Web or Support Structure and Method for Making the Same

Abstract

A web structure includes a generally hexahedron-shaped frame, wherein the frame includes a plurality of points oriented in a manner that no more than three points lie in a common plane. Each pair of the points is connected by a frame segment. A plane includes three of the points, and one frame segment passes through the plane and includes first and second ends, which are generally equidistant from the plane. The frame includes six points or vertices.

Description

FIELD AND BACKGROUND OF THE INVENTION

The present invention is directed to a web or support structure, and more particularly to a web or support structure that could be utilized to form structural elements.

Architects, civil and structural engineers conventionally utilize various web structures for supporting, for example, trusses, floors, columns, etc. Typically, web structures form various lattices or framework that support underlying or overlying supports. In this regard, structural engineers are quite familiar with a “Fink truss” (FIG. 2), the geometry of which encodes an approximation of a “Sierpinski triangle”—the “limit” of the recursive design indicated in FIGS. 1-3.

It has been observed in the past that the geometry of the hardest substance known to man, namely diamonds, and the modern roof truss encode and represent the approximations to certain fractals. The Fink truss (FIG. 2) is an engineering design that is a level-1 2-web. In nature, carbon-carbon bonding in diamond encodes a level-1 3-web.

In my earlier U.S. Pat. No. 6,931,812, which is hereby incorporated herein in its entirety by reference, I disclosed a 4-web structure represented in a 3-dimensional space that at a level-0 contains 10 triangles. In my another U.S. Pat. No. 8,826,602, which is hereby incorporated herein in its entirety by reference, I disclosed a 5-web structure represented in a 3-dimensional space that at level-0 packs or accommodates 15 Fink struts and 20 hyperbolic triangles.

The 2-web and 3-web date to circa 1900, while the 4-web from the 4^th dimension was realized within human vision late in the 19^th Century, and eventually published in the literature circa early 2003 (Reference No. 3). The 4-web is pictured on the cover of my book (Reference No. 2). Each of the 2-web, 3-web, 4-web, and 5-web are concrete examples of an abstract space that is referenced in the literature as “Lipscomb's Space” that I invented to solve a half-century old problem in dimension theory.

Page 20 of my book (Reference No. 2) contains mathematical details about the lower dimensional webs. In particular, the “w with superscript 5” notation in the book denotes the 5-web, and the “J with subscript 6” notation also denotes the 5-web, where the 6=5+1 indicates the number of vertices of the 5-web. In general the “ω with superscript n” denotes an n-web and the “J with subscript n+1” also denotes the n-web, where n+1 indicates the number of vertices of the n-web.

Simply put, it has been an open problem to create a picture of an approximation to a 5-web within 3-space (human visual space). In the present disclosure, I use an innovative geometry to show how to visualize within 3-space (human visual space) such approximations to the 5-web. Specifically, one of the new concepts/embodiments extends the earlier 4-web design to contain six (6) vertices and 20 triangles. Perhaps more importantly, however, is an observation in a test that a 4-web structure, embodying my 4-web concept disclosed in my patent, U.S. Pat. No. 6,931,812, yielded a strength of over 6-ton/sq. in., while weighing merely 0.30 oz. It is not difficult, therefore, to note that a 5-web structure with 10 extra triangles would be even stronger, if not, at least twice in strength. Such low weight and super strength would particularly be useful, at least in, for example, the currently used 4-web medical implants.

Recalling again the value of “triangles” when it comes to designing high-strength structures, let us also recall that the 3-web level-0 (FIG. 4) has six struts and four triangles. The strength increases as the number of triangles increases. For example, I have shown in my unpublished article (Reference No. 1), that the addition of a single polar strut (compare FIG. 4 to the top half of FIG. 7), could increase compressive strength by as much as 20%. That is, the polar strut provides more triangles.

In order to understand the new 5-web designs (subject of this application), recall that the “4” in “4-web” refers to the “4^th-dimension”—the place where the 4-web originally existed. There are also “2-webs”, which exist in 2-dimensional planes, and “3-webs”, which exist in 3-dimensional space (human visual space). Mathematically, this list of webs and corresponding dimensions continues ad infinitum. Sample illustrations of the webs existing in lower-dimensional space are shown in FIGS. 1-9.

