Hexagon Prototile Boundaries for Diverse Periodic and Nonperiodic Tiling
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Solution Overview
Problem
Existing tiling systems, particularly those based on regular hexagons, suffer from high manufacturing costs, lack of unified artistic beauty, and limited variety in tiling effects due to multiple types of pieces, with periodic tiling being too simple and nonperiodic or aperiodic tiling being difficult and lacking variation.
Innovation Solution
A periodic and nonperiodic tiling system using regular hexagons with seven types of prototiles, each featuring specific boundary contours that can form complex patterns by engaging with each other, allowing both periodic and nonperiodic tiling, and incorporating animal, plant, or human figures, with a single type of prototile capable of creating various tiling effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Shape
If multiple types of pieces are used in tiling puzzles, then the artistic beauty and variety of tiling effects are improved, but the manufacturing cost increases and the structure becomes more complex
Solution Approach 1:
The patent applies universality by designing a single type of prototile that can serve multiple functions - it can be arranged in periodic patterns, nonperiodic patterns, and rotated at different angles (0°, 60°, 120°, 180°, 240°, 300°) to create diverse tiling effects. This single versatile piece replaces the need for multiple specialized pieces, reducing manufacturing complexity while maintaining artistic variety
2Shape
If multiple types of pieces are used in tiling puzzles, then the artistic beauty is improved, but the manufacturing cost increases
Solution Approach 1:
The single prototile design with universal applicability allows manufacturers to produce only one type of piece, significantly reducing tooling costs, inventory complexity, and production expenses while still achieving diverse artistic effects through different arrangement patterns and orientations
3Ease of manufacture
If periodic tiling with simple geometric structure is used, then the manufacturing is simple, but the challenge and attractiveness are reduced
Solution Approach 1:
The prototile is designed with specific boundary contours that enable it to function in multiple modes - it can create simple periodic tilings for beginners while also supporting complex nonperiodic arrangements and multiple rotation angles for advanced challenges, all using the same piece design
4Adaptability or versatility
If nonperiodic tiling with complex structure is used, then the variety of solutions is improved, but the difficulty increases and the number of solutions decreases
Solution Approach 1:
The single prototile design with carefully designed boundary contours enables nonperiodic tiling while maintaining manageability - the universal piece can be arranged in numerous different patterns and orientations (0°, 60°, 120°, 180°, 240°, 300°), creating high solution variety without requiring complex multi-type piece systems
Data Source
AI summary
The present invention discloses a periodic and nonperiodic tiling system based on regular hexagons, comprising seven different types of prototiles. Each type of prototiles are based on a regular hexagon structure, and external contours of each type of prototiles are composed of six boundary contours. In a connected pattern enclosed by the six boundary contours, the areas of parts convex from and concave into a regular hexagon are correspondingly equal. A specific shape of an animal, plant or human figure is enclosed by the six boundary contours, and a plurality of specific shapes enclosed by the six boundary contours are engaged with each other to form a tiling surface. The prototiles are provided with a corresponding pattern according to the boundary contours of the specific shape. The present invention is simple in structure and diversified in tiling effect, and has a wide application prospect.