a program you may try for yourself 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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2 Responses to Three Archimedean Solids Which Fill Space Together: The Great Rhombcuboctahedron, the Truncated Tetrahedron, and the Truncated Cube

  1. Pingback: Three Archimedean Solids Which Fill Space Together: The Great Rhombcuboctahedron, the Truncated Tetrahedron, and the Truncated Cube — RobertLovesPi.net – BellEva Worldwide

  2. Very nonintuitive, great!

    Liked by 1 person

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