Mathematics and philosophy have long been intertwined. The ancient Greek philosopher Plato was also a mathematical thinker.
He conceived the idea that these five convex and symmetrical polyhedrons with equivalent faces, the only ones that could exist, were the building blocks of the universe. That's why they're called the Platonic solids.
The Story of Math, a film by Oxford math prof Marcus du Sautoy, mentions the connection between these figures and the old idea of the four basic elements. These elements in turn connect with the chakras. Earth (Root chakra) is represented by the cube and Water (Sacral chakra) by the 20-sided isocahedron. The octahedron or Fire element relates to the Solar Plexus chakra and the tetrahedron, Air, to the Heart chakra. The fifth solid, the dodecahedron, is a twelve-sided figure associated with a fifth element, Spirit or Ether, which connects to the Throat chakra, seat of communication.
It is interesting to note that yogic tradition also teaches of five elements, Earth, Water, Fire, Air and Ether. Traditional Chinese medicine postulates five elements as well: Earth, Metal, Wood, Fire and Water.