Archimedean Solids

In euclidean space, there are two famous families of polyhedra. The platonic solids are characterized by the property that each face is an identical regular polygon. The Archimedean solids are characterized by the property that all faces are regular polygons, and all vertices are equivalent.
Sometimes the terms regular and semi-regular are used instead of Platonic and Archimedean, resp. There are also regular star solids which dont fit into this category, so probably one has to specify regular convex polygons (to disqualify the star-shaped faces.)
Platonic and Archimedean solids can be characterized by their vertex figure: the sequence of regular polygons that surround a vertex. This is well-defined since all vertices are identical in both cases. The polygons themselves can be represented by their number of sides n.
So, the name of the cube in this nomenclature is 4.4.4, since 3 squares meet at each vertex. Each of these polyhedra also has a dual polyhedra, formed by joining the midpoints of the faces along edges which are perpendicular bisectors of the original edges. By duality, the resulting dual polyhedra has identical faces (since the original figure has identical vertices) but the vertices are different.
With this application the user can explore these two families of solids and their duals.
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