Abstract:
Expandable surfaces made from sheet materials with slits distributed on the surface of sheet material where the surfaces expand by application of force along or/and across the surface of sheet material. The unexpanded surfaces are flat sheets, or closed surfaces like cylinders, spheres, tubes, or custom-designed organic shapes marked with pre-formed or post-formed slit designs. The expanded surfaces can be single units or modules which can be attached to one another through various means. The sheet materials range from hard surfaces like metals, to softer materials like papers and plastics, or pliable materials like fabrics, rubbers, synthetic surfaces or bio-surfaces. The slits are arranged in patterns ranging from periodic, non-periodic to irregular designs. The slits can be straight, bent, curved or irregularly shaped with even or uneven spacing. Slitting can be achieved by digital cutting or punching devices like laser-cutting, water-jet cutting, digital punching, automated dies, etc. or pre-formed when casting the sheet material. Force can be applied manually with tools or through the use of machines and special set-ups. Applications range from architectural surfaces, walls, ceilings, panel systems, structures and sculpture. On a smaller scale, applications include containers, packaging material, fabrics and human wear. On micro- to nano-scale, applications range from expandable surfaces for gauzes, band-aids, stent designs, skin grafts, semi-permeable membranes and micro-filters for various industries including purification of fluids and chemical substances.
Abstract:
A method for bending sheet metal includes introducing to the sheet metal thinned regions which are positioned either along or immediately adjacent to a bending line. These thinned regions allow the metal to be easily bent along the bending line using conventional hand tools or non-specialized machines. The thinned regions may be shaped as slots having a specific width, length, end shape, spacing from each adjacent slot, and depth into the metal sheet. According to one embodiment of the invention, each slot is cut through the entire thickness of the metal sheet. Other related embodiments require that the slots be only partially cut or etched thereby having a depth that is less than the thickness of the metal sheet. The thinned regions may be any appropriate shape as controlled by the shape of the bend, the type of metal, the thickness of the metal, the ductility of the metal, the angle of the bend, and the application of the metal (e.g., load bearing, etc). According to a second embodiment, two generally parallel sets of thinned regions are formed adjacent and generally parallel to the bending line. In a preferred application, the two sets of thinned regions are slots (cutting through the metal) and are staggered or offset with respect to each other.
Abstract:
A family of convex and non-convex tiles which can be tiled together to fill a planar surface in a periodic or non-periodic manner. The tiles are derived from planar space frames composed of a plurality of regular p-sided polygonal nodes coupled by a plurality of struts. p is any odd number greater than three and an even number greater than four. The nodes and struts, along with the areas bounded by them, make up a tiling system. In addition, the lines joining the along the center lines of the struts define a large family of convex and non-convex tiles. The convex tiles include zonogons, and the non-convex tiles include tiles with one or more concave vertices. The latter comprise singly-concave, bi-concave and S-shaped tiles. The tiles can be converted to 3-dimensional space-filling blocks. When these blocks are hollow and inter-connected, architectural environments are possible. Other applications include tiles for walls, floors, and various architectural and other surfaces, environments, toys, puzzles, furniture and furnishings. Special art pieces, murals and sculptures are possible.
Abstract:
Families of node shapes based on prismatic symmetry for space frame constructions. The node shapes include various polyhedral, spherical, elipsoidal, cylindrical or saddle shaped nodes derived from polygonal prisms and its dual. The node shapes are determined by strut directions which are specified by various directions radiating from the center of a regular prism of any height. A plurality of such nodes is used in single-, double- or multi-layered space frames or space structures where the nodes are coupled by a plurality of struts in periodic or non-periodic arrays. The space frames are suitably triangulated for stability. Applications include a variety of architectural structures and enclosures for terrestrial or (outer) space environments. Suitable model-building kits, toys and puzzles are also possible based on the invention.
Abstract:
A building system composed of space-filling convex and non-convex saddle zonogons which fit together periodically and non-periodically into a variety of orderly and irregular looking space structures including saddle zonohedra, single-, double- and multi-layered structures, multi-directional space-filling structures and curved space labyrinths. The saddle zonogons are derived from the infinite class of plane zonogons, and the saddle zonohedra from the infinite class of plane-faced zonohedra. The surfaces of the saddle polygons could be continuously curved surfaces of faceted polygonal surfaces derived from minimal surfaces. The curved surfaces could be flexible membranes or nets in tension used by themselves or in combination with space frames, or stiff shell-like surfaces, and the edges could be hinged or fixed to others. Applications of the system include architectural and environmental structures, fixed or retractable space frames, decks or platforms, educational kits or toys, curved tiles, and saddle polyhedra nodes for space frames.
