Tag Archives: truncated tetrahedron

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

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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.

The Truncated Truncated Tetrahedron

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twice truncated tet

This is the result, if one performs a second truncation to the truncated tetrahedron, in such as a way as to make the resulting dodecagons regular. To do this, however, regularity of the triangles and hexagons must be sacrificed — they are merely isosceles and equiangular, respectively.

[Image made using Stella 4d, software available here.]

Truncated Tetrahedron Decorated with Mandalas

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Truncated Tetrahedron Decorated with Mandalas

The image on the hexagons is the same that appears in the previous post here, and was created with Geometer’s Sketchpad and MS-Paint. Projecting those images onto the larger faces of this polyhedron, and then creating this rotating .gif file, was accomplished with the use of Stella 4d, polyhedron-manipulating software you can try and/or buy at http://www.software3d.com/stella.php.