1. An apparatus for producing a three-dimensional kaleidoscopic image, the apparatus comprising: a screen for the generation of images thereon; and a plurality of mirrors surrounding the screen, wherein the screen is substantially shaped as a portion of an outer surface of a sphere or polyhedron having icosahedral group symmetry, wherein the plurality of mirrors are aligned with planes extending through a projected centre of said polyhedron or sphere and intersecting each edge of the screen, and wherein each mirror is aligned with an icosahedral plane of symmetry of said sphere or polyhedron having icosahedral group symmetry such that a source image generated on the screen is reflected in the mirrors to produce an apparent three-dimensional image of an outer surface of said polyhedron or sphere.