designing optimal spatial meshes: cutting by parallel trihedra ...

VOL. 41 (2000) n. 133Figure 19Figure 20by means of its own Fundamental Grid, whichallows different patterns of triangulation.Whichever polyhedron it is, the scale produced isrhombic-shaped (starting with a regular polyhedra)or rhomboid-shaped (starting with a semi-regularone). Figures 19 and 20 shows different views of asolution derived from the icosahedron (the roof hasonly 10 scales); its fundamental grid, but notriangulation, is drawn over it.6. CONCLUSIONThe parallel trihedra (or pyramids) procedure makespossible the intersection of spheres in such a waythat new “inflated polyhedra” can be designed. Thefollowing summary-table shows the type ofobtained spatial mesh, when the starting polyhedronis regular.Similarly, 14 semi-regular polyhedra generate asmany inflated and rhombic models. In short, 28 newshapes made up by scales of sphere, cutting eachother along arcs of minor circle. Their internal gridof triangles is, nevertheless, always optimal.