Musing about the octahedron shape

One of the Platonic Solids, or their edge equivalents, has long been of interest to me; and am not sure why, but is again on my mind now. It is called the octahedron.

That shape seemed to draw my attention during breaks when working as a contract electronic technician at the Jet Propulsion Laboratory, when I would often wander next door to the Von Karman Auditorium's window display, showing replicas of their spacecraft as of back in the early 1970's when I worked there. Although not of equal sides, that octahedron basically was a horizontal triangle coupled to a smaller horizontal triangle above it, rotated by 30º, and the corners all connected by similar rods, each set forming another triangle itself. This clearly had the effect of a minimum yet stiff structure that defined two parallel surface's relationships with each other. In other words, the support of a higher parallel surface, by a lower surface; rigidly held yet with fewest parts to do it.

Although composed only of triangles, the octahedron shape also contains a square, if one looks for it. Cut through the plane of this square, it creates two pyramid structures that have a four-sided base. I don't know if this has anything to do with my interest in it at this time. I seem more interested in the aspect of supporting two parallel planes with maximum stiffness for the amount of material involved.

Maybe I need to make a table? Where to put it in my tiny already overstuffed house? And a triangular-shaped tabletop is not an efficient way to use space in a basically rectangular house structure. Yet it is interesting to me again now.

Maybe I could adapt it to become a major part of the solar concentrator projects in my back yard, coupling ground level up to swivel level of the six foot diameter dishes.