More specifically, FIGS. 1-3 depict “levels” of 2-webs. Specifically, FIGS. 1-3 show a “level-0” (a single triangle), a “level-1” (three level-0 2-webs, illustrated as red, green, and blue), and a “level-2” 2-web (containing three level-1 2-webs), respectively. As the level-numbers increase, these structures approach a “limit”, which is called the “2-web”.

FIGS. 4-6 depict “levels” of 3-webs. Specifically, FIGS. 4-6 show a “level-0” (a single tetrahedron), a “level-1” (four level-0 3-webs, illustrated as red, green, blue, and gold), and a “level-2” 3-web (containing three level-1 3-webs), respectively. As the level-numbers increase, these structures approach a “limit”, which is called the “3-web”.

FIGS. 7-9 depict “levels” of 4-webs. Specifically, FIGS. 7-9 show a “level-0” (a single hexahedron), a “level-1” (five level-0 4-webs, illustrated as red, green, blue, gold, and black), and a “level-2” 4-web (containing five level-1 4-webs), respectively. Again, as the “level numbers” increase these structures approach a “limit” that is called a “4-web”.

The key is to observe the inductive process, illustrated in FIGS. 1-9. The “inductive process” is a process that allows us to start at a given level, and then move to the next level using the given level. In more detail, the process is a two-step process. First, congruent copies of a given level are made. Second, these congruent copies are positioned so that each is just touching the others. To say that two congruent structures are “just touching” is to say that there exists one and only one point that is contained in both structures.

For example, consider the inductive process illustrated in FIGS. 4-6. We start with a tetrahedron (FIG. 4—four vertices), which is a level-0 3-web. Then, we create four congruent copies (colored red, green, blue, and gold). Next, we position these four copies so that each is just touching the other three. This positioning is shown in FIG. 5. To find the just-touching points, simply seek the points where two distinct colors meet. In particular, find the point where the red congruent copy meets the green congruent copy. That point is the “just touching point” for those copies. The construction of congruent copies followed by the “just touching” positioning allows one to move from one level to the next to infinity. Such an algorithm defines the inductive process.

In summary, the Fink truss (FIG. 2), which is a level-1 Sierpinski triangle, has been utilized for many years in constructing various support structures. To date, diamond which has the geometry of a level-1 Sierpinski cheese as its basic building structure is known to be the hardest structure. In the present invention, I now disclose geometrical structures that represent the next step over the 4-web structure, i.e., the new 5-web structures, over those disclosed in my earlier patent, U.S. Pat. No. 8,826,602.

ASPECTS AND SUMMARY OF THE INVENTION

The present disclosure is directed to various aspects of the present invention.

One aspect of the present invention is to provide the medical, scientific, engineering, technical, and architectural communities with access to new fundamental designs, i.e., designs that systematically produce homogeneous structures that contain large numbers of triangles constructed with a minimum amount of material. That is, light-weight but exceptionally strong structures.

Another aspect of the present invention is to provide a web structure which could be utilized at both macroscopic and microscopic levels to create stronger and more stable structures. On a microscopic scale, for example, a web structure made in accordance with the present invention would produce new compounds and new crystals. Another example is to create structures, such as medical implant devices that enhance bone growth. On a macroscopic scale, for example, a web structure made in accordance with the present invention would create super strong and stable architectural and structural support structures. For example, a web structure of the present invention can be utilized to create super strong and stable trusses, beams, floors, columns, panels, airplane wings, etc.

Another aspect of the present invention is to provide the scientific and solid-state physics communities with access to new fundamental web-structure designs that would indicate how to build new compounds and new crystals having utility, for example, in the solid-state electronics industry.

Another aspect of the present invention is to provide a web structure that accommodates or packs more triangular shapes into a given volume than conventional web structures. A web structure made in accordance with the present invention could be used in building bridges, large buildings, space-stations, etc. In the space-station case, for example, a basic, modular and relatively small web structure can be made on earth, in accordance with the present invention, and a large space-station could be easily built in space by shipping the relatively small (level-0) web into space, and then joining it with other members according to the “just-touching” feature of web designs.

