Snub hexaoctagonal tiling

Uniform tiling 86-snub

Snub Hexaoctagonal Tiling is a unique and complex form of tiling in the realm of geometry, particularly within the study of uniform tilings. It is a part of the Euclidean plane tiling family, characterized by its intricate pattern that combines both hexagons and octagons in a snub fashion. This tiling is notable for its aesthetic appeal and its application in various fields such as mathematical art, architecture, and tiling theory.

Definition

The Snub Hexaoctagonal Tiling is defined by its specific arrangement of polygons in a repeating pattern. It consists of alternating hexagons and octagons, with each hexagon being surrounded by octagons and vice versa. The term "snub" refers to the manner in which these shapes are arranged in a skewed, non-regular manner, which distinguishes this tiling from regular hexagonal or octagonal tilings.

Properties

One of the key properties of the Snub Hexaoctagonal Tiling is its symmetry. It exhibits a specific type of symmetry known as chiral symmetry, meaning it lacks reflective symmetry and cannot be superimposed on its mirror image. This property contributes to the tiling's aesthetic appeal and complexity.

Additionally, the Snub Hexaoctagonal Tiling is aperiodic, meaning it does not repeat exactly over finite distances. This aperiodicity adds to the visual interest of the pattern, making it a subject of study in both mathematical and artistic contexts.

Applications

The Snub Hexaoctagonal Tiling finds applications in various areas due to its unique properties. In mathematical art, it is used to create visually appealing designs that showcase the beauty of mathematical patterns. In architecture, it can be seen in floor and wall tilings that aim to create unique and engaging spaces. Furthermore, the study of this tiling contributes to the broader field of tiling theory, enhancing our understanding of geometric patterns and their properties.

See Also

• Uniform tilings
• Euclidean plane
• Symmetry in mathematics
• Aperiodic tiling

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