Interlocking Components forming Arbitrary Solids with Complex Curvatures

Abstract

An improved design of interlocking components is disclosed. The components may be used to form arbitrary solid shells with complex curvatures, including, for example, three dimensional puzzle games.

Description

CROSS REFERENCES TO RELATED APPLICATIONS

This application claims the benefit of Applicant's prior provisional application No. 61/990,564 filed on May 8, 2014, and Applicant's prior provisional application No. 62/003,379, filed on May 27, 2014. The disclosures of these two provisional patent applications are hereby incorporated by reference.

FIELD OF INVENTION

The technology relates to the general field of interlocking structures, and has certain specific application to fabrication of complex structures from interlocking components.

BACKGROUND

There is a long-felt need for efficient methods of designing interlocking solid structures. “Interlocking puzzles are very challenging geometric problems with the fascinating property that once we solve one by putting together the puzzle pieces, the puzzle pieces interlock with one another, preventing the assembly from falling apart. Though interlocking puzzles have been known for hundreds of years, very little is known about the governing mechanics. Thus, designing new interlocking geometries is basically accomplished with extensive manual effort or expensive exhaustive search with computers.” Peng Song, Recursive Interlocking Puzzles, (Nov. 1, 2012). Thus, there is a long-felt need for methods of designing interlocking solids that does not require extensive manual effort or expensive exhaustive search with computers.

The disclosed technology teaches an interlocking structure that can be created without “extensive manual effort” or “expensive exhaustive search with computers.”

Moreover, additive manufacturing has created a need for interlocking pieces that can be individually manufactured and then assembled into a larger finished product. Such products should ideally achieve a secure fit between separate pieces, be easy to assemble and disassemble, and maintain a consistent appearance among the pieces in terms of seam curvature and width, especially across complex curvatures. For complex curvatures, the orientation of edge surfaces vary dramatically over a component, making it extremely difficult, and sometimes impossible, for a simple wrapping connection to achieve a stable interlock. Therefore, there is a need for new types of interlocking connections between components with complex curvatures.

There is a need for interlocking components where the interlocking arms are smoothly integrated into the component body. There is a need for interlocking components connectable by way of a transverse insertion (along the length of the arms) as opposed to a lateral insertion (orthogonal to the length of the arms).

SUMMARY

The disclosed solid geometries and process for designing interlocking 3D geometries with complex shell curvatures affords several advantages. It results in geometries with arms of relatively consistent widths and that securely interlock between adjacent components. The resulting shapes are easy to assemble and disassemble. The process may be particularly useful in combination with an additive manufacturing process.

The following is a detailed description of exemplary embodiments to illustrate the principles of the invention. The embodiments are provided to illustrate aspects of the invention, but the invention is not limited to any embodiment. The scope of the invention encompasses numerous alternatives, modifications and equivalent; it is limited only by the claims.

Numerous specific details are set forth in the following description in order to provide a thorough understanding of the invention. However, the invention may be practiced according to the claims without some or all of these specific details. For the purpose of clarity, technical material that is known in the technical fields related to the invention has not been described in detail so that the invention is not unnecessarily obscured.

The following detailed description makes reference to the accompanying drawings. In the drawings, similar symbols typically identify similar components, unless context dictates otherwise. The illustrative embodiments described in the detailed description, drawings, and claims are not meant to be limiting. Other embodiments may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented here.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view of an exemplary section of interlocking mesh.

FIG. 2 is a view of an exemplary section of interlocking mesh with separated pieces.

FIG. 3 a view of an exemplary section of interlocking mesh.

FIG. 4 is a view of an exemplary section of interlocking mesh with separated pieces.

FIG. 5 is a view of a plurality of centerlines.

FIG. 6 is a view of a plurality of centerlines split at their continuous midpoints.

FIG. 7 is a view of the continuous midpoints.

FIG. 8 is a view of an exterior mesh.

FIG. 9 is a view of an interior mesh.

FIG. 10 is a view of an interior and exterior mesh.

FIG. 11 is a view of an interior and exterior mesh.

FIG. 12 is a view of an interior surface and an exterior surface of a piece.

FIG. 13 is a view of separated interlocking pieces.

FIG. 14 is a view of connected interlocking pieces.

FIG. 16 is a view of connected interlocking pieces.

FIG. 17 is a view of separated interlocking pieces.

