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Keh-Ming Lu, Alan S. Tsaur, Mei-Fan Chen; Napoleon paper building blocks. Journal of Vision 2007;7(9):847. doi: 10.1167/7.9.847.
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A general concept of building blocks is of 3D geometric graphics presented by their different appearance. The shape of each individual building block is initially confined. Constructors must conceive the design pattern and then select different building blocks to construct the patterns. Therefore, converting a rhombic tessellation motif into a 3D tessellation model is an essential goal of paper building blocks. Reusability and capability of coloring are two specific features of paper building blocks. Combinations of building blocks including the prime models are reusable. These important features are irreplaceable by wooden or plastic building blocks.
This study starts with a description of the basics of Napoleon plane tessellation and a development of 8 basic building blocks such as Bowtie, Wing, Teardrop, Bar, Boat, Star, Chevron, and Carp that are made of a rhombic 32-iamond through four construction processes. In order to increase the number of types of building blocks, we developed two steps to create 54 types of primary, secondary, and derivative models. Since these models, topologically, are of polyhedral object that is comprised of faces, edges, and vertices of regular triangles, we can calculate their Euler characteristic that amazingly is equal to 2.
We also create innovative modules including through holes or handles by combining these building blocks. The topological name for the number of handles in an object is genus. Based on a polyhedron's numbers of vertices, faces, and edges, we developed two categories of applications of these modules: a) modules that connected building blocks by vertices and edges such as flip flop toy, rotation toy, and lantern spheres; b) modules that connected building blocks by faces such as a torus genus-1 donut and a genus-1 rhombus. For the modules of the second category, we developed a novel approach to calculate Euler characteristic and finally verify the genus-n modules.
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