example of non regular triangle tessellation

To these, in 1960 Stanko Bilinski added a second rhombic dodecahedron, additionally proving it as (the last) convex isozonohedron (Grünbaum 2010: 5).

The crystallographer Evgraf Fedorov listed, in 1885, the cube (representative of all rhombohedra), the semiregular hexagonal prism, the rhombic dodecahedron, the elongated dodecahedron and the truncated octahedron (Grünbaum 2010: 4) as all the possible combinatorial types of convex polyhedra that fill space in monohedral tessellations, without changing orientation. 1, 2, 3, 4, 5 and 6 are convex polyhedra with centrally symmetric faces that fill space by translation of their replicas. The six primary parallelohedra illustrated in Figs. The search goes on, but here we will focus on primary parallelohedra, convex uniform tessellations and some topological interlocking assemblies. In 1980, two types of asymmetrical convex polyhedra with thirty-eight faces, each of which fill space monohedrally, were discovered by Peter Engel (Grünbaum and Shepard 1980: 965). The enumeration of polyhedra that fill space in infinite replicas (in other words, plesiohedra, whose centroids outline lattice points), Grünbaum and Shepard denote, “has no finite answer” ( 1980: 966) and remains an open problem in mathematics.

Example of non regular triangle tessellation