Design Geometry

A dodecahedron is a three-dimensional polyhedron with twelve flat, regular pentagonal faces, twenty vertices, and thirty edges. It is one of the Platonic solids and is highly symmetrical, with each face being a regular pentagon. The dodecahedron’s shape is unique among the Platonic solids because…

An icosahedron is a three-dimensional polyhedron with twenty triangular faces, twelve vertices, and thirty edges. It is one of the five Platonic solids and is highly symmetrical, with all faces being equilateral triangles. A regular icosahedron has equal edge lengths and angles between its faces,…

An octahedron is a three-dimensional polyhedron with eight triangular faces, six vertices, and twelve edges. It is one of the Platonic solids and has high symmetry, with all of its faces being equilateral triangles. A regular octahedron can be visualized as two pyramids joined at…

A tetrahedron is a three-dimensional shape with four triangular faces, four vertices, and six edges. It is the simplest polyhedron and, in its regular form, has equilateral triangles as faces, with all edges of equal length. Thus, known as one of the Platonic solids, a…

Lattice deformation in parametric design refers to the process of manipulating a grid or mesh structure so that it changes shape in response to specific inputs or parameters. We use this approach widely in computational design for creating complex, organic forms and adaptive systems. Also,…

Parquet deformation refers to a transformation technique applied to a grid or tiling pattern, particularly one that resembles traditional parquet flooring, to create visually interesting and dynamic patterns. This concept is used in parametric design to alter repeating geometric tiles, producing effects such as warping,…

Using a compass and straightedge enables precise geometric constructions, allowing for the creation of complex tessellations. To begin these constructions, a single starting point is sufficient. Circles, which represent a collection of points at a specific distance from the center, and straight lines, which represent…

Escher tilings, inspired by the work of Dutch artist M.C. Escher, are inspiring tessellations that cover a plane using repeated geometric shapes without gaps or overlaps. He often used interlocking, recognizable figures like animals and birds to create these patterns, blending art with mathematical precision….

Snub Square Tiling is a semi-regular tessellation of the plane, composed of two squares and three regular triangles at each vertex. The arrangement of these two regular shapes seamlessly covers the plane without any gaps or overlaps. It is one of the eight semi-regular tessellations…

In Japanese, “kagome” refers to basket weaving, and the name of this tiling derives from the traditional basket-weaving craft of Japanese culture. In geometry, we know Kagome tiling as a semi-regular tessellation, Tri-Hexagonal Tiling. This tiling is composed of regular hexagons and triangles that cover…

The term “hexa” generally refers to the number six, derived from the Greek word. It is commonly used in mathematics, geometry, and other scientific fields