A cube’s space diagonal is a line segment that starts at one vertex, passes through the center of the cube and ends at the opposite vertex. A cube has four space diagonals.
Its name comes from the Greek kubos, meaning a die. You recognized it at once: it is the cube, an object that you may think holds no more mysteries for you. But what if we took a closer look? Let’s cut the cube into four slices perpendicular to one of its space diagonals.
These cross-sections will allow us to illustrate several concepts: the vertex figure, the cube’s order-3 and order-6 symmetries, the Petrie polygon, and Coxeter numbers and planes.
A meeting at the vertex
