Rhombicuboctahedron

Vi Hart's balloon polyhedra reminded me of Leonardo da Vinci's rhombicuboctahedron (right), first  printed in the Divina Proportione.  This Archimedean solid has eight triangular and eighteen square faces, along with 48 edges. There are 24 identical vertices, with one triangle and three squares meeting at each.  

Described as a Italian polymath, da Vinci was a painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist, and writer. He was a genius who, perhaps more than that of any other person, epitomized the Renaissance humanist ideal -- a man of insatiable curiosity with an endless and inventive imagination.

"Whoever despises the high wisdom of mathematics nourishes himself on delusion.” 
            – Leonardo DaVinci