What is the Geometric and Linguistic Name for Half of a Hexagon?

The Geometry and Nomenclature of a Semi-Hexagon

When exploring the geometric landscape, dividing polygons often reveals fascinating linguistic gaps. While a half-circle gives us the familiar 'semicircle' and a half-ellipse yields a 'semi-ellipse,' the division of a regular hexagon—a six-sided polygon—does not possess a singular, ubiquitous everyday word in the English language.

Formal Geometric Classification

Mathematically, when you cut a regular hexagon directly in half through its opposing vertices or parallel sides, the resulting shape is a trapezoid (known as a trapezium in British English). Specifically, it is an isosceles trapezoid with interior angles of 60 and 120 degrees. In the context of tessellation and tiling—most notably in mathematical art and recreational geometry, such as the famous Blocks and Boards manipulative toys—this shape is frequently and simply referred to as a semi-hexagon or a trapezoid tile.

Etymological Roots

The prefix semi- comes from the Latin semi, meaning "half," which has been safely grafted onto Greek-derived roots throughout scientific and mathematical nomenclature (e.g., semitone, semicolon). Hexagon, meanwhile, derives from the Greek hex (six) and gonia (angle or corner). Therefore, a "semi-hexagon" is etymologically transparent, denoting precisely a six-angled figure split in half, even if the resulting shape only retains four physical corners.

Modern Nuance

In colloquial speech, laypersons rarely encounter the need to describe half a hexagon unless engaging in quilting, tiling, or puzzle assembly. In those specialized subcultures, the shape is universally called a trapezoid, co-opting the broader category name for this specific, aesthetically pleasing 60-degree slice.