Externally Octet-Trussed Geodesic Patches

David Anderson
Originally written in July 1998

One of the reasons I like geodesic structures is the way they look. To me, they're just cool. Take a locally simple structure and extend it outward, scaling the edges slightly according to some theoretically staightforward rules, and you have a tesselated surface that curves back on itself - that you can build. Mathematical elegance in action.

One of the reasons I wrote the software to bend the octet truss for use in geodesic patches (see Planning a Bigger Dome, Part II) was to support a large geodesic, keeping it from dimpling when radial pressure was applied. I placed the truss inside the dome, since it made sense that supporting structures should be underneath the thing they support, and aesthetically, I wanted to preserve the geodesic look on the outside. Looking back however, I realize this aesthetic choice might not be pleasing in some cases, and that the supporting structure does not really support the geodesic by itself - the inner and outer shells are mutually supportive. The bracing can be moved from the inside to the outside the dome.

If you spend most of your time inside a dome, you want it to look geodesic inside. After all, if you went to all that time and trouble to put up a geodesic dome instead of a nice rectilinear box, it stands to reason that you don't want a lot of internal bracing getting in your way, and you don't want to see the patch connectors on the inside walls. And, there's usually lots of room outside. When the internal space is at a premium, if you put the struts outside you get more room inside.

To think about this easily, we start by looking at the old internally-trussed world differently. We change the meaning of the shells we previously designated as inner and outer:

With this change in logical orientation, it's easy to move the truss to the outside by making the tetrahedrons point outward instead of inward. In the code, this simply amounts to changing a sign from minus to plus. Instead of subtracting the stretched height of the tetrahedron from the truss point's radius, it is added. The geodesic shell becomes the inner shell, while the truss shell becomes the outer. The gd.coffee code has been to include the sign change.

Keeping with the coloring used in earlier paper (geodesic shell is white, truss shell is red, and shell connectors are pink) links to the vrml views and html tables for geodesic examples, are given below. The vrml and html are given for 5-frequency geodesics with a untesselated side length of 3 units. In addition, a set of 24 viewpoints is provided to enhance your vrml experience.

Vrml World Html Tables
tetra-5-3.wrl tetra-5-3.html
octa-5-3.wrl octa-5-3.html
icosa-5-3.wrl icosa-5-3.html

I can imagine space where the inner surface of the geodesic surrounds premium space, while the external structure can be used as scaffolding: to attach rigging and support facilities. Simple living spaces have these needs, but space or underwater vehicles come to mind as well. If both the shells were covered, and appropriately pressurized, the space in between could be used for many purposes, to hold storage closets, vessels, or even machinery. It could be a space for ductwork, or material or electrical transport - out of site to observers on the inside or the outside, but necessary to the smooth operation of any house or vehicle. And since the trussed geodesic patches could be prefabricated (each patch could be built whole, or as sections of tesselations) they could be shipped to a remote site and then assembled into possibly very large structures.

In the end, mathematically, it doesn't really matter if the bracing is on the inside or the outside of the geodesic. What matters is the purpose to which the structure will be put.