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STATEMENT OF GOVERNMENT INTEREST 
   Under paragraph 1(a) of Executive Order 10096, the conditions under which this invention was made entitle the Government of the United States, as represented by the Secretary of the Army, to the entire right, title and interest therein of any patent granted thereon by the United States. This patent and related ones are available for licensing. Contact Phillip Stewart at 601 634-4113. 

   BACKGROUND 
   Heretofore, providing a lateral attachment between laterally adjacent elements in a paving system has been a problem. U.S. Pat. No. 5,054,253, Rigid Grating Mat with Unidirectional Elements, to Bedics, Oct. 8, 1991, describes a system for building a mat that has separate plank-like elements that are joined laterally by a tongue and groove construction. This makes for a complicated extrusion that is difficult to construct and is easily extended laterally only in one direction. 
   U.S. Pat. No. 5,429,451, Grid Matrix System Including Interconnected Revetment Blocks, to Pettee, Jul. 4, 1995, describes a grid matrix system that has interconnected revetment blocks. These square or hexagonal blocks have alternate recesses and locking protrusions (or ears). A disadvantage of this construction is that it can be easily vandalized because the individual blocks or elements can be lifted vertically. Further, casting the units in concrete presents problems because the ears and edges of the locking recesses can be relatively easily broken. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1A  shows a plan view of a bottom half of embodiments of the present invention as used in a small array. 
       FIG. 1B  depicts a perspective view of a single unit used in the array of  FIG. 1 . 
       FIG. 2  depicts how the individual unit of  FIG. 1B  is inverted onto the array of  FIG. 1A  to effect an embodiment of the present invention. 
       FIG. 3  depicts a top view of three interlocking units inverted over one edge of the array of  FIG. 1A  as used in an embodiment of the present invention. 
       FIG. 4  shows a side view of the relationship of vertically interlocking units of  FIG. 1B , showing the edge of the array of FIG.  1 A through  1 — 1  of  FIG. 3 . 
       FIG. 5  shows the array of  FIG. 1A  with a connecting means embedded therein. 
       FIG. 6  shows how staggering patterns of the array of  FIG. 5  permits interlocking of inverted arrays over un-inverted arrays to effect an embodiment of the present invention. 
       FIG. 7  illustrates a way to change direction of a pathway using top portions of the arrays of  FIG. 5  for illustrative purposes only. 
       FIG. 8  depicts an alternative configuration using hexagon and diamond shapes to effect an embodiment of the present invention. 
       FIG. 9  illustrates an alternative configuration using squares and right triangle shapes to effect an embodiment of the present invention. 
   

   DETAILED DESCRIPTION 
   Embodiments of the present invention comprise in part a component having a first section with first sides parallel to a first plane containing a first bearing surface and a first thickness in a second plane orthogonal to the first plane, the first thickness of a dimension less than that of any of the first sides and a second section having second sides parallel to both the first plane and a second plane containing a second bearing surface, the second plane parallel to the first plane, the second section contacting the first section uniformly along a part of the first plane, the second section oriented to the first section such that the second sides are contained entirely within the perimeter formed by the first sides. 
   One embodiment is a component having the first sides form a first square and the second sides form a second square set at about a 45° angle to the first square, the second square having sides of a length approximately 0.707 that of the first sides. 
   Another embodiment is a component having the first sides form a hexagon and the second sides form a diamond with the long axis of the diamond extending in a line joining the center of two parallel sides of the hexagon and the short axis of the diamond chosen to be the same width as that formed by two parallel first sides of the hexagon. 
   Another embodiment is a component having the first sides form a square and the second sides form a single right triangle along two adjacent sides of the square. 
   In select embodiments of the present invention, the components may have first and second sections fabricated such that the first and second sections are incorporated inseparably in the component. In select embodiments of the present invention, the components may have at least one of the first and second sections formed of a lamination of at least two layers. In select embodiments of the present invention, the components may have at least one of the layers made of a material flexible under compression. 
   An embodiment of the present invention may comprise an array of any of the components above comprising a first set of four components, each component arranged in a plane to abut a first component along a first axis in that plane and a second component arranged along a second axis in that plane, the second axis orthogonal to the first axis, and a second set of four components arranged as above, the second four components inverted and arranged to interlock vertically with the first four components. 
