Abstract: An architectural structure capable of generating a virtual polyhedral space includes a plurality of walls, each having a first side edge, a second side edge, and a reflective surface. The walls are disposed adjacent one another, with the first side edge of each wall adjacent the second side edge of an adjacent wall, each wall lying in an associated one of a plurality of planes intersecting at a common apex, thus forming a pyramid shaped structure. So disposed, the walls define an interior space of the architectural structure, with the reflective surfaces of the walls facing the interior space. Each wall further includes a base edge. Together, the base edges of the reflective walls form a support base for supporting the architectural structure on a floor surface. The images of the floor surface in the reflective surfaces of the walls forms a coherent image of a virtual polyhedron. Three-sided, four-sided, and five-sided embodiments are described.