A chiralkine game can be played on a gameboard bearing a hexagonal array of coloured recesses configured to receive correspondingly coloured corners of a chiral tetrahedron, such that the tetrahedron can be rolled between six different positions around a central recess in a hexagon. The relationship between the recesses and corners of the tetrahedron models the relationship between the six different numbers in the new mathematics. The position of a tetrahedron in a hexagon thus records a state in a token space, which state is one of the six numbers in the new mathematics. Each number remembers its previous position and anticipates its next position. The gameboard is like a computer hard drive in which each bit can be in one of six states.
As a tetrahedron rolls around a hexagon, each edge acts successively as a pivot. This is related to the noncommutativity of the mathematics that the hexagon and tetrahedron embody in the game.
Coloured tetrahedrons can be found in the game apparatus for Coloured Yatzy, which used to be sold by Paul Lamond Games.
The game is described in British patent application, publication number GB2548981.
One player plays blue and the other plays yellow. The possible positions of the tetrahedrons, their meanings and their possible next positions are summarized below.
The game board and tokens could instead be used to control exchange of goods and services in an economy. Two hexagons are assigned to each good or service being exchanged, one for a buyer and one for a seller. The possible positions of the tetrahedrons, their meanings and their possible next positions are summarized below.