M Theory Lesson 161

The permutohedron in three dimensions is the octahedron with truncated vertices, which form six square faces between eight hexagons. Recall that the octahedron is dual to a cube, which in turn gives the permutohedron via the Loday maps. That is, the permutohedron (and the associahedron) acts as an intermediary between the two dual objects. Beneath duality lurks the shadow of triality!