:: seasons greetings ::
Some may find the title misleading as there's a Martian Math spin to this post, by which I mean I'm blending in some of what I also call Quaker geometry in posts gone by.
Given the primacy of the tetrahedron in New England Transcendentalist late 1900s poetics, aka 4D per Bucky Fuller, we have some obligation, in Quakerism, to sustain the inertia (our heritage, after all).
So the teaching is this: at the XYZ origin, instead of something boring like a bowling ball with hooks, the XYZ vectors stretching away at right angles, we substitute a wrought iron tetrahedron, hooking our six vectors to that, reinforcing the understanding the opposite edge pairs are mutually perpendicular.
Inscribing a tetrahedron as face diagonals in a cube is an easy way to demonstrate this fact, plus to allow for an inverse tetrahedron (the dual in the "duo-tet cube", Bucky's 3-volume).
I imagine a clear plastic cube of beveled faces, six squares glued, with chains pulling hard against the tetrahedron in the middle, in the XYZ directions.
:: model by Skip ::