| 摘要 |
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. The interlocking and stacking characteristics of these objects result from the saddle shaped compound curvature of the DT hyperbolic paraboloids. Three new three faced geometric objects or trihedrons (FIGS. 3A 3B, and 3G) have been created from each DT, each has two DT isosceles triangular faces with the third face being one of the three hyperbolic paraboloids which divide the DT in half. These trihedrons have stacking, interlocking, and strength and rigidity characteristics similar to the n-fold hyperbolic paraboloids. Thickening the surfaces of the three hyperbolic paraboloids which divide the DT in half (FIGS. 4B, 4E, and 4G) results in new thin geometric objects specifically defined by the DT. These new thin geometric objects can be used to build repeating cellular structures which effectively harness material properties to result in inherent strength and rigidity due to the hyperbolic paraboloid shape of the cell walls. They can also be applied to appurtenances of other geometric objects such as square bars, spheres, etc such that these other geometric objects can be joined in an interlocking fashion
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