Build a fundamental region of a Platonic solid out of mirrors facing inward, e.g., $1/48$ of a cube, omitting the side of the tetrahedron which is part of the exterior of the solid. When you look into those three mirrors, you see copies of yourself looking into a Platonic solid from each of the other fundamental regions.
If you truncate the vertex corresponding to the center of the regular polyhedron appropriately with an opaque triangle, the mirror images of the triangle form the polyhedron or the dual. I think a few of these, made by another math major in my year, might still be in the math lounge at New College.
This is a striking visual effect which can be observed by nonmathematicians in passing. Similarly, two large vertical mirrors set at an angle of $\pi/n$ show the viewer as one of $2n$ copies.