ArchiCad, uses a parametric sub-language called GDL (Geometric Descriptive Language), whose spatial system is X, Y, Z based. In order to more easily find relationships among the classical platonic polyhedra, we have had to modify and re-code these polyhedra in order to more easily manipulate them (namely to rotate and scale them) to build all possible relationships between them, and networks of these forms into structures such as octet or space frame trusses, domes, shells, and so on. This is not something I have had the math or programming chops to pull off on my own, and I have been completely supported in this endeavour by the brilliant mind of Olivier Dentan. With these various polyhedra available to us, we can then rotate, scale, interlock and/or nest these solids together to understand the relationships among the forms, and find ways to design spaces and structures that are defined by their boundaries which, if we are sensitive to, can result in some unique, intelligent, rational and unexpected structures. These objects are available to download for any user of ArchiCad, free of charge, however the noted $10.00 flat rate is the fee related to hosting and posting the objects here.
Without delving into the details of how these objects are coded (one can open them to study the scripts), suffice it to say that these should be the fundamental building blocks of form in any CAD/BIM system. I have always imagined that the polyhedra, scaled however you like (you could use le Corbusier’s Modulor), could be the cursor used to draw in four dimensional space. Buckminster Fuller referred to this system of geometry as Nature’s Coordinate System, and most serious students of his thinking, from physicists to astronomers to programmers tend to be in agreement that Fuller had caught a glimpse of something that nobody else had. It’s up to all of us to take it further. Eventually, we would hope to use this series of objects to form a kind of 3D cursor, that could ‘point’ to any direction in space, and cast vectors to them, building a framework of triangulated, strong and materially efficient architecture – like a kind of fractal geodesic spiderman.
Below is a link (click on the folder icon) to the series of polyhedra developed for ArchiCad to date. Be sure to try them out with the ‘debugger’ script switched on, which will allow you to graphically rotate and scale the objects in the 3D window. Features to be added will include rotation around polygon normals (as axes).
Now the cool thing about Olivier Dentan’s objects is that it allows the following parametric options to be switched on or off, namely;