Josep Rey Nadal
Mathematician, former teacher, artist, mathematical and creative museographer of Mathematics Museum of Catalonia.
Polyhedra duality is like a couple relationship. Two dual polyhedra are dual to each other: the dual of the dual has to be the original again. Dual polyhedra are usually built by intersecting perpendicularly each pair of edges. However, in this piece we considered the two dual polyhedra to be inscribed in the same sphere. Thus, created with edges, the two polyhedra don't touch each other. There is the dodecahedron surrounding its dual, the icosahedron, but they don't touch. Are we in front of a Platonic relationship? Transparent arches of the common sphere were added to hold them, connecting each vertex of one polyhedron with the closer vertexes of its dual. These transparent arches draw a spherical rhombic triacontahedron.