Abstract: A puzzle of the cuboid mechanical type having six faces forming a closed surface, wherein in the solved state the puzzle has a geometry in which each face comprises a non-planar surface formed from a set of interconnected elements rotatable about one of three mutually perpendicular and intersecting axes to convert the puzzle to/from the solved state geometry. In the preferred form each non-planar face is a hyperbolic-paraboloid or saddle-like surface.

Abstract: An umbrella (1) in which the canopy is supported, tensioned and retained on a frame without any external points. The ends of conventional ribs (6,7) are provided with force spreading components (8) which are located within pockets (9) at the periphery of the umbrella canopy (3). As the umbrella is erected, the force spreading components open to provide a surface which pushes outwardly against a bearing surface formed between a pocket and the canopy, which “spread” outwards. The spreading of the components (8) is initiated by the radially outward movement of slidable tubes (7) upon inner rods (6) attached at their inner ends to the shaft (2) of the umbrella. Inner rods (6) and outer tubes (7) together form the ribs or spokes of the umbrella which are supported and raised/lowered by primary struts (11) connected between the ribs and a primary shaft slider (12).