Abstract:
This invention describes a 4-dimensional periodic table of elements (4D PT) based on the 4 known quantum numbers of the atom—n (principal), l (azimuthal), m (magnetic) and s (spin)—which determine the 4D Cartesian co-ordinates (n,l,m,s) of a 4-dimensional cubic lattice. Since the four quantum number combinations of each element are unique by Pauli's exclusion principle, each chemical element occupies a different vertex of this lattice and has a unique location in 4D space and hence in the periodic table. The 4D PT of elements extends to chemical molecules and compounds by adding coordinates of individual elements into composite coordinates of molecules and compounds in a larger expansive PT. The higher-dimensional table of elements and compounds can be represented in any digital media or print media as 2D charts or cards. The 4D PT #can be physically built as 3D model kits comprising nodes and connecting struts or 3D blocks or connected 2D panels.
Abstract:
New designs for a sports ball comprising at least two polygonal panels and having an improved performance and uniformity. Each panel has doubly-curved edges that curve along and across the surface of the sphere. The panels are p-sided curved polygons, where p is an integer greater than 1. The single panels, in an imagined flattened state, have curved edges where each edge curves inwards, outwards or undulates in a wave-like manner. The edges are arranged so each individual panel is without mirror-symmetry and the edge curvatures are adjusted so the panel shape can be varied to achieve more uniform panel stiffness as well as economy in manufacturing. The ball also has a possible shape-induced spin due to the panel design and the overall rotational symmetry of the design. In various embodiments, the ball comprises at least two multi-paneled layers that are topological duals of each other, wherein each layer provides a compensatory function with respect to the other layer such that the ball has a uniformly performing surface. Applications include but are not limited to designs for soccer balls, baseballs, basketballs, tennis balls, rugby, and other sports or recreational play. The shape of the ball can be spherical, ellipsoidal or other curved convex shapes.
Abstract:
New designs for a sports ball comprising at least two polygonal panels and having an improved performance and uniformity. Each panel has doubly-curved edges that curve along and across the surface of the sphere. The panels are p-sided curved polygons, where p is an integer greater than 1. The single panels, in an imagined flattened state, have curved edges where each edge curves inwards, outwards or undulates in a wave-like manner. The edges are arranged so each individual panel is without mirror-symmetry and the edge curvatures are adjusted so the panel shape can be varied to achieve more uniform panel stiffness as well as economy in manufacturing. The ball also has a possible shape-induced spin due to the panel design and the overall rotational symmetry of the design. In various embodiments, the ball comprises at least two multi-paneled layers that are topological duals of each other, wherein each layer provides a compensatory function with respect to the other layer such that the ball has a uniformly performing surface. Applications include but are not limited to designs for soccer balls, baseballs, basketballs, tennis balls, rugby, and other sports or recreational play. The shape of the ball can be spherical, ellipsoidal or other curved convex shapes.
Abstract:
A family of non-convex and convex tiles which can be tiled together to fill a planar surface in a periodic or non-periodic manner. The tiles are derived from planar space frames composed of a plurality of regular p-sided polygonal nodes coupled by a plurality of struts. p is any odd number greater than three and an even number greater than six. The nodes and struts, along with the areas bounded by them, make up a tiling system. In addition, the lines joining the along the center lines of the struts define a large family of convex and non-convex tiles. The convex tiles include zonogons, and the non-convex tiles include tiles with one or more concave vertices including singly-concave, bi-concave (doubly-concave), multiply-concave and S-shaped tiles. The tiles can be converted to 3-dimensional space-filling blocks. When these blocks are hollow and inter-connected, architectural environments are possible. Other applications include tiles for walls, floors, and various architectural and other surfaces, environments, toys, puzzles, furniture and furnishings. Special art pieces, murals and sculptures are possible.
Abstract:
Building structures based on polygonal members with coplanar straight edges and icosahedral symmetry. The building structures comprise a set of ten elementary polygonal members, including four triangular members and six parallelogram-shaped members, that are combined to form tetrahedral, octahedral and half-octahedral or trucated tetrahedral, cuboctahedral and truncated octahedral or rhombohedral and parallelpiped building members that in turn fill a three-dimensional space periodically or non-periodically. The orientation of the building members is such that all edges are parallel to the fifteen two-fold axes of rotation of icosahedral symmetry.