Abstract:
Methods for making and assembling various orthogonal multifaceted polydeltatrihedral self-supportable corner reflectors. Planar two-dimensional network or pattern products and orthogonal polyhedra products-by-process evolving from the various methods find unique applicability in the radar industry, the educational toy industry, the navigation aid/hazardous warning industry, and the lighting industry.

Description:
GOVERNMENT INTEREST 
     The invention described herein may be manufactured and used by or for the United States Government for governmental purposes without the payment of any royalties therefor or thereon. 
    
    
     BACKGROUND AND OBJECTS OF THE INVENTION 
     The present invention relates to a method of assembling from a network of deltatrihedrals a multifaceted corner polyhedra reflector and, more specifically, to a network and method of constructing polydeltatrihedral corner reflector having three mutually perpendicular intersecting planes. 
     It is a well known phenomenon that a triplanar corner formed by the intersection of three mutually perpendicular planes will focus and redirect radar energy directly back toward the source. The term &#34;corner reflector&#34; as known in the art is typically utilized for marking obstructions, serving as navigation points and for radar purposes. In its most typical configuration, a radar reflector polyhedron, referred to as an octahedron, is formed from eight such corners and provides eight maximum reflecting lobes within a circumscribed sphere, each lobe consisting of a 40° cone. The present invention provides a novel system for assembling any number of similar configurations, some of which have never been considered, until now, for use in the manner herein prescribed. 
     A theoretically perfect omnidirectional radar reflector reflects incident waves uniformly in all directions and takes the form of a sphere. However, the convex reflective surface which a sphere presents to incident waves for the most part reduces the percentage of transmitted energy which is reflected back to a receiver. It has been determined that the theoretical optimum retrodirective response of a reflector is produced by a perfectly conductive planar member in which the incident radar energy is transmitted toward the plane normal thereto. However, such a reflector is considered to be extremely directional, and even a slight departure from the normal axes produces a substantial reduction in the usable reflected energy. 
     An omindirectional radar corner reflector, for example, has been developed wherein an array of twenty trihedral corners, i.e., three planes each mutually perpendicular, are distributed on the surface of a sphere as described in U.S. Pat. No. 3,039,093. The solid formed by this configuration is referred to as an icosahedron corner reflector, being a variation of the regular polyhedron referred to as an icosahedron, wherein each of the trihedrals consists of mutually perpendicular planes having an open frontal face projection of an equilateral triangle. The icosahedral corner reflector described by the instant patent is constructed of a plurality of triangular corner reflectors disposed in an edge-to-edge relationship such that the outer edges thereof from a portion of the resulting icosahedron conforming to a quasi-spherical shape. Twenty right trihedrals are assembled in edge-to-edge relationship with their apexes directed inwardly toward a common center and the planes of their outer edges defining an icosahedron. Corner reflector trihedrals having equilateral triangle face plane projections are referred to hereinafter as deltatrihedrals. 
     Although the above-described omnidirectional icosahedral radar reflector has been found useful in its functional capacity, the method of assembly is entirely restrictive. The manner of construction appears to describe a method whereby twenty individual corner reflectors (i.e., deltatrihedrals) are prepared and assembled accordingly to provide the particular configuration. Such an approach is cumbersome, time-consuming and relatively expensive and, therefore, a more expedient and economical approach in the fabrication of this particular icosahedron radar reflector as well as a family of similar multifaceted test devices would be highly desirable. 
     Therefore, it is an object of the present invention to provide a method of fabricating an omnidirectional orthogonal polydeltatrihedral having 90° reentrant triplanar cavities; which will overcome the above-noted and other disadvantages. 
     It is a further object of the present invention to provide a method of constructing an omnidirectional corner reflector configuration of a compact, collapsible nature, one that is amenable to both rigid construction and inflatable construction. 
     A further object of the present invention is to provide an omindirectional radar reflector which can be folded into a compact assembly for ease in storage and transportation. 
