¶ Cube: Two Tetra as Cube
Index Entry
The accomplishment of experienceable, structurally stabilized cubes with a minimum of nonredundant structural components will always and only consist of one equiangled and equiledged ‘regular’ tetrahedron on each of whose four faces are congruently superimposed asymmetrical tetrahedra, one of whose four faces is equiangled and therefore congruently superimposable on each of the four faces of the regular tetrahedron; while the four asymmetrical tetrahedra’s other three triangular–and outwardly exposed–faces are all similar isosceles triangles, each with two 45-degree-angle corners and one corner of 90 degrees. Wherefore around each of the outermost exposed corners of the asymmetrical tetrahedra, we also find three 90-degree angles which account for four of the cube’s eight corners; while the other four 90-degree surrounded corners of the cube consist of pairs of 45-degree corners of the four asymmetric tetrahedra that were superimposed upon the central regular tetrahedron to form the stabilized cube. More complex cubes that will stand structurally may be compounded by redundant strutting or tensioning triangles, but redundancies introduce micro-invisible, high- and low-frequency, self-disintegrative accelerations, which will always affect structural enterprises that overlook or disregard these principles.
