Abstract: Utilizing the three different hyperbolic paraboloids which each divide a set of correlating tetrahedrons in half, new, unique interconnectable structural members and toys have been created. They include the n-fold hyperbolic paraboloids, the n-fold hyperbolic paraboloid lattice assemblies and many other cellular, lattice and labyrinthal structures. Some have stacking properties and all have interlocking characteristics and are inherently strong and rigid due to the use of hyperbolic paraboloids. The interlocking and stacking characteristics of these structural members result from the saddle shaped compound curvature of the hyperbolic paraboloids. These structural members can be combined in multiple ways to build aesthetic and utilitarian components such as beams, trusses, packaging foams, toys, as well as other repeating cellular, lattice and labyrinthal structures.

Abstract: Utilizing the three different hyperbolic paraboloids which each divide a set of correlating tetrahedrons in half, new, unique interconnectable structural members and toys have been created. They include the n-fold hyperbolic paraboloids, the n-fold hyperbolic paraboloid lattice assemblies and many other cellular, lattice and labyrinthal structures. Some have stacking properties and all have interlocking characteristics and are inherently strong and rigid due to the use of hyperbolic paraboloids. The interlocking and stacking characteristics of these structural members result from the saddle shaped compound curvature of the hyperbolic paraboloids. These structural members can be combined in multiple ways to build aesthetic and utilitarian components such as beams, trusses, packaging foams, toys, as well as other repeating cellular, lattice and labyrinthal structures.

Abstract: A new connecting node set that is unique and surprisingly effective at aligning interfacing holes in connecting nodes is illustrated by their application to radial tetrahedral structures. This method of connecting one node to another requires that a left handed node be connected to a right handed node. They are called left handed or right handed because their lines of interface in at least two directions of intended use are geometrically coincident with straight line rulings of a hyperboloid of revolution of one sheet which itself consists of two families of straight line rulings, designated a left handed and a right handed family respectively. With these nodes, magnets could be placed on the lines of interface (opposite placement in a left handed one from a right handed one) and thus the magnets would always attract or repel as preferred.

Abstract: The radial tetrahedral structures consist of four spokes radiating outward from a hub at the center of a tetrahedron with each spoke terminating in a connecting node at one of the four vertices of the tetrahedron. Each of the left handed and right handed radial tetrahedral structures (FIGS. 1A & 1B) of the embodiments described in detail in this application fit within a cubic envelope (although other envelopes are possible) and each is capable of being connected to its opposite version at any or all of its six cubic envelope faces. This results in versatile modular structures that can be used to extend into all three spatial dimensions just as cubes could be stacked to produce a multidimensional stack of any shape that results from the addition of more cubes. For example, a left handed and right handed radial tetrahedral structure could be assembled to replace the common 2 by 4 piece of wooden lumber in everyday use.

Abstract: Utilizing the three different hyperbolic paraboloids which divide each of the defining tetrahedra (DT) in half, new geometric objects have been created which have unique stacking and interlocking characteristics and are inherently strong and rigid due to their triangular and hyperbolic paraboloid faces. These geometric objects can be utilized to build aesthetic and utilitarian components such as beams, trusses, packaging foams, toys, repeating cellular structures and others. The n-fold hyperbolic paraboloids are new geometric objects. The “n-” in the title stands for any integer greater than or equal to three. The fourfold hyperbolic paraboloid (FIG. 2C) has the special attribute of being space filling. Like the cube the fourfold hyperbolic paraboloids can be continuously stacked so that there is no unenclosed volume between them. All of the n-fold hyperbolic paraboloids have unique stacking and interlocking attributes.

Abstract: A series of static structures formed from a plurality of interconnected rigid compression members or struts and flexible tension members or guys (e.g. wire cables, chains or elastic cords) is disclosed. The struts are discontinuous in several embodiments of the invention, intersect at an internal or peripheral point in others, or radiate outwardly from an internal central point in still others. Different configurations of guy arrangements may be described and claimed for each of the embodiments of this invention. Self Guyed Structures (SGS's) can be utilized as a stand-alone module or modules can be combined by connecting them at any point on a strut or guy in a nested, or an adjacently attached configuration to assemble composite SGS 's.

Abstract: A series of static structures formed from a plurality of interconnected rigid compression members or struts and flexible tension members or guys (e.g. wire cables, chains or elastic cords). Each strut is in pure compression (i.e. no bending or twisting forces) and each guy is in pure tension. The struts are discontinuous in several embodiments of the invention, intersect at an internal or peripheral point in others, or radiate outwardly from an internal central point in still others. Three or four configurations of guy arrangements are described and claimed for each of the five embodiments of this invention. Self-Guyed Structures (SGS's) can be utilized as a stand-alone module or modules can be combined by connecting them at any point on a strut or guy in a nested (overlapping) or an adjacently attached configuration to assemble composite SGS's.