A semiregular polyhedron box and method of assembly provides a rectangular cross-section, ten faces, twenty-four edges, and sixteen vertices. The box is plastic corrugated and has two rectangular sidewalls, two square sidewalls, and four corner sidewalls. The sidewalls join at their lateral edges to form an enclosed region defined by a generally rectangular shape and four chamfered edges. Four rectangular panels hingedly join two opposing upper edges of rectangular sidewalls. Each rectangular panel has two L-shaped slots. Four irregular panels hingedly join two opposing upper and lower edges of the square sidewalls. Each irregular panel comprises an irregular top edge having a convex curve, and top angled corners. Each irregular panel also comprises irregular lateral edges having a lateral notch and bottom angled corners. The top angled corners of the irregular top edge and lateral notch detachably interlock with the L-shape slots of the rectangular panel to close the box.