   In select embodiments of the present invention, a configuration of arrays as above further comprises a plurality of the arrays abutting one to another and arranged to cover a pre-specified area. In select embodiments of the present invention, the above configuration further comprises partial components for forming finished edges of the configuration, such as a component cut in half. 
   In select embodiments of the present invention, the configuration may be arranged to form a pathway. 
   In select embodiments of the present invention, the arrays may be joined by flexible means incorporated between the first and second sections during fabrication and extending in a plane approximately parallel to each of the first and second sections so as to permanently connect and position each of the four components in the array. The flexible means may comprise material selected from the group consisting essentially of a mesh, a fabric, roving, a web-perforated fabric, a wire mesh, an elastomer, and combinations thereof. 
   In select embodiments of the present invention, a plurality of the connected arrays abutting one to another may be arranged to cover a pre-specified area, such a road or pathway. In select embodiments of the present invention, the configuration may comprise partial components, such as components cut in half, for forming finished edges of the configuration, e.g., a road or pathway. 
   Also provided as an embodiment of the present invention is a method for covering a pre-specified area, comprising leveling the pre-specified area; arranging any of the components as described above in an array as described above, abutting a number of arrays to cover the pre-specified area in a first plane, and inverting a second configuration of pre-specified like arrays over the first configuration such that the second configuration interlocks vertically with the first configuration and adding partial components, such as components cut in half, for forming finished edges of the interlocked configurations. 
   In select embodiments of the present invention, the method employs components comprising first sides forming a first square, second sides forming a second square set at about a 45° angle to the first square, the second square having sides of a length approximately 0.707 that of the first sides. 
   In select embodiments of the present invention, the method employs components comprising first sides forming a hexagon and second sides forming a diamond with the long axis of the diamond extending in a line joining the center of two parallel sides of the hexagon and the short axis of the diamond chosen to be to be the same width as that formed by two parallel first sides of the hexagon. 
   In select embodiments of the present invention, the method employs components comprising first sides forming a square and second sides forming a single right triangle along two adjacent sides of the square. 
   In select embodiments of the present invention, the method employs a component comprising first and second sections fabricated such that the first and second sections are incorporated inseparably in the component. 
   In select embodiments of the present invention, the method employs a component in which at least one of the first and second sections is formed of a lamination of at least two layers. In select embodiments of the present invention, at least one of the layers may be constructed of a material flexible under compression. 
   Also provided as an embodiment of the present invention is a method of fabricating components for a vertically interlocking configuration, comprising providing a first mold to form a first section as described above, providing a second mold to form a second section as described above; pouring a fluid mixture of a first material into the first mold to be at least partially hardened in the mold as the first section; permitting the first mixture to at least partially harden in the first mold; placing a second mold over the first at least partially hardened mixture in a pre-specified orientation; pouring a fluid mixture of a second material into the second mold to be hardened in the mold; upon hardening of the first and second mixtures to a pre-specified level, removing both molds and trimming the component as necessary. 
   In select embodiments of the present invention, the above method of fabricating may also comprise arranging at least four like components in a pre-specified array and adding a connecting means over at least a portion of each of the first sections of each before placing the second mold so that the connecting means is embedded in each component, both connecting and orienting the components in an array. The connecting means may comprise material selected from the group consisting essentially of a mesh, a fabric, roving, a web-perforated fabric, a wire mesh, an elastomer, and combinations thereof. In select embodiments of the present invention, fabrication may employ the same material for the first and second sections. 
   In select embodiments of the present invention, the sections may be a mixture containing at least some Portland cement. In select embodiments of the present invention, the method may employ different materials for fabricating the first and second sections. In select embodiments of the present invention, the method of fabrication may employ layers of different materials for at least one of the first and second sections such that at least one of the first and second sections is a laminate of at least two layers. In select embodiments of the present invention, at least one material flexible in compression may be employed in at least one of the layers. 
   Embodiments of the present invention form a continuous paved traffic way without having to laterally interlock a paving block with its neighbor. One embodiment, suitable for quickly forming a pavement, is termed PORTAPAVE™. 
   This is achieved in one aspect by a paving mat that comprises an array of paving blocks, and means for connecting the paving blocks together in the array. Each paving block includes a bottom part having a first shape, and a top part having a second shape. Neighboring top parts of blocks form a cavity between them having the same shape as the top part of a block so that a second similar array of paving blocks can be turned upside down and overlapped and interlocked with the first array of paving blocks to make a two-layered block paving unit. 