FIG. 18 is a view of connected interlocking pieces.

FIG. 19 is a view of separated interlocking pieces.

FIG. 20 is a view of connected interlocking pieces.

FIG. 21 is a view of separated interlocking pieces.

FIG. 22 is a view of connected interlocking pieces.

FIG. 23 is a view of separated interlocking pieces.

FIG. 24 is a view of connected interlocking pieces.

FIG. 25 is a view of separated interlocking pieces.

FIG. 26 is a view of connected interlocking pieces.

FIG. 27 is a view of separated interlocking pieces.

FIG. 28 is a view of connected interlocking pieces.

FIG. 29 is a view of separated interlocking pieces.

FIG. 30 is a view of connected interlocking pieces.

FIG. 31 is a view of separated interlocking pieces.

FIG. 32 is a view of connected interlocking pieces.

FIG. 33 is a view of separated interlocking pieces.

FIG. 34 is a view of connected interlocking pieces.

FIG. 35 is a view of separated interlocking pieces.

FIG. 36 is a view of connected interlocking pieces.

FIG. 37 is a view of separated interlocking pieces.

FIG. 38 is a view of separated interlocking pieces.

FIG. 39 is a view of connected interlocking pieces.

FIG. 40 is a view of separated interlocking pieces.

FIG. 41 is a view of connected interlocking pieces.

FIG. 42 is a view of connected interlocking pieces.

FIG. 43 is a view of separated interlocking pieces.

FIG. 44 is a view of connected interlocking pieces.

FIG. 45 is a view of separated interlocking pieces.

FIG. 46 is a view of separated interlocking pieces with extreme curvature.

FIG. 47 is a view of an interlocking piece with extreme curvature.

FIG. 48 is a view of separated interlocking pieces with slight curvature.

FIG. 49 is an elevation view of an interlocking piece.

DETAILED DESCRIPTION

Structural Solid

The disclosed 3-dimensional geometry comprised of interlocking pieces may be applied to, or embodied in, any arbitrary closed shape or structure. Some applications include mechanical and industrial design, and the production of large components using additive manufacturing techniques, as well as 3-dimensional puzzles and related toys.

Several types of interlocking connections may be used between pieces. The type of connection may vary depending on the nature of curvature they describe. For example, for relatively gentle curvature one piece may be wrapped around its mate. On areas of more acute curvature, the edge surfaces vary dramatically over the piece, making it difficult or impossible for a simple wrapping connection to achieve a stable interlock, and therefore the present disclosure teaches several alternatives. The connection type may be a function of the curvature of the exterior mesh.

Exterior and Interior Mesh

FIG. 1 depicts an example of a section of an exterior mesh 101. The 3-dimensional geometry may be created by receiving a digital model of the final exterior form of the geometry. This is the exterior 3-dimensional form that the pieces will create when connected. “Exterior mesh” refers to this exterior three-dimensional form. The exterior shape may be any arbitrary closed or semi-closed geometry.

An “interior mesh” 103 is a geometry that may be defined by offsetting 105 the exterior mesh 101. The depth and direction of the offset may depend, for example, on the overall size of the exterior mesh, the material being used in production, and necessary structural strength requirements.

In an exemplary embodiment, the exterior mesh 101 is offset inwardly 105 on a closed geometry to define an interior mesh 103. The interior mesh describes the boundaries of an interior void. This void is the interior space that will be encapsulated by the pieces when engaged together. In a preferred embodiment, each piece of the system will include a first face that establishes a section of the exterior mesh and a second face that establishes a section of the interior mesh.

In a preferred embodiment, a consistent offset distance 105 between the exterior mesh and the interior mesh is used throughout the described geometry. In such a preferred embodiment, the offset distance may be approximately ⅓ of an inch. The offset distance defines the thickness of the pieces of the system.

In other embodiments, e.g., 301, 401, the offset distance may vary to establish necessary physical and mechanical characteristics, or to conserve material during fabrication, or to balance weight, material, or center-of-gravity of the finished product.

In another embodiment, the interior mesh defines a plane that does not intersect with itself. Self-intersection of the interior mesh may result, for example, when the exterior thickness is less than twice the offset distance. Under such conditions, the interior mesh is more likely to define a plane that intersects with itself. In such an embodiment, an improved structure may be achieved by removing the self-intersecting portion of the interior mesh. If a constant offset distance of an exterior mesh results in an interior mesh that intersects with itself, for example in areas with extreme curvature, the interior mesh may require adjustment. Self-intersecting surfaces may be removed automatically through software, or manually by minor remodeling.

