Archimedean Excogitation consists of a metal and glass display case framing a system of nine tracks on two main levels.

[1][3] The lower level tracks contain billiard balls, which encounter a series of mechanical obstacles as they roll, some of which (such as a drum and xylophone) produce noise.

[4][1] The upper level tracks contain larger duckpin bowling balls,[5] which push windmill blades and encounter similar obstacles.

[1][4] Metta Winter, writing for The Christian Science Monitor, described it as "a noisy, unpredictable affair observers find hard to walk away from".

[1] Hayley Kaufman, writing for The Boston Globe, called it "seemingly unstoppable [and] delightfully complex".