     Yet, a further object of the present invention is to provide a method of fabricating a three-dimensional omnidirectional radar reflector from a two-dimensional network. 
     Yet, still another object of the present invention is to provide novel deltatrihedral corner reflectors. 
     Still a further object of the present invention is to provide a method of manufacturing an omnidirectional radar corner reflector having a reflector response as uniformly close to a perfect sphere as theoretically possible. 
     BRIEF SUMMARY OF THE INVENTION 
     The foregoing objects and others are accomplished in accordance with the present invention, generally speaking, by providing a method for constructing a geometric solid or enclosed configuration representing an orthogonal polydeltatrihedral. The deltatrihedral is a variation of the deltahedra which is a convex polyhedra whose faces or surfaces consist entirely of plane equilateral triangles. The deltatrihedral as defined herein refers to a trihedral comprising three orthogonally assembled planes whose open frontal face is a projection of an equilateral triangle. A single deltatrihedral is constructed of three right isosceles triangles, hinged together such that they have a common vertex formed by the mutual coincidence of the individual apexes of each triangle. The three adjoining triangles may constitute a subpattern. Folding the triangles along their common edges in the same direction forms a triplanar cavity known as a deltatrihedral or corner reflector. The frontal face projection of the resulting trihedral forms an equilateral triangle. The proper placement of these individual trihedral patterns into a defined network provides the basis for constructing all members of the deltatrihedral family. By the continuous joining of edges in the assembly of the network of deltatrihedrals a continuous solid surface comprising the deltatrihedral corner reflectors, which is a stellated polyhedra, corresponding to the number of patterns defining the network is produced. The family of orthogonal polydeltatrihedral corner reflectors and their related orders of tesselations defined by the present invention opens the door to an entirely new spectrum of radar reflecting devices. The equilateral triangular facings have the capability of being subdivided or tesselated into infinitely smaller trihedrals. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention is further illustrated by way of the accompanying drawings which are intended to illustrate but not limit the subject matter of the present invention, and wherein: 
     FIG. 1 represents the basic deltatrihedral developed planar pattern from which the polydeltatrihedral corner reflectors of the present invention are fabricated; 
     FIGS. 2a-2f illustrate several representations of polydeltatrihedral corner reflectors of the present invention; 
     FIGS. 3a-3f illustrate the networks from which the developed planar patterns or specified polydeltatrihedral reflectors of FIGS. 2a-2f are assembled; 
     FIG. 4a represents the basic second order subdivision (tesselation) of the plane equilateral triangle, and FIG. 4b the network for the second order tesselation of the analagous deltatrihedral; 
     FIGS. 5a and 5b represent a second order tesselated network for the icosadeltatrihedral and corresponding assembled 80 corner array; 
     FIG. 6 represents a third order tesselation of the icosadeltatrihedral having 180 corners; 
     FIG. 7 represents a variation of the tetraicosadeltatrihedral of FIG. 3f, this having 36 corners; 
     FIGS. 8a-8c and 9a-9f represent an alternate method of assembling the tetracaidecadeltatrihedral corner reflector array; and 
     FIGS. 10a-10c and 11a-11g represent an alternate method of assembling the hexacaidecadeltatrihedral corner reflector array. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to FIG. 1, there is seen a single deltatrihedral developed planar pattern from which a single deltatrihedral corner reflector is constructed. The right isosceles triangles AEB, DEC and BEC are joined together at edges BE and CE. By folding triangle AEB upward along edge BE and triangle DEC upward along edge CE, edges AE and DE merge into a common edge which when permanently fixed or hinged forms a triplanar cavity referred to as a trihedral corner reflector. The front face projection of this trihedral configuration inscribes an equilateral triangle (B)·(AD)·(C), wherein AD represents the common vertex formed by joining edges AE and DE. 
