This origami piece is Five Intersecting Tetrahedra, designed by Thomas Hull. The tetrahedron is the simplest platonic solid, but this model connects naturally to the dodecahedron – a 3D object with 12 pentagonal faces. Given a regular dodecahedron, we can choose 4 equidistant vertices which then correspond to a tetrahedral outline when connected. Repeating this process produces 5 unique sets of 4 vertices, thus yielding intersecting tetrahedrons within the dodecahedron. The rotational symmetries of the dodecahedron act naturally on the tetrahedral model, demonstrating the alternating group A5.
Rachel is a Mathematics and Statistics Undergraduate in the Mathematical Institute and Department of Statistics, University of Oxford.