Tetractine

Tetractine is a term that can refer to a few different concepts, primarily in the fields of geometry and ancient Greek philosophy.

In geometry, a tetractine is a type of four-pointed star polygon. Specifically, it is a stellation of a tetrahedron. Imagine extending the faces of a tetrahedron outwards; where these extended planes intersect, they form a star shape. The tetractine is the shape of the core polyhedron of this stellated form. It can also be understood as a specific arrangement of points in space.

The term is also strongly associated with the Pythagoreans, an ancient Greek philosophical school. For them, the tetractys was a sacred triangular figure composed of ten dots arranged in four rows. The number ten was seen as the sum of the first four integers (1 + 2 + 3 + 4 = 10), and this pattern held profound cosmological and musical significance. The tetractys, and by extension the concept of four, was central to their understanding of the universe and its underlying numerical harmony. While the geometric tetractine is a star shape, the Pythagorean tetractys is a triangular arrangement of dots representing the number ten. The connection lies in the significance of the number four and its role in constructing fundamental patterns and structures.