Material: Silicon Bronze
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.