This Demonstration can serve as a reminder of certain geometrical features—for instance, that the icosahedron has 5
6 edges, corresponding to the number of faces of the rhombic triacontahedron, and that the arrangement of 1
6 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.
