Playing 4D Chess is a visualization of a knight’s tour on a four-dimensional chessboard. The 80 chambers on the 3x3x3x3 chessboard (removing the central chamber) are each represented by a vertex; a knight’s move is a displacement of two units in one direction and one unit in an orthogonal direction. The first three dimensions (x,y,z) are shown in a standard 3D grid. A unit move in the fourth dimension is represented by a translation of (1/4,1/4,1/4); vertices for a fixed 3D slice have a consistent form (cube, sphere, octahedron) to aid in the visualization. As the viewer plays four-dimensional chess by following this Hamiltonian cycle around all 80 vertices, they will see that no two consecutive moves involve the same two coordinates.
Play three-dimensional chess while everyone else is playing checkers.
While your friends play checkers, these earrings allow you to play three-dimensional chess! On a chessboard, a knight moves diagonally along a path shaped like an L. These earrings take knight moves into the third dimension. This coordinated pair contains two tours of knight moves in a 3x3x3 cube.
A knight's tour is a walk visiting every step of a chessboard where each step is a knight's move. The earrings are a three-dimensional knight's tour --- of a 3x3x3 chessboard. (For parity and symmetry reasons, I removed the center cube and two others.)
I used Mathematica to find all the Hamiltonian cycles in this grid of 24 vertices, and chose two of them at random to create this mismatched but coordinated pair in black and white like the pieces on a chessboard.
Each earring is a cube and measures 1.1 in (28mm) diagonally.
These earrings are created through a lost-wax casting process, with molten silver replacing a high-resolution 3D printed wax model, white and black rhodium plating applied, and finished with sterling silver earwire.