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This Demonstration can serve as a reminder of certain geometrical features—for instance, that the icosahedron has 56 edges, corresponding to the number of faces of the rhombic triacontahedron, and that the arrangement of 16 edges corresponds to the faces of the cube. The assembly is a good illustration of the self‐similarity property of fractals. It also shows a geometrical example of how an infinite set of volumes can have a finite boundary. Related schoolroom exercises could include the calculation of the height of a tower, the volume of a tower, and the proportions of icosahedra.