Kajikawa, Yasushi Growing icosahedra. (English) Zbl 0882.52006 Symmetry Cult. Sci. 3, No. 2, 117-136 (1992). From the text: “I first divided an icosahedron into ten types of small modules, then reconstructed various polyhedra by combining the modules radially and symmetrically. I found a beautiful hierarchical structure in the polyhedra, where in each layer in the reconstruction process there appear various 5-fold symmetrical polyhedra including the dedocahedron, icosahedron, and rhombic triacontahedron. Furthermore, it is possible to fill the entire space in these models while maintaining a hierarchical structure in the filling pattern.Although this discovery was done outside the territory of translational symmetry in crystallography, it is quite suggestive of a solution to the structure of 5-fold symmetrical crystals that grow radially and symmetrically in the natural world”. MSC: 52B15 Symmetry properties of polytopes 82D25 Statistical mechanics of crystals Keywords:icosahedron; 5-fold symmetrical polyhedra; translational symmetry; crystallography PDFBibTeX XMLCite \textit{Y. Kajikawa}, Symmetry Cult. Sci. 3, No. 2, 117--136 (1992; Zbl 0882.52006)