Steiner Surface model, c 1875.

Jacob Steiner was one of the leading geometers of the mid 19th Century. This plaster surface model was made for Sir Arthur Cayley (1821-1895), another pioneer in the field. It has the equation root x + root y + root z + root w = 0, where x, y, z and w are proportional to the perpendicular distance from the faces of a regular tetrahedron. The surface is scooped down to the centre and intersects itself.