Drawing the Centerlines and Arms

In one embodiment, the exterior mesh will be divided into a plurality of different pieces. Piece may have one or more origin points.

A plurality of “centerlines” 501 are projected onto the exterior mesh. These centerlines will form the central lines of the system's interlocking pieces. Centerlines may start at an origin point and travel away from the origin point.

In one embodiment, a designer may draw the Centerlines onto the exterior mesh manually. In another embodiment, an algorithm selects the appropriate length and direction for the set of centerlines and draws them onto the exterior mesh.

Centerlines are placed in relationship to one another as needed to create one of the connection types described below. Generally, the centerline geometry tends to be either forming a “U” around another piece, or a parallel to another piece.

The individual pieces that compose the resulting shape include a plurality of “arms” 107. An arm may be defined by an area encompassing a first centerline 501, with a width determined by the relationship between the first centerline and the nearest adjacent centerlines.

In a preferred embodiment, each piece includes more than one centerline to afford each piece at least 3 “arms”. In other embodiments, pieces may have fewer than 3 Arms.

Defining an appropriate relationship between the Centerlines allows the pieces of the resulting structure to more securely interlock with each other. Because of the interlocking nature of the Centerlines, using one of the connection types facilitates a more secure fit between the pieces.

In a preferred embodiment, the distance between centerlines of adjacent pieces is no less than 0.3 inches. In an embodiment where centerlines are each 0.3 inches apart from the next closest centerline, then the arms of all of the pieces will be 0.3 inches wide at the exterior mesh, and 0.15 inches wide on either side of the centerline. In other embodiments, the centerlines may be distributed at different widths to accommodate other types of structures.

In a preferred embodiment, the adjacent centerlines are drawn parallel to each other for a suitable minimum length. A longer length of parallel directionality tends to result in a structure with pieces that are easy to assemble, while simultaneously ensuring a secure fit when assembled. Where the interlocking pieces contain extreme curvatures, alternative centerline techniques may be used to improve interlocking characteristics.

In a preferred embodiment, the centerlines' parallel directionality 503 in adjacent pieces will overlap for at least 0.4 inches. In other embodiments, a smaller section of adjacent-arm overlap will provide a sufficient fit. In still other embodiments, the minimum length of parallel directionality between adjacent centerlines is defined in proportion to the overall size of the structure. In still other embodiments, the minimum length of parallel directionality between adjacent centerlines is between one-fifth and one-one-hundredth of the length of the Structure. In still other embodiments, the minimum length of parallel directionality between adjacent centerlines is defined in proportion to the size of the pieces.

In a preferred embodiment, each piece that is not an “end piece” is connectable to at least 3 other pieces. This facilitates the creation of an assembled structure with a secure fit. In another embodiment, where there are total number of pieces is relatively small, pieces may contain fewer than 3 connections. In another embodiment, where the pieces are located on a thin area of the exterior mesh, pieces may contain fewer than 3 connections.

Splitting the Pieces

The exterior mesh may be split along a path that defines a continuous midpoint 601 between the centerlines 501, as described below.

Division points 601 are created between adjacent centerlines 501. Division points are located on the exterior mesh and spaced equally between all of the centerlines.

Division points are defined by starting at a first point on a first centerline 605, finding a second point that is the closest (either closest along curvature of the mesh, or closest in normal direction) point on an adjacent second centerline 607, finding a third point that is the midpoint between the first point and the second point 609, and incrementally moving down the first centerline, and repeating the process. Curves are drawn through the lines described by the Division Points. These curves describe the seams of the pieces.

In a preferred embodiment, the increment is 1/200 of an inch. Other embodiments may iterate over different sizes for coarser or finer tolerances.

Exterior Curves.

The “exterior curves” 701, 801 are defined by connecting the division points on the exterior mesh. In one embodiment, each exterior curve defines a seam 707 between two pieces 703, 705. In an embodiment where a piece intersects with two other pieces, the curve stops at the 3-way intersection 709 and two new curves begin.

This method of drawing the shape of interlocking pieces tends to result in self-interlocking components with improved consistency in appearance among the pieces in terms of seam curvature and width.