Another aspect of the present invention is to provide a web structure that represents a 5-web in a 3-dimensional space.

Another aspect of the present invention is to provide a 5-web structure that packs or accommodates more triangles in a given volume than the previous 4-web structure.

Another aspect of the present invention is to provide a web structure that at level-0 packs or accommodates 20 triangles.

Another aspect of the present invention is to provide a web structure including six points (or apices or vertices), wherein no two points are equal, no three points lie on a straight line, no four points lie on a plane, each pair of points is connected, by a generally straight segment, which, in pairs, meet in a single common vertex, and, in addition, the structure serves as a level-0 5-web, copies of which may be used to build a level-1 5-web, etc.

Another aspect of the present invention is to provide a web structure that includes a generally hexahedron-shaped frame, wherein the frame includes a plurality of points oriented in a manner that no more than three points lie in a common plane. Each pair of the points is connected by a frame segment. A plane includes three of the points, and one frame segment passes through the plane and includes first and second ends, which ends are generally equidistant from the plane. The frame comprises six points or vertices.

Another aspect of the present invention is to provide a web structure that includes a generally hexahedron-shaped frame with first and second generally trihedron-shaped portions joined at the bases thereof. The first and second portions include first and second vertices, respectively. The frame includes a plane. A frame segment joins the first and second vertices and passes through the plane. The frame includes third, fourth, fifth and six vertices, wherein the six vertex is situated at approximately 0.429, −0.166, 0.746 coordinates corresponding to x, y, z axes of the frame.

Another aspect of the present invention is to provide a web structure that includes a generally hexahedron-shaped frame with first, second, third, fourth, fifth, and sixth vertices generally situated at approximately 0, 0, 1; −0.5, −0.866, 0; 1, 0, 0; −0.5, 0.866, 0; 0, 0, −1.414; and 0.429, −0.166, 0.746 values for x, y, z coordinates, respectively.

Another aspect of the present invention is to provide a web structure that includes a frame with first and second triangles, which are spaced from each other by a predetermined distance. The first and second triangles are disposed in first and second generally parallel planes, and the vertices of one of the first and second triangles are offset from the corresponding vertices of the other of the first and second triangles by about 45 degrees. Each of the vertices of one of the first and second triangles is connected to each of the vertices of the other of the first and second triangles by a segment. The frame includes twenty triangles.

In summary, the main aspect of the present invention is to provide a 5-web structure in a 3-dimensional space. The invention can be utilized to generate new structural designs that relate to both macroscopic and microscopic structures. These structures would be stronger and more stable than the presently known structures, including diamond and those utilizing the 4-web structure shown in my earlier patent, U.S. Pat. No. 6,931,812.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

One of the above and other aspects, novel features and advantages of the present invention will become apparent from the following detailed description of the non-limiting preferred embodiment(s) of invention, illustrated in the accompanying drawings, wherein:

FIG. 1 illustrates a Sierpinski's triangle or a level-0 2-web;

FIG. 2 illustrates a Fink truss or a level-1 2-web;

FIG. 3 illustrates a level-2 2-web;

FIG. 4 illustrates a level-0 3-web;

FIG. 5 illustrates a level-1 3-web;

FIG. 6 illustrates a level-2 3-web;

FIG. 7 illustrates a level-0 4-web;

FIG. 8 illustrates a level-1 4-web;

FIG. 9 illustrates a level-2 4-web;

FIG. 10 illustrates a level-0 4-web structure formed in accordance with my earlier invention, shown in U.S. Pat. No. 6,931,812;

FIG. 11 is a view of the web structure shown in FIG. 10, formed in accordance with a preferred embodiment of the present invention, shown with x, y, z coordinates of six vertices;

FIGS. 12-15 illustrate (in purple color) various sets of ten new triangles, in accordance with a preferred embodiment of the present invention;

FIG. 16 illustrates another embodiment of a web structure, in accordance with the present invention; and

FIGS. 17-20 illustrate (in color) a preferred sequence for the formation of the web structure shown in FIG. 16.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S) OF THE INVENTION

As described above, a 3-web may be viewed as a systematic packing of tetrahedra in 3-dimensional space, and a 4-web may be viewed as a systematic packing of hexahedra in 3-dimensional space. As also noted above, the present invention is an extension of my 4-web design described hereafter.

