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Decatria – Sculpture for Sale

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The Decatria (dek-a-TRIA) is a form with thirteen faces discovered by Frank Chester.  Frank tells about the form below:

In 2007 I was told by a former mathematical section leader at the Goetheanum, George Glockler, that if the dual of the Chestahedron could be found, it would be the form that surrounds the heart at night during its rebuilding process for the next day. Esoterically the dual relationship between the two forms is also a day and night relationship, weaving from a day to a night and a night to a day.

What is a dual? A dual is a form that will fit inside or outside of each other. It is a reversal based on points to planes or planes to points. If you truncate a cube (cut off its corners), you will create an Octahedron and if you truncate an Octahedron, it will produce a Cube. The Cube corners will touch the inside faces of the Octahedron or the Octahedron corners will touch the inside faces of the Cube. The rule is to cut each corner at 90 degree to the form’s center and stop cutting one half the distance from the corner to the center.

Following this dual procedure, the Chestahedron resulted in having to cut off three edges instead of three corners. The reason for this was that both the edges and the corners were at 90 degrees to the axis. This is the first lawfully objective use of the traditional form of transformation using both corners and edge truncations at the same time.  The resulting form has three edges and four corners, resulting in a 13-sided polyhedron, the Decatria. Each form fits perfectly inside the other; they form a dual pair.

The Decatria is to being studied in New York for a possible use as a new beehive design because of its unique shape.  Inside the Decatria, formed out of a cross-section, is a perfect hexagon, which is the natural organizing shape for honeycomb construction.

HoneycombThis sculpture (solid, gold-colored in the pictures below) is for sale. If you are interested in purchasing one of Frank’s unique sculptures, please fill out this contact form.


  1. Hi Frank, I so enjoyed your talk at RISD on the evolvement of your forms and how it is truly belies the principles and foundation of our universe. As a small beekeeper I am fascinated by your new hive formation. How do you get frames in that construction to fit or do you allow for a free form hive to develop? I have studied Colony Collapse Disorder at length and find it fascinating re your comment about the fellow that was using this type of hive had the only living hives about. Do the bees exit your hive from the top? Why do you think this form is working or is it? I would love to talk to your beekeeper in NY.
    My daughter graduated from RISD and I have forwarded your marvelous lecture to her and some of her post grad friends. I so enjoyed how you have related your discovery to the human heart, etc. It goes down to the cellular level and how these forms change and evolve. I can’t help but believe that fractals and other dimensions that are current thought on the string theory are related. I think you perhaps have opened a window of understanding of some other dimensions we have yet to discover or comprehend. Perhaps we are seeing a symetrial parallell universe on some level. Thank you your talk. I so enjoyed it.

    I think you belong on a would be amazing.
    Please check out these links. I think they are relavent to your work.

  2. Joe Dubs

    Hi , Wonderful work!! I was wondering if you could tell me what shapes make up the decatria and how many of each..
    I can see there are mostly pentagons and maybe one or two quadrilaterals??


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