Interior curves 901 are defined by projecting the exterior curves onto their closest respective locations on the interior mesh. In a preferred embodiment, this interior curve position is in the direction of the interior normal vector of the exterior mesh at the location through which the exterior curves run. If, for example, the exterior curve is located in an area of the structure with extreme curvature, the closest point on the interior mesh may not be the location of the normal line projected from the exterior mesh onto the interior mesh.

In a preferred embodiment, surfaces 1101 are extruded along the exterior curves 1201 normal to the exterior mesh. In a certain embodiment, the exterior surface and interior surfaces are extruded a small distance to create a splitting geometry that continually intersects the exterior mesh and interior mesh. In an embodiment, this small distance is, for example, 0.1 inch. In embodiments where certain pieces include extreme curvature, these surfaces may wave or bend as the curves run across such areas of extreme curvature.

Surfaces are extruded along the interior curves 901 that are normal to the interior mesh at the location of the interior curves. This results in a set of “exterior surfaces” 1201 and “interior surfaces” 1203. These surfaces split the exterior mesh and interior mesh along the paths of the exterior curves and interior curves. In other embodiments, no extrusion is necessary, particularly where the lines run precisely across the surface of the meshes.

In a preferred embodiment, the extrusions from the exterior surface 801 and interior surface 901 result in exterior surfaces that continuously intersect the exterior mesh and the interior surfaces that continuously intersect the interior mesh.

In another embodiment, seams projected normal to the exterior surface at the exterior curves at every 100^th of an inch. Other embodiments may use a higher resolution, or may use an infinite number of normal projections (continuous projections).

The structure is now a set of split exterior mesh and interior mesh pieces with edges that are defined by paths created as previously described. Each respective exterior and interior mesh piece will define the major faces of a piece of the structure. The individual pieces may be closed by modeling surfaces that connect the edges of the respective exterior and interior mesh. The enclosing faces are referred to as “boundary-surfaces” 1205.

In a preferred embodiment, Respective exterior and interior mesh pieces are not connected all the way around by a single boundary-surface. Instead, boundary-surfaces start from locations where each piece intersects with at least two other pieces. In such an embodiment, all pieces will contain at least two boundary-surfaces. In such an embodiment, where boundary-surfaces are modeled individually, each boundary-surface may be used as a surface for both pieces that it bisects.

When adjacent pieces use similar or identical boundary-surface geometry, the pieces are more likely to fit together securely. In addition, it reduces the possibility of overlapping Boundary-surfaces. Increased boundary-surface area tends to facilitate improved interlocking connections between the arms of adjacent pieces.

After all of the surfaces have been modeled, an exterior mesh piece, its respective interior mesh piece, and all of the boundary-surfaces that connect the two pieces are selected. Then, a copy of the selection is made. Then, the copied pieces are joined together to form a closed geometry. The original surfaces remain available to be used as boundary-surfaces to connect the exterior and interior mesh pieces of adjacent pieces.

In a preferred embodiment, the closed, solid geometries are offset inwardly a very small distance. Such an offset creates a small gap between adjacent pieces. This gap facilitates assembly of the pieces, and accounts for tolerance limitations in the digital fabrication machinery. The size of the gap may be proportional to the size of the pieces. In a preferred embodiment, an offset distance of 0.006 inches is appropriate.

The modeled pieces are fabricated. In a preferred embodiment, a fused deposition modeling (“FDM”) printing method is used for fabrication. Any material suitable for additive manufacturing may be used. Commonly used materials may include ABS (acrylonitile butadiene styrene), PLA (polylactic acid), PC (polycarbonate), SOFT PLA, Steel, Stainless steel, Titanium, Gold, Silver, Aluminum, nylon, glass-filled polyamide, epoxy resins, wax, and photopolymers.

After fabrication, the pieces are tested for fit and hold. If the pieces do not connect in a suitably secure manner, the Centerlines may be redrawn, and the pieces re-fabricated.

Geometries and Connection Types

In certain embodiments, the following characteristics tend to facilitate assembly, disassembly, and secure hold while assembled. Piece connecting to at least 2 other pieces tend to result in a more stable interlocking structure. Selecting the right connection type for the local curvature of the piece tends to result in a more stable interlocking structure. The parallel nature of connection, and necessary parallel length tends to affect the cohesive stability of the final interlocking structure. For examples, larger pieces tend to require longer parallel connection lengths to achieve appropriate interlocking stability. Some piece or some group of pieces may need all-parallel connections to improve insertion and removal. In certain embodiments, slotting pieces together (transverse insertion) results in a better hold than pressing pieces in from a normal direction (like a traditional jigsaw—where pieces have a negligible thickness and are pressed in from normal direction).