As shown in FIG. 10, the web structure W includes a generally hexahedron-shaped frame F including an upper generally triangular or trihedron-shaped sub-frame 10 and a lower generally triangular or trihedron-shaped sub-frame 12. The upper and lower sub-frames 10 and 12 are joined at their bases to form a common equatorial sub-frame 14.

The frame F includes upper and lower points or apices 16 and 18, respectively, and three equatorial points or apices 20, 22, and 24. The points 16, 18, 20, 22, and 24 are oriented in a three-dimensional space in a manner that no more than three points lie in a same plane. The equatorial points 20, 22, and 24 are disposed in a generally common, generally horizontal plane represented by equatorial sub-frame 14.

As illustrated in FIG. 10, each pair of the points 16, 18, 20, 22, and 24, is connected by a line or frame segment. For instance, equatorial points 20 and 22 are connected by a frame segment 26, the equatorial points 22 and 24 are connected by a frame segment 28, and equatorial points 20 and 24 are connected by a frame segment 30. Likewise, upper and lower points 16 and 18 are connected by a frame segment 32. In the same manner, the points 16 and 20, 16 and 22, 16 and 24, 18 and 20, 18 and 22, and 18 and 24, are connected by frame segments 34, 36, 38, 40, 42, and 44, respectively.

The frame segment 32 is disposed preferably generally perpendicular to the plane of sub-frame 14 and passes generally through the geometrical center (GC) thereof. Alternatively, the frame segment 32 may be generally skew or slanted.

The frame F forms ten triangles represented by points 16, 20, and 24; 16, 20, and 22; 16, 22, and 24; 20, 22, and 24; 18, 20, and 24; 18, 22, and 24; 18, 20, and 22; 16, 18, and 20; 16, 18, and 22; and 16, 18, and 24. Each of these triangles functions as a Fink truss when each frame segment thereof is braced in the middle.

Preferably, each of the frame segments 26, 28, 30, 32, 34, 36, 38, 40, 42, and 44 is a generally straight segment.

As illustrated, the 4-web includes five (5) points or apices 16, 18, 20, 22, and 24. In an embodiment of the present invention of a web structure WW, shown in FIG. 11, a sixth apex or vertex 46 is added at 0.429, −0.166, 0 values of x, y, z coordinates of the frame FF. The sixth apex 46 is connected to each of the other five apices 16, 18, 20, 22, and 24 by a line or frame segment 48, 50, 52, 54, and 56, respectively. The addition of the apex 46 produces a new set of ten (10) triangles in the frame F. Table 1 below lists the ten (10) new triangles with reference to the relevant apices and the associated frame segments, shown progressively in purple in FIGS. 12-15, for clarity.

TABLE 1
10 New Triangles
	No.	SETS OF APICES	SEGMENTS	FIGURE
	1	46, 16,20	48, 34, 52	12
	2	46, 16,24	48, 32, 56	12
	3	46, 16,22	48, 36, 54	12
	4	46, 16, 18	48, 32, 50	12
	5	46, 20, 24	52, 30, 56	13
	6	46, 20, 22	52, 26, 54	13
	7	46, 20, 18	52, 40, 50	13
	8	46, 24, 22	56, 28, 54	14
	9	46, 24, 18	56, 50, 44	14
	10	46, 22, 18	54, 50, 42	15

The formula for calculating the number of triangles is well known. Specifically, the number of combinations of ‘n’ different values taken ‘r’ at a time is calculated by n!/[(r!) (n−r)!] Thus, for the 5-web with six vertices, the number of triangles is calculated to be 6!/[(3!) (6−3)!]=720/[6×6]=720/36=20.

