geometride

Geometride is a term used in speculative or recreational geometry to denote a family of geometric objects defined by a controlled, uniform local geometry. In the broad sense, a geometride can refer to either a planar tiling or a three‑dimensional polyhedron constructed by joining regular polygonal faces so that all edges have the same length and the arrangement of faces around every vertex is the same.

In planar geometrides, the unit cell is repeated by translational symmetry to fill the plane. Typical examples involve mixtures of regular polygons arranged so that at each vertex the same configuration occurs. A common illustrative pattern is a vertex configuration such as 3.4.6.4, where a triangle, square, hexagon, and square meet in succession around every vertex. Such tilings highlight the emphasis geometride places on uniform edge lengths and consistent local geometry.

In three dimensions, a geometride can be described as a convex polyhedron with equal edge lengths and a uniform vertex figure, meaning the sequence of faces meeting at each vertex is the same. While not part of formal geometric taxonomy, these objects are discussed in puzzle literature and classroom explorations as a way to study symmetry, tiling in space, and the relationship between local and global structure.

Etymology reflects a blend of geometry and the familiar suffix used in naming geometric derivatives. The term geometride appears in online discussions and some educational materials as a conceptual tool rather than a standardized category. See also tiling, polyhedron, symmetry, and uniform tilings.