Connection Type A, or “single-U connection” includes a single arm 1301 mated to a U-shaped connection 1303. It includes a first piece with a single arm 1301, 1703, 1903, 2103 and a second piece with a pair of parallel (U-shaped) arms 1303, 1701, 1901, 2101. The arm of the first piece securely interlocks between the arms of the second piece 1401.

When connected, the pieces form a continuous surface of arbitrary curvature. Such a connection may be useful in a variety of gently curving mesh conditions 1601, 1701, 1703, 1801, 1901, 1903, 2001, 2101, 2103.

The arms have an interior surface 1305, an exterior surface 1307 and a boundary-surface 1309. The boundary-surface is perpendicular to the exterior surface. The interior surface is substantially parallel to the exterior surface at any particular point.

Each arm has a centerline. When connected, the boundary-surface of each arm is a plane perpendicular to the exterior mesh at the division points. The division points are located the midpoint between the arm's centerline and the centerline of the closest adjacent arm.

Connection Type B, or “double U connection” 2201, includes a first U-shaped end 2301, 2501, 2701, 2901 engaged to a second U-shaped end 2303, 2503, 2703, 2903. This connection may provide more secure interlocking properties in areas of more extreme curvature, e.g., 4401. For example, connections in areas of acute curvature on the exterior structure may not lock into place when a simple arm-and-U type connection is used. This double-U type connection increases the parallel surface area between interlocking components. Such a connection may be useful in a variety of curving mesh conditions 2201, 2301, 2303, 2401, 2501, 2503, 2601, 2701, 2703, 2801, 2901, 2903.

Connection Type C 3001 includes a U-shaped arm 3101, 3501, 3701 engaged to two separate single-arms 3101, 3105, 3503, 3505, 3703, 3705. The two separate single-arms are components of two separate pieces. The two single-arms are both mated to the U-shaped arm of a third piece to form a locked connection. This connection type is useful on areas of most extreme curvature, but may not provide as secure a hold as other connection types, as each piece is only in a friction-type hold with one other piece on each side, as opposed to a “U” condition. Such a connection may be useful in a variety of highly curving mesh conditions 3201, 3301, 3303, 3305, 3401, 3501, 3503, 3505, 3601, 3701, 3703, 3705.

Connection Type D includes one piece engaged to one or more other pieces by lateral insertion. That is, a first piece 3803 is inserted at an angle that is substantially normal to the surface of the second piece 3801 and/or the structure. This connection type 4101 may be useful when the curvature of the base surface is so great that transverse push-in connections are ineffective. Such a connection may be useful in a variety of curving mesh conditions 4101, 3801, 3803, 3901, 4001, 4003, 4005.

Connection Type includes one piece 4303 engaged to one or more pieces 4301 wherein the first piece 4007, 4503, 4303 forms an end of an object or structure. Such a connection may be useful in a variety of terminal mesh conditions 4201, 4301, 4303, 4305, 4401, 4501, 4503.

Various combinations of these connection types may be used in any particular connection. Various combinations of these connections types may be used within an overall structure.

In one embodiment, when the ratio of volume to piece size is small, and therefore a single piece can cover a great deal of curvature and its connections may go in very different directions and have very different boundary-surface directionalities, the assembly order may be important. In other embodiments, the pieces can be assembled in any order.

In certain embodiments, in areas of extreme curvature, the thickness of pieces may be less important. In such an embodiment 4601, the differing boundary-surface directionality 4607, 4609 achieves firm hold between pieces 4605, 4603, 4611. In such an embodiment, the slotted connection type should also be considered to achieve a firm connection.

In certain embodiments, areas of low curvature 4701 a slotted connection may be safely replaced by lateral-insertion type pieces while maintaining a locking structure. Such a lateral-insertion type piece 4703 may require additional thickness 4705.