Table 2 below lists the preferred coordinates of apices 16, 18, 20, 22, 24, and 46.

TABLE 2
X, Y, Z Coordinates of Apices 16, 18, 20, 22 24, 46
APEX COORDINATES
16   0, 0, 1
18   0, 0, −1
20   −5, 0.866, 0
22   −5, −0.866, 0
24   1, 0, 0
46   0.429, −0.166, 0

FIG. 16 illustrates an alternative embodiment of the instant invention. As shown, this embodiment of the web structure WWW includes a frame FFF. This embodiment is constructed by positioning two triangles generally along parallel planes, but spaced apart from each other by a distance, about an axis generally perpendicular to the planes. For example, as shown in FIG. 17, an upper triangle 58 (shown in red and extending in x-y axes) is spaced from the lower triangle 60 (shown in blue and extending in x-y axes), along the z axis, where GC is the geometric center at 0, 0, 0 coordinates. The triangles 58 and 60 are oriented so as to be congruent. Preferably, the distance D₁ between the triangle 58 and the geometric center GC is equal to or substantially the same as the distance D₂ between the triangle 60 and the geometric center GC. The distances D₁ and D₂ can be measured/selected based on any unit of measurement, such as nanometer, Angstrom, millimeter, centimeter, inch, foot, meter, etc., as an integer or fraction thereof.

Preferably, the triangle 60 is then rotated counter-clockwise (arrow AAA) by about 45 degrees to reach the position shown in FIG. 17 (shown in solid lines). It is noted that the z axis passes through the center of each triangle 58 and 60. Each of the three vertices 62, 64, and 66 of triangle 58 are then connected to the three vertices 68, 70 and 72 of the triangle 60, as shown progressively in FIGS. 18-20 (described below).

As best shown in FIG. 18, vertex 62 of the triangle 58 is connected to the vertices 68, 70, and 72 by a line or frame segment 74, 76 and 78, respectively (shown in green). Likewise, vertex 64 is connected to the vertices 68, 70 and 72 by a line or frame segment 80, 82 and 84, respectively (shown in gold in FIG. 19). Finally, vertex 66 of the triangle 58 is connected to the vertices 68, 70 and 72 of the triangle 60 by a line or frame segment 86, 88, and 90, respectively (shown in magenta in FIG. 20).

One skilled in the art would appreciate from FIG. 20, that the segments 74, 76, 78, 80, 82, 84, 86, 88 and 90 do not intersect.

Table 3 below lists the twenty (20) triangles formed in the embodiment shown in FIGS. 16-20, with reference to the relevant apices and the associated segments. (It is noted herewith that for clarity and ease of understanding the frame segments of triangles 58 and 60 are designated as A, B, C and AA, BB, CC, respectively.)

TABLE 3
20 Triangles (FIG. 16)
No.	SETS OF APICES	SEGMENTS
1	66, 72, 70	88, 60, 90
2	66, 72, 68	90, AA, 86
3	66, 72, 62	90, 76, A
4	66, 72, 64	90, 84, B
5	66, 70, 68	88, CC, 86
6	66, 70, 62	88, 78, A
7	66, 70, 64	88, 82, B
8	66, 68, 62	86, 74, A
9	66, 68, 64	86, 80, B
10	66, 62, 64	A, B, C
11	72, 70, 68	AA, BB, CC
12	72, 70, 62	BB, 78, 76
13	72, 70, 64	BB, 82, 84
14	72, 68, 62	AA, 74, 76
15	72, 68, 64	AA, 80, 84
16	72, 62, 64	76, C, 84
17	70, 68, 62	CC, 78, 74
18	70, 68, 64	CC, 80, 82
19	70, 62, 64	78, C, 82
20	68, 62, 64	74, C, 80

Table 4 below lists three preferred coordinates for apices 62, 64, 66, 68, 70, and 72.

