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.
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.