When the ratio of total volume to piece size is smaller (and therefore a single piece traverses more curvature) the ability to slot pieces together (transverse insertion) instead of push-in (lateral insertion) may become important. This is because a lateral push-in might require pushing in connections from different directions on the same piece, and may require bending pieces out of plane. In such an embodiment, slotted connections would not require stretching the pieces out of plane. Stretching and bending pieces may result in breakage or depending on the flexibility of the materials, may be impossible to achieve.

When a single piece traverses very different curvature, its boundary-surfaces will have different directionality (because of the change of the normal to the base surface). These different boundary-surface directionalities may help secure fast connection between pieces.

With a larger volume to piece-size ratio, the choice between a slotted and push-in connection type may have a smaller impact on the stability of the overall interlocking structure. Such pieces can generally be pushed in because they do not describe much curvature, and can easily be moved out of plane. The thickness may have more influence on connection strength, because the directionality of the boundary-surfaces on either side of a single piece does not vary much. In such an embodiment, thicker pieces tend to provide more stability.

In one embodiment, the boundary-surfaces are normal to the exterior surface. They are the connection between exterior and interior surfaces. This means that, between the exterior and interior surface, whichever has more convex curvature will have more surface area.

In one embodiment, the curvature is inversely proportional to the thickness of the piece. Where the curvature is steep, the pieces may be thicker to help ensure a secure connection. In other embodiments, the thickness is only constrained by a minimum bound necessary to achieve Boundary-surface directionality.

In one embodiment, the disclosed structures interlock because centerlines of adjoining pieces run parallel for at least the distance needed to establish the surface area and curvature change of the adjoining edge surfaces to form a locked connection. Where there are parallel center lines, one piece is locking around another. The parallel distance is generally about ⅓ the length of the piece being locked to, if the pieces are relatively flat. In areas of intense curvature, the parallel length may be smaller

In an exemplary embodiment, non-end pieces each connect to two or more pieces. End pieces may connect to one or more other pieces.

CAD.

The disclosed process may be modeled on standard Computer Aided Design software, for example in AutoCAD, Rhinoceros 3D, Inventor, ProEngineer, SolidWorks, or similar design software.

The disclosed technology is much more than a standard jigsaw puzzle wrapped around a 3 dimensional shape. In a jigsaw puzzle, slotted connections are impossible, boundary-surface directionality is irrelevant, and piece thickness is irrelevant to securing a strong connection between pieces. Moreover, jigsaw puzzle repeat the same connection geometries over and over, whereas the disclosed technology uses connection geometries that are a product of the nature of the geometry over which the pieces run. Various embodiments of the disclosed technology use slotted connections, boundary-surfaces normal to exterior surfaces, vary piece thickness achieve a secure hold between 3 dimensional pieces.

The following material is hereby incorporated by reference.

• a. Geometric Puzzle Design. S. T. Coffin. (A. K. Peters, 2007).
• b. Recursive Interlocking Puzzles, Peng Song (Transactions on Graphics (TOG), Volume 31 Issue 6, Nov. 1, 2012).
• c. Puzzling World of Polyhedral Dissections. Stewart T. Coffin (Oxford University Press in 1990). Available at www.johnrausch.com/PuzzlingWorld/contents.htm.

CONCLUSION

The disclosed embodiments are illustrative, not restrictive. While specific configurations of the arbitrary interlocking surface and methods of designing an arbitrary interlocking surface have been described, the present invention can be applied to a wide variety of surfaces and design methods. There are many alternative ways of implementing the invention.

While particular aspects of the technology have been shown and described, people skilled in the art will understand that, based upon the teachings herein, modifications may be made without departing from the subject matter described herein and its broader aspects.

Claims

1. A toy curved shell structure, comprising,

a. a plurality of interlocking pieces, wherein a piece has an interior surface and an exterior surface that are separated by a boundary-surface, and

b. a first interlocking piece with a plurality of arms, and

c. a second interlocking piece with an arm; and,

d. the boundary-surface of each arm is located at the midpoint between a centerline of the arm and a centerline of the closest adjacent arm of the second interlocking piece; and

e. the boundary-surface of the arms are parallel to each other for sufficient length to achieve a stable interlocking connection.

2. The toy shell structure of claim 1, wherein,

a. the first interlocking piece and the second interlocking piece are reciprocally matable by slotted insertion along the axis of their arms.

