Look into a kaleidoscope of mirrors angled just right and you will see an image of a platonic solid in the reflections.
You will need some mirror board (paper coated with a reflective surface), plastic mirrors that you can cut, or some other highly reflective material. I found a disposable plastic tray at a party supply store that had a highly reflective surface (silvered Mylar). It cuts easily but is rigid enough to hold its shape.
Place the patterns on the mirrored surface.
Poke a pin through the key points on the pattern to transfer the pattern to the mirror. Using a knife, lightly score lines connecting the pinholes to mark the lines you will cut and fold on.
Turn the plastic mirror over and score the fold lines (cut partly through the plastic). Cut the piece out along the lines from step 2.
Fold the mirror so the shiny side is facing in to make a kaleidoscope and tape the tab in place.
Place the mirror on a table so the smaller opening is facing down. Look straight down into the mirrored surfaces. The reflections form an image of a platonic solid.
The isosceles triangle used to make the icosahedron kaleidoscope is the same shape as the faces of the Cheops (Khufu) Pyramid.
This illusion takes advantage of the symmetries in platonic solids. The spherical model project shows the mirror symmetries.