tensided

Tensided is an adjective used to describe a polygon that has ten sides. In mathematics the standard term for such a shape is decagon, or ten-sided polygon; tensided is a descriptive alternative and is seldom used in formal terminology.

For any simple ten-sided polygon, the sum of interior angles equals (n-2)×180 degrees, giving 1440 degrees for n = 10. A regular tensided polygon—known as a regular decagon—has all sides and all interior angles equal, with each interior angle measuring 144 degrees and each exterior angle 36 degrees. A regular decagon is cyclic, meaning its vertices lie on a common circle, and it has the dihedral symmetry group D10 (order 20). It also has 35 diagonals.

Beyond the regular case, tensided polygons can be irregular: the ten sides may vary in length, and some interior angles may be reflex (greater than 180 degrees) in concave ten-sided polygons. There are also star-shaped ten-sided figures, such as certain star polygons, though these are typically treated separately from simple tensided polygons.

In applications, tensided figures appear in geometry education, design, and architectural motifs. In tiling theory and the study of symmetry, decagonal (tenfold) motifs feature in Penrose tilings and in the study of quasicrystals, where decagonal patterns arise despite a lack of periodic repetition.

Etymology: the term tensided is built from ten and sided, analogous to other polygon descriptors; the conventional name for a ten-sided polygon is decagon.