TABLE 4
X, Y, Z Coordinates of Apices 62, 64, 66, 68, 70, and 72
APEX COORDINATES
62   −0.5, −0.866, 1
64   1, 0, 1
66   −0.5, 0.866, 1
68   −0.966, 0.259, −1
70   0.707, 0.707, −1
72   0.259, −0.966, −1

As noted above, the present invention is an extension of my 4-web design disclosed in U.S. Pat. No. 6,931,812. In an independent test, the load bearing strength of a rib cage for medical applications, made in accordance with the 4-web design disclosed in U.S. Pat. No. 6,931,812, was determined to be over 6-ton/sq. inch. The present embodiments of 5-web double the number of triangles to 20, from 10 in my earlier 4-web design. One skilled in the art would readily appreciate that a similar article made in accordance with the 5-web design disclosed herein, would therefore be significantly more strong, if not twice in strength.

A web structure constructed in accordance with the present invention can be made of any suitable material such as wood, plastic, metal, metal alloy such as steel, fiberglass, glass, polymer, concrete, etc., depending upon the intended use or application, or choice. Further, it can be used alone or part of another structure, or used as a spacer. For example, one or more web structures can be arranged between two or more panels as spacers to add strength to the overall structure.

It is noted herewith that while the invention has been described for constructing level-0, level-1 and level-2 5-webs, it may be applied to create webs of higher levels. It is further noted herewith that the invention is not limited in any way to any color choice or scheme, which is used here merely for the purpose of illustration and ease of understanding.

While this invention has been described as having preferred/illustrative mathematical levels, sequences, ranges, steps, order of steps, materials, structures, symbols, indicia, graphics, color scheme(s), shapes, configurations, features, components, or designs, it is understood that it is capable of further modifications, uses and/or adaptations of the invention following in general the principle of the invention, and including such departures from the present disclosure as those that come within the known or customary practice in the art to which the invention pertains, and as may be applied to the central features hereinbefore set forth, and fall within the scope of the invention and of the limits of the claims appended hereto or presented later. The invention, therefore, is not limited to the preferred embodiment(s) shown/described herein.

REFERENCES

The following references, and any cited in the disclosure herein, are hereby incorporated herein in their entirety by reference. (These references are of record in U.S. Pat. No. 8,826,602.)

• 1. S. L. Lipscomb, Compression and Core Geometry of two panels, Unpublished, 2005.
• 2. S. L. Lipscomb, Fractals and Universal Spaces in Dimension Theory, Springer Monographs in Mathematics, 2009.
• 3. J. Perry and S. Lipscomb, The generalization of Sierpinski's triangle that lives in 4-space, Huston Journal of Mathematics, vol. 49, No. 3, 2003, pp. 691-710.
• 4. Greenberg, Marvin J. “Euclidean and Non-Euclidean Geometries” Development and History (second edition). Published by W.H. Freeman and Company. Copyright 1972 by Marvin Jay Greenberg and Copyright 1974, 1980 by W.H. Freeman and Company.

Claims

1. A web structure, comprising:

a) a generally hexahedron-shaped frame;

b) said frame comprising a plurality of points oriented in a manner that no more than three points lie in a common plane;

c) each of the points being connected by a frame segment;

d) a plane comprising three of said points;

e) one frame segment passing through said plane and including first and second ends;

f) said first and second ends of said one frame segment being generally equidistant from said plane; and

g) wherein said frame comprises six points.

2. The web structure of claim 1, wherein:

a) said frame comprises twenty triangles.

3. The web structure of claim 2, wherein:

a) said frame comprises fifteen frame segments.

4. The web structure of claim 1, wherein:

a) one of said plurality of points is situated at approximately 0.429, −0.166, 0 values of x, y, z coordinates, respectively, of said frame.

5. The web structure of claim 4, wherein:

a) said one of said plurality of points is connected to each of the remaining said plurality of points by a frame segment.

6. The web structure of claim 5, wherein:

a) said one of said plurality of points forms ten triangles with the remaining said plurality of points.

7. The web structure of claim 1, wherein:

a) one of said first and second ends is disposed at one of said plurality of points situated at approximately 0, 0, −1 values of x, y, z coordinates of said frame.

8. The web structure of claim 1, wherein:

a) the three points in said plane form a triangle.

9. The web structure of claim 1, wherein:

a) said first and second ends of said one frame segment are generally coincident with two of the six points.