3. A toy shell structure of interlocking pieces, comprising,

a. a plurality of interlocking pieces, wherein a piece has an interior surface and an exterior surface that are separated by a boundary-surface, and

b. a first interlocking piece with a plurality of arms, and

c. a second interlocking piece with an arm; and,

d. the boundary-surface of the arms are parallel to each other for sufficient length such that the force of friction between adjacent pieces is greater than the force of gravity pulling adjunct pieces apart, and

e. the first interlocking piece and the second interlocking piece are reciprocally matable by slotted insertion along the axis of their arms.

4. A shell structure, comprising,

a. a plurality of interlocking pieces, wherein a piece has an interior surface and an exterior surface that are separated by a boundary-surface, and

b. a first interlocking piece with a pair of parallel arms, and

c. a second interlocking piece with a pair of parallel arms; and,

d. the boundary-surface of each arm is located at the midpoint between an arm's centerline and the centerline of the closest adjacent arm of the second interlocking piece.

e. the first interlocking piece and the second interlocking piece are reciprocally matable by slotted insertion along the axis of their arms.

5. A shell structure, comprising,

a. a plurality of interlocking pieces, wherein a piece has an interior surface and an exterior surface that are separated by a boundary-surface, and

b. a first interlocking piece with one or more arms wherein, the arms have a centerline; and

c. a second interlocking piece with a one or more arms wherein, the arms have a centerline, and the boundary-surface of the arms is perpendicular to the exterior surface; and

d. the boundary-surface of each arm is a curve defined by the local midpoint between the arm's centerline and the centerline of the closest adjacent arm of an adjacent interlockable piece.

6. The shell structure of claim 5, wherein,

a. the first interlocking piece and the second interlocking piece are reciprocally matable by slotted insertion along the axis of their arms.

7. The shell structure of claim 5, wherein,

a. The first interlocking piece has two or more arms,

b. The second interlocking piece has one or more arms,

c. A third interlocking piece has one or more arms, and

d. An arm on the second piece and an arm on the third piece are matable between a first arm and a second arm of the first piece; and

e. the boundary-surface of the arm on the third piece is a curve defined on one side by the local midpoints between a centerline of the arm of the third piece and the centerline of the adjacent arm of the second piece, and defined on the other side by the local midpoints between a centerline of the arm on the third piece and the centerline of an adjacent arm of the first piece.

8. The shell structure of claim 5, wherein,

a. the first interlocking piece and the second interlocking piece are reciprocally matable by lateral insertion perpendicular to the axis of their arms.

9. The shell structure of claim 5, wherein,

a. the exterior surface and the interior surface are separated by an offset distance, and

b. the offset distance is constant.

10. The shell structure of claim 5, wherein,

a. the exterior surface and the interior surface are separated by an offset distance, and

b. the offset distance between the exterior surface and the interior surface is between ¼ inch and ½ inch.

11. The shell structure of claim 5, wherein,

a. the exterior surface and the interior surface are separated by an offset distance, and

b. the offset distance between the exterior surface and the interior surface is between ⅕ and 1/100 of the structure's width.

12. The shell structure of claim 5, wherein,

a. the exterior surface and the interior surface are separated by an offset distance, and

b. the offset distance is non-uniform and adjusted to establish a center of gravity above a surface-engaging support component.

13. The shell structure of claim 5, wherein,

a. the exterior surface and the interior surface are separated by an offset distance, and

b. the offset distance is inversely proportional to the local curvature of the piece.

14. The shell structure of claim 5, wherein,

a. the minimum thickness of a piece is constrained by a minimum bound necessary to achieve boundary-surface directionality.

15. The shell structure of claim 5, wherein,

a. a boundary-surface originates from a location where a piece intersects with at least two other pieces.

16. The shell structure of claim 5, wherein,

a. the centerlines of adjoining pieces run parallel for at least the distance necessary to establish a surface area and curvature change of an adjoining edge surface to form a lockable inter-connection.

17. The shell structure of claim 5, wherein,

a. the parallel directionality of the centerlines of two adjacent pieces overlaps for at least 0.4 inches.

18. The shell structure of claim 5, wherein,

a. the minimum length of parallel directionality between adjacent centerlines is between one-fifth and one-one-hundredth of the length of the shell structure.

19. The shell structure of claim 5, wherein,

a. the minimum length of parallel directionality between adjacent centerlines is between one-half and one twentieth of the length of the piece.

20. The shell structure of claim 5, wherein,

a. each piece that is not an end piece is connectable to at least 3 other pieces.