The Apeirohedron (infinite faces) stool is inspired by forms visualized by early 20th century geometers. Our Apeirohedron stool is a muoctahedron (a 14 sided polyhedron). The Apeirohedron stool has an infinite number of uses including as a side table, ottoman, cat hideaway, mood lighting fixture, and stackable sculpture. The stool is fabricated from 8 hexagons cut with trigonometric precision and joined leaving 6 alternating square voids. Each stool is fabricated from birch plywood and finished in beeswax ( an appropriate finish for an object that is also referred to as a convex uniform honeycomb).