Equilateral Triangular Tiles Symmetry Pattern Design
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Triangular tiles have not been effectively utilized for floor or wall coverings due to the misconception that they cannot create attractive patterns, as they have only been available in a single color and not been designed with varied colors like square tiles.
Innovation Solution
A set of equilateral triangular tiles with a combination of two types (A and B) using symmetry operations like C2 and C3 rotations, and inorganic burnt glaze or laser-printed color pigments to create mirror images and patterns, with the tiles being at least 90% ceramic or concrete, and having specific thickness and edge length ranges.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If triangular tiles are used with single color only, then manufacturing is simple, but attractive patterns cannot be created
Solution Approach 1:
The patent applies local quality by assigning different colors to different regions (tiles) within the overall floor covering system. Individual tiles are colored based on their position and orientation in the pattern, allowing complex visual patterns to emerge from locally differentiated elements while maintaining simple manufacturing processes for each individual tile.
Solution Approach 2:
The patent utilizes asymmetry by employing triangular tiles with specific asymmetric color distributions and orientations. The coloring is applied asymmetrically relative to the tile geometry, and tiles are arranged in asymmetric patterns that create visually attractive designs while maintaining the simple triangular form factor.
2Adaptability or versatility
If square tiles with different colors are used, then attractive patterns can be created, but triangular tiles remain unused
Solution Approach 1:
Instead of forcing triangular tiles to conform to conventional square tile patterns, the patent inverts the approach by developing a pattern system specifically tailored to triangular geometry. The coloring and arrangement methods are designed around the triangular form, allowing the unique geometric properties of triangles to be exploited for pattern creation rather than being constrained by square-based design conventions.
Solution Approach 2:
The patent introduces a new dimensional approach to tile patterning by utilizing the angular and orientational properties specific to triangular tiles. The pattern design incorporates rotational symmetry and angular relationships that are inherent to triangular geometry, creating a fundamentally different pattern dimension compared to conventional square tile arrangements.
Data Source
Figure 1a~1b
Figure 2a~2c
Figure 3a~3c
AI summary
The set has coloring materials provided on a visible side of the set. The materials having the same color are representable by a symmetrical operation of one tile (A) mapped with another tile (B) in case of the set with a combination of two tiles or by a symmetrical operation of a tile in case of the set with single tile. The operation is selected from rotation of a symmetry element along a rotational axis vertical to the visual side or rotation of another symmetry element along a rotational axis along a vertex of the triangle and a center between other vertexes of the triangle. The tiles are designed as triangle shaped tiles i.e. equilateral triangle shaped tiles. Independent claims are also included for the following: (1) a method for providing a tile set (2) a method for imaging using tiles (3) a computer program comprising a set of instructions to execute a method for imaging using tiles.