10. The web structure of claim 1, wherein:

a) said one frame segment comprises a generally straight frame segment.

11. The web structure of claim 10, wherein:

a) said one frame segment forms a triangle with each of the three points in said plane.

12. The web structure of claim 11, wherein:

a) two of the three points in said plane form two triangles with the remaining two points of said six points in said one frame segment at said first and second ends of said one frame segment.

13. A web structure, comprising a plurality of frames of claim 1.

14. A web structure, comprising:

a) a generally hexahedron-shaped frame;

b) said frame comprising first and second generally trihedron-shaped portions joined at the bases thereof;

c) said first and second portions comprising first and second vertices, respectively;

d) said frame comprising a plane;

e) a frame segment joining said first and second vertices;

f) said frame segment passing through said plane;

g) said frame comprising third, fourth, fifth and six vertices; and

h) said sixth vertex being situated at approximately 0.429, −0.166, 0 values of x, y, z coordinates of said frame.

15. The web structure of claim 14, wherein:

a) said frame comprises twenty triangles.

16. The web structure of claim 15, wherein:

a) said frame comprises fifteen frame segments.

17. A web structure, comprising:

a) a generally hexahedron-shaped frame; and

b) said frame comprising first, second, third, fourth, fifth, and sixth vertices generally situated at approximately 0, 0, 1; −0.5, −0.866, 0; 1, 0, 0; −0.5, 0.866, 0; 0, 0, −1; and 0.429, −0.166, 0 values of x, y, z coordinates, respectively.

18. The web structure of claim 17, wherein:

a) said frame comprises twenty triangles.

19. A web structure, comprising:

a) a frame comprising first and second triangles;

b) said first and second triangles being spaced from each other by a predetermined distance;

c) said first and second triangles disposed in first and second generally parallel planes;

d) the vertices of one of said first and second triangles being offset from the corresponding vertices of the other of said first and second triangles by about 45 degrees;

e) each of the vertices of one of said first and second triangles connected to each of the vertices of the other of said first and second triangles by a segment; and

f) said frame comprising twenty triangles.

20. The web structure of claim 19, wherein:

a) said frame comprises nine non-intersecting segments.

21. The web structure of claim 20, wherein:

a) a plurality of said segments comprise generally straight frame segments.

22. The web structure of claim 20, wherein:

a) each of said segments comprises a generally straight frame segment.

23. The web structure of claim 19, wherein:

a) said first triangle is located at a first distance corresponding to a unit of measurement from 0, 0, 0 values of x, y, z coordinates;

b) said second triangle is located at a second distance corresponding to a unit of measurement from 0, 0, 0 values of x, y, z coordinates; and c) said first and second triangles being spaced from each other along one of x, y, z axes by about twice of one of said first and second distances.

24. The web structure of claim 23, wherein:

a) said first and second distances are substantially the same.

25. The web structure of claim 23, wherein:

a) the unit of measurement comprises one of nanometer, Angstrom, millimeter, centimeter, inch, and meter, in an integer or fraction thereof.

26. The web structure of claim 19, wherein:

a) said first and second triangles comprise congruent triangles.

27. A method of forming a web structure, comprising the steps of:

a) positioning first and second triangles in a spaced apart relationship about a central axis;

b) the first and second triangles extending in first and second generally parallel planes, respectively, that are generally perpendicular to the central axis, wherein the midpoint between the first and second triangles lies at 0,0,0 values for x, y, z coordinates on the central axis;

c) rotating one of the first and second triangles about 45° about the central axis; and

d) connecting each of the vertices of the one of the first and second triangles to each of the vertices of the other of the first and second triangles by a segment.

28. The method of claim 27, wherein:

the segments comprise generally straight segments and do not intersect each other.

29. The method of claim 28, wherein:

the web structure comprises twenty triangles.

30. The method of claim 27, wherein:

a) the distance between the first triangle and the midpoint is substantially the same as the distance between the second triangle and the midpoint.

31. The method of claim 27, wherein:

the first and second triangles comprise congruent triangles.