septendecagonal

Septendecagonal refers to a shape or object that has seventeen sides. The term is derived from Latin, with "septem" meaning seven, "decem" meaning ten, and "angulus" meaning angle, collectively indicating seventeen angles or sides.

In geometry, a septendecagonal polygon is a polygon with seventeen sides and seventeen vertices. A regular septendecagon has all its sides equal in length and all its interior angles equal in measure. The interior angle of a regular septendecagon can be calculated using the formula (n-2) * 180 / n, where n is the number of sides. For a septendecagon, this is (17-2) * 180 / 17, which simplifies to 15 * 180 / 17, resulting in approximately 158.82 degrees.

The construction of a regular septendecagon was first achieved by Carl Friedrich Gauss in 1796. His discovery was a significant achievement in geometry, as it was the first new regular polygon constructible with ruler and compass to be discovered in over two millennia. The constructibility of the septendecagon is related to the fact that 17 is a Fermat prime.

The term septendecagonal can also be used in other contexts to describe objects or arrangements that have a seventeen-sided structure, although its most common usage is within geometric discussions.