     FIGS. 2a-2f illustrate several of the polydeltatrihedral corner reflector configurations produced according to the process of the present invention constructed by the basic pattern represented in FIG. 1. FIG. 2a represents a duadeltatrihedral (2), FIG. 2b represents an octadeltatrihedral (8), FIG. 2c represents a tetracaidecadeltatrihedral (14), FIG. 2d represents a hexacaidecadeltatrihedral (16), FIG. 2e represents a icosadeltatrihedral (20), and FIG. 2f represents a tetraicosadeltatrihedral (24) configuration. FIGS. 3a-3f illustrate the various networks from which the polydeltatrihedral configurations of FIGS. 2a-2f are fabricated. In the assembly of the specified polydeltatrihedrals all lines and edges when merged form a continuous solid surface deltatrihedral (concave) corner reflector. To assemble the respective configurations the diagonal edges are folded upward and the horizontal and vertical edges are folded downward. All exposed edges will join together and are fastened to form the deltatrihedral cavities. The respective networks of FIGS. 3a-3f are assembled into the first order deltatrihedrals of FIGS. 2a-2f. 
     FIG. 4a illustrates a developed planar two dimension equilateral pattern surface with each side of the triangle bisected in a second order subdivision, and FIG. 4b illustrates the corresponding deltatrihedral second order tesselation network. Thus, replacing the deltatrihedral configuration of FIG. 1 with that of FIG. 4b and inserting the resulting network for each deltatrihedral network of FIGS. 3a-3f, a polyhedra will result in which the number of corner reflector cavities is four times that of the originals, FIGS. 2a-2f. When assembled the network of FIG. 4b consists of four smaller deltatrihedrals within an equilateral triangle. FIG. 5a represents a planar pattern or network of a second order tesselated network for the icosadeltatrihedral, with the appropriate network substitution taking place and FIG. 5b represents the assembled second order icosadeltatrihedral of FIG. 5a comprising eighty deltatrihedrals. The areas identified as O in FIG. 5a stand for open areas. 
     Similarly, by trisecting the edges of an equilateral triangle, nine smaller equilateral triangles are formed. By using smaller techniques as discussed above with respect to FIGS. 4a and 4b, the resulting network representing the third order tesselation is fabricated into a corresponding collection of deltatrihedral corner reflectors and substitution of the resulting configuration for the original first order tesselation resulting from the basic network of FIG. 1 produces a third order 180 corner icosadeltatrihedral structure represented by FIG. 6. 
     The tetraicosadeltatrihedral of FIG. 2f constructed from the network of FIG. 3f is derived from a semiregular antiprism core having a central belt of 12 alternating equilateral triangles and open ends that are projections of hexagons. This 24 cornered solid surface reflector is obtained by replacing each equilateral triangle by a deltatrihedral and filling the hexagonal ends with six deltatrihedrals (i.e., hexadeltatrihedral). It is also further possible to construct a configuration of an unlimited number of the core sections stacked in series, of which there are two such core sections identified in FIG. 7, with the terminal hexagonal faces capped by the beforementioned six deltatrihedrals. For antiprisms having central cores with more than twelve deltatrihedrals, the open end polygon projections are no longer hexagon and the trihedrals formed have a frontal face projection of isosceles triangles rather than equilateral triangles. 
     Referring now to FIGS. 8a-8c, there is represented in FIG. 8a an extended top view wherein three square reflecting plates adge, eghf, and fhcb are hinged along edges eg and fh. On the top of each square plate are four 45° right triangles hinged along the heavy dark lines as represented. Adjoining edges ef and gh are deltatrihedral networks indicated in FIG. 1. When each of the four right triangles per square plate are lifted up about the hinges the four elevated edges will merge forming four trihedral corners per plate. The folded three plates produce twelve of the fourteen trihedrals of the forementioned tetracaidecadeltatrihedral with the remaining two being formed from the upper and lower deltatrihedral networks when edges in and jn and km and lm are joined. By folding the right and left plates down and behind the center plate, edges ad and bc will merge and be joined. The upper and lower trihedral corners are folded down and behind the center plate such that edges ae/ie, bf/jk, ch/lh and dg/kg will merge and be joined together. FIG. 8b represents a front view of the partially assembled deltatrihedra and FIG. 8c a frontal perspective view of the completely assembled tetracaidecadeltatrihedral. FIGS. 9a-9f represent a stepwise pictoral description for assembling the tetracaideltatrihedral according to the alternate procedure of FIGS. 8a-8c accompanied by verbal description. 