   Also provided in an embodiment of the present invention is a method of making a paving mat that comprises: providing a first array of the above described paving blocks and providing means for connecting the paving blocks together in the array. In one embodiment, since neighboring top parts of blocks form a cavity between them having the same shape as the convex top part of a block, in one method a second similar array of paving blocks is turned upside down, thus overlapping and interlocking with the first array of paving blocks to make a two-layered block paving unit. 
   Embodiments of the present invention, unlike conventional “articulated concrete mats,” overlap interlocking arrays vertically thus maintaining integrity of the mat. In one embodiment, placement of the blocks involves staggering the positions of the blocks so that a block in an upper layer partly covers the intersection of the contacting blocks in the lower layer. This reduces the chance for vegetation to grow through the paving unit. In one embodiment the means for connecting the paving blocks together in an array is an opaque material, such as a fabric or an elastomer. This opaque material blocks light and either kills vegetation or confines it. 
   In one embodiment runoff water can be controlled by inserting a mesh fabric between layers or providing drain holes in the connecting means. In one embodiment, paving units may be moved by lifting upper layers (mats), so that the lower layers (mats) may be separated. In embodiments to be installed permanently, a layer of mortar may be spread over the lower layer and the upper layers bonded thereto. Embodiments of the present invention may facilitate a change in the direction of the pavement by staggering the layers (mats) laterally so the track “curves” as needed. 
   Embodiments of the present invention provide arrays of vertically interlocking units that may be employed in applications otherwise suitable for conventional individual paving blocks. In embodiments of the present invention, the connecting means prevent individual blocks from moving laterally. In conventional systems this is accomplished by attaching the connecting means from one array of blocks to adjacent arrays. A cavity formed between neighboring top parts of the un-inverted units has the same shape as a unit&#39;s top section so that a second similar array of units may be inverted and interlocked with the un-inverted array to make a two-layered paving mat, for example. Thus, in embodiments of the present invention, interlocking an un-inverted array with an inverted array of units obviates the need for any “holding” means. 
   In embodiments of the present invention, arrays of vertically interlocking units may be employed as “portable” pathways, e.g., pedestrian or vehicle thoroughfares that may be temporary or permanent. Embodiments of the present invention may also be employed on fords where it is necessary to anchor the units on a slope. Embodiments of the present invention may also be used to prevent stream bank erosion, as a base for a waterproof liner, or as a weed-free break to limit or control grass fires. 
   Refer to  FIG. 1A  showing a rectangular array  100  of four abutting units  110  each comprising a bottom section  101  and a smaller raised top section  102  comprising an integral part of a unit  110 . The units  110  may be top and bottom portions of what are termed “pavers” in the construction industry. The units  110  may be constructed of moldable materials such as Portland cement and its variations, any of a variety of plastics, fiberglass, steel, carbon or KEVLAR® fibers, and combinations of these. The two sections  101 ,  102  may be formed in a mold as a single entity such that they are not individual parts that may be separated. In the embodiment shown in  FIG. 1A , the perimeter of the top section  102  is defined by drawing a line from the middle of a side of the bottom section  101  diagonally across to the middle of an adjacent side of the bottom section  101  and continuing around the sides until the shape of the top section  102  is obtained, as seen in the top (plan) view of  FIG. 1A . In one embodiment of the present invention, all such units  110  are identical and symmetrical with respect to top  102  and bottom  101  sections. The symmetry enables the use of like units  110  by inverting an array  100  of units  110  over an un-inverted array  100  of units  110  such that each of the top sections  102  mate in the space created in the un-inverted array  100  where four corners of the units  110  of the un-inverted array  100  come together. 
   Refer to  FIG. 1B , a perspective view of a unit  110  shown in a top view in the array  100  in  FIG. 1A . This unit  110  is essentially a “small box-on-large box” arrangement with the top section (small box)  102  being arranged so that each of its comers are at the center of the sides of the bottom section (large box)  101 , resulting in a small box having sides in the plane parallel to the bottom section (large box) of approximately 0.707 that of the sides of the bottom section  101 . Each of the sections  101 ,  102  is square in the plane at which they contact and set at approximately 45° with respect to each other in that plane. The thickness, t 1  and t 2 , of each of the sections  101 ,  102 , respectively is chosen according to structural and esthetic requirements of the user and need not be the same for each section  101 ,  102 . 
