Let us consider a dodecahedron. By selecting different sets of vertices, we can create 5 different cubes. The intersection of the 5 cubes is a so-called [url=https://en.wikipedia.org/wiki/Rhombic_triacontahedron]triacontahedron[/url].[br]The original version of this GeoGebra applet was contributed by [url=https://en.wikipedia.org/wiki/Lajos_Szilassi]Lajos Szilassi[/url].