     For the hexacaidecadeltatrihedral there is illustrated a pair of networks 10a and 10b consisting of a single square plate having on each edge a deltatrihedral network as represented in FIG. 1 and on the top of each plate four hinged right triangles as described above hinged at the dark lines. Each network pair forms an eight corner trihedral reflector and when joined along their exposed edges as in FIG. 10c form the sixteen cornered hexacaidecadeltatrihedral. FIGS. 10a and 10b are shown in both a top view (extended) and frontal view (partially assembled). FIGS. 11a-11g represent a stepwise pictoral description for assembling the hexacaidecadeltatrihedral according to the alternate procedure of FIG. 10a-10c accompanied by the appropriate verbal description. 
     In accordance with the present invention, certain members of the deltahedra family cannot be constructed as first order polydeltatrihedral because of insufficient internal volume, such as the pentagonal dipyramid. However, this is not necessarily true of the second order and higher tesselations. Thus, an entire class of polyhedra can be constructed as omnidirectional corner reflectors depending upon the degree and distributions of reflection desired. 
     Any suitable material may be utilized from which the radar reflector of the present invention may be fabricated such as metal sheet, wire mesh, or cardboard and plastic with the outer surfaces metallized. The edges of the respective triangles and triplanar cones in the construction of a practical configuration may be permanently joined by hinges, such as door hinges or piano hinges, tape, suitable adhesives or the like. Inexpensive reflectors can be constructed of metallized plastic film for the triangular planes and rolled paper for edge struts. Such a configuration is collapsible and can be folded with edges joined so as to form airtight seals and, as such, are inflatable. In use the reflector can be attached to a naturally low reflecting object and mark the presence of hazards and obstacles. To appear on a radar screen as a moving target, the reflector can be spun at a known angular rate and, thus, the object will be identifiable. If a random velocity is desired, the specific corner reflector can be inserted at the tip end of a flexible pole, such as a fiberglas rod, that is anchored to the base and permitted to whip around in the wind. Depending upon the length of arc of travel, the tip velocity desired will determine the flexibility of the rod. Because of the approximately 70 percent maximum radar cross-section viewing available, the reflector is ideally suited in providing a moving target radar return regardless of the angular attitude of the flexible rod. If mounted on a vehicle, it will serve the purpose as a decoy and tend to shift the target centroid away from the vehicle and towards the reflector. 
     A unique application of a moving reflector is in a linear array along the ground, that is, one reflector per radar resolution cell. In this application runways and roads may be marked and will appear as line segments on a radar display. It should be pointed out that in such an application moving vehicles traveling beneath the array may be masked to the radar, especially if the velocity of the reflector exceeds that of the vehicle traffic. 
     It has been determined in the course of the present invention that multifaceted omnidirectional corner reflectors may be assembled from planar surfaces, a fact which permits the manufacturing of the radar reflector by a continuous process. The corner array reflector of the present invention can be folded into a compact assembly for storage and transportation and reassembled into the reflector array as defined for ready utilization. 
     Although the subject matter of the present invention has been discussed primarily in a specific application to the construction of radar reflecting devices, the invention is equally applicable to the toy industry specifically of the educational variety. The networks defined above can be utilized to teach small motor coordination in children as well as geometrically express a three dimensional form of the products produced thereby. 
     Furthermore, the numerous geometrical configurations obtainable by the processes disclosed are useful for ornamental purposes such as lighting fixtures and chandeliers since the same reflecting surfaces that retroreflect radar energy can retroreflect light energy from the highly polished surfaces. It does not matter whether the source of light energy is from the conventional incandescent bulbs or directed from a laser. 
     The invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the present invention, and all such modifications to be included within the scope of the following claims.