   Refer to  FIG. 2 . For clarity, a single inverted unit  110  is shown as a shaded area over the array  100  of Fig,  1 A in a configuration  200  that highlights the “interlocking” feature of the present invention. The dark shaded portion represents a top section  102  for the inverted unit  110 . The un-inverted array  100  of  FIG. 1A  is shown in  FIG. 2  with a perimeter of dashed lines since this un-inverted portion will not be visible in any installation of this embodiment of the present invention, being covered by inverted units  110  that will be placed outwardly in the direction of the arrows  201 . The interlocking occurs at each intersection of the corners of the un-inverted units  110 . At the edges of an intended installation of multiple arrays  100 , the inverted units  110  maybe cut in half diagonally to make a smooth edge that matches the edges of the un-inverted array  100  on bottom. Alternatively, “half-units” (not shown separately) may be molded at the factory for forming portions of the edges of installations (e.g., pathways or thoroughfares). 
   Refer to  FIGS. 3 and 4 . A configuration  310  of three inverted abutting units  110  is placed over an edge  301  of the array  100  of  FIG. 1A  to further illustrate the interlocking feature of an embodiment of the present invention. An end (edge) view of the resultant configuration as taken with a vertical cut through  1 — 1  of  FIG. 3  is shown in  FIG. 4 . The “half-squares” of the top sections  102  cover the intersection between the two abutting un-inverted units  110  below the edge insuring a “double thickness” of coverage above each intersection of the un-inverted units  110 . Conversely, where the inverted units  110  abut is at the middle of one of the un-inverted units. 
   Refer to  FIG. 5 . In one embodiment of the present invention a means  501  for connecting together a small array  100  of units  110 , such as a web of perforated fabric or a wire mesh of metal or suitable roving, is provided in a configuration  500  for ease in placing and maintaining spacing of the units  110  should one wish to make a permanent installation with mortar and grouting between units  110 . The spacing, d, may be adjusted to accommodate performance and esthetic requirements of the user. 
     FIG. 6  shows how staggering the pattern of the inverted units  110  over the un-inverted units  110  enables interlocking of the configuration  600  and keeps the units  110  from moving laterally with respect to each other. Thus, the units  110  may be kept together without having to manually attach them to each other, forming a two-layered configuration that may be used for such applications as a pathway, a thoroughfare, a ford, or for stabilizing embankments. For a permanent arrangement embodiments of the present invention may be provided with a spacing to enable mortar or grout to be placed between neighboring units  110  although they may be useful as installed with only the mechanical interlocking described above. Since individual units  110  cannot be lifted from an installation, it is difficult for vandals to damage the installation by removing units  110 . For illustrative purposes,  FIG. 6  also shows a single “half-block”  601  as it may be used on an edge of a pathway or pavement. 
   Refer to  FIG. 7 , a simplified representation of the units  110  of  FIG. 1A  as arranged in a manner that enables changing direction to establish a desired pathway  701  that results in the configuration  700 . The representation of  FIG. 7  is illustrative only, demonstrating that pathways may be made in various configurations enabling changing of direction. For illustrative purposes,  FIG. 6  shows a single “half-block”  601  as it may be used on an edge of a pathway to provide a smooth edge to the configuration  700 .  FIG. 7  is for illustrative purposes only and depicts only the inverted units  110  with the un-inverted units  110  implied as being installed under the inverted units  110 . 
   The units  110  may be manufactured in a variety of ways. For example, in one embodiment, bottom sections  101  may be made by filling a first mold or form with a self-hardening mixture such as a Portland cement-based concrete. A connecting means  501 , such as web-perforated fabric or metal wire mesh, may be placed over the uncured mixture in the first form and a second form placed over the connecting means  501  to establish the top section  102 . An additional layer of mixture is cast over the connecting means  501  such that the second mixture bonds to the first mixture through perforations in the connecting means  501 . 
   A second way of manufacturing the units  110  is to pre-cast the top  102  and bottom  101  sections and bond or attach them to opposite sides of the connecting means  501 . 
   It is obvious that many modifications and variations of the present invention are possible in light of the above teachings. The basis for getting the inverted and un-inverted units  110  to interlock is to use a “regular tessellation” on each of the top and bottom surfaces of the unit  110 . The “large box-small turned box” combination of an embodiment of the present invention is two square tessellations  101 ,  102  with the smaller “box”  102  tessellation on the top of the “layer” of units  110  placed on the bottom and rotated 45 degrees with a grid spacing, or side length, that is 0.707 times that of the larger “box”  101  tessellation. Another usable combination would be triangles, but with triangles the orientation of the base and apex of the triangle is important since adjacent triangles are oriented in opposite directions in a regular tiling of triangles. There are exactly three regular tessellations composed of regular polygons tiling a plane. They are hexagons, squares and triangles. 
   Refer to  FIG. 8  for an example of hexagon sections  810  in an array  800 . The bottom section  801  of this array is a hexagon while the top section  802  is a symmetric “diamond” with the long axis of the diamond-shaped top section  802  extending in a line joining the center of two parallel sides of the hexagon of the bottom section  801  and the short axis of the diamond-shaped top section  802  chosen to be the same width as a side of the hexagon-shaped bottom section  802 . The array  800  of hexagon-shaped units  810  is also amenable to connection of individual units in small arrays, using a mesh or fabric, such as the four-unit array  500  of  FIG. 5 . These small connected arrays, such as array  500  of  FIG. 5  may be connected with or without spacing, d, for mortar or grouting. Unlike the “small box-large box” arrangement of  FIG. 1 , the “interlocking” section, i.e., the diamond-shaped top section  802  of the bottom layer of the hexagon array  800 , is exposed in the top layer of the array  800 . Thus, the hexagon array  800  may be chosen for other reasons, such as esthetics. 
   Refer to  FIG. 9 . A configuration involves overlapping units  910  that are squares with a raised right triangle  902  covering half of one side of each of the units  910 , leaving a like right triangle  901  that is not raised on the other half of that side of the unit  910 . The configuration of  FIG. 9  may consist of arrays  900  of individual units  910  each having one raised right triangle section  902  on one side or, alternatively rather than having four individual units  910  making an array  900 , a single large square may be fabricated as the array  900  with four raised right triangles  902  formed on the single large square comprising the array  900 . This alternative “large square” array  900  with four integral raised right triangles  902  on one side would have the benefit of not needing a mesh or other means to hold together the units  910  and would eliminate four seams, two of which are shown between the arrows  903  so that overlapping inverted arrays  900  each would have fewer portions where seams overlapped as compared to using individual units  910 , each with only one raised triangle  902 . To minimize the number of seams exposed, an inverted four-unit configuration  900  could overlap a single small square as indicated by the arrow  904  or overlap half of a bottom layer as indicated along the line represented by the arrow  903 . 
   The easiest interlocking units  110 ,  810 ,  910  to fabricate and install are those involving different sized squares, as described above for the array of  FIGS. 1A and 5 , and a combination of squares with raised right triangles on half of one side as depicted in  FIG. 9 . The most practical interlocking system may be the small box-large box combination of  FIGS. 1A and 5 . It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as described. 
   Accordingly, all such modifications are intended to be included within the scope of this invention as defined in the following claims. In the claims, means-plus-function clauses are intended to cover the structures described herein as performing the recited function and not only structural equivalents, but also equivalent structures. Thus, although a nail and a screw may not be structural equivalents in that a nail employs a cylindrical surface to secure wooden parts together, whereas a screw employs a helical surface, in the environment of fastening wooden parts, a nail and a screw may be equivalent structures. 
   The abstract is provided to comply with the rules requiring an abstract, which will allow a searcher to quickly ascertain the subject matter of the technical disclosure of any patent issued from this disclosure. 37 CFR § 1.72(b). Any advantages and benefits described may not apply to all embodiments of the invention.

Summary:
A continuous covered area, such as a sidewalk or patio, is formed by vertically interlocking tessellated components. One embodiment, termed PORTAPAVE™, achieves this interlocking via an array of uniquely configured two-sectioned pavers. Each paver has a first section of a first shape and a second section of a second shape impressed upon the first section and bonded together. In one embodiment, first sections of pavers in an installed bottom layer form a cavity between them having the same shape as the second section of a paver that is inverted onto the pavers of the bottom layer, thus providing a top layer. Each inverted paver in this top layer is fitted to interlock in that cavity formed between the un-inverted pavers in the bottom layer. Also provided is a method of making the components, e.g., pavers, and a method of installing them.