© 2009 Frank Chester. All rights reserved.

Relationship between the Chestahedron and the Icosahedron

The chestahedron relates to the various Platonic forms in surprising ways. Take, for instance, the icosahedron. In the images below (click images for larger versions), you can see that the triangle faces of the icosahedron (the two bottom yellow triangles) are the same size as the triangle formed between the three points of the chestahedron (red form), as indicated by the upper yellow triangle.

This is nothing special in itself, as any single scale congruency like this can be found in isolation. However, finding an additional simultaneous scale congruency is non-trivial, and indicates a deep relationship between the chestahedron and the icosahedron. In this case, the second congruency is shown by the blue triangle, which forms the base of the chestahedron as well as an exact cross section of the icosahedron.

To help indicate this in another way, imagine the chestahedron unfolding out of a tetrahedron as in this animation. Start with the base (blue in the images below) embedded as pictured inside the static icosahedron. Now, as the tetrahedron unfolds, what is pictured below as the top-most yellow triangle starts very small (actually as the top point of the tetrahedron), and slowly grows in size. Here is the interesting thing: the moment when the unfolding of the tetrahedron reaches the exact point of creating the chestahedron, the top-most yellow triangle reaches the exact same size as one face of the icosahedron. In other words, ratios which apply to the internal structure of the icosahedron also apply to the internal structure of the chestahedron; the forms are intimately related.

Chestahedron and its relation to the Icosahedron 1

Chestahedron and its relation to the Icosahedron 2

Chestahedron and its relation to the Icosahedron 3


  1. adriana

    Hey Frank!

    Love the website! I wonder have you seen the sephirot tree of life? I was just taken by the similarity of the above (relationship between the chestahedron and the Icosahedron) You problably have seen it but it did strike me as interesting.

    Much love to you

    • Waller

      Yes! After reading the latest Lillipoh article on Frank’s amazing work, I was seeing the same similarities to the Tree of Life and also the FLower of Life. I played around with it alittle, but am such an amateur at sacred geometry, esepcially when we move into the realm of 3D, I couldn’t get to any real, concrete connections. Would LOVE to know if Frank or others have explored this. This work is amazingly powerful and profound. Many blessings!

Leave a Reply

Your email address will not be published.
Required fields are marked:*