Pinagons

Pinagons are a type of geometric shape that combines the properties of both a pentagon and a hexagon. The term "pinagon" is a portmanteau of "pentagon" and "hexagon," reflecting its unique structure. Pinagons are characterized by having five sides and two vertices that are each shared with an adjacent pinagon, effectively creating a tiling pattern. This results in a shape that is neither a regular pentagon nor a regular hexagon, but rather a hybrid with distinct geometric properties.

The most common type of pinagon is the pinagon-5-6, which has five sides and two vertices that are shared with adjacent pinagon-5-6 shapes. This creates a tiling pattern that is both aesthetically pleasing and mathematically interesting. Pinagons can be used in various applications, including tiling patterns in architecture, art, and design. They are also studied in mathematics for their unique geometric properties and the way they can be used to create complex tiling patterns.

Pinagons are a fascinating example of how simple geometric shapes can be combined to create complex and interesting patterns. Their unique structure and properties make them a valuable tool in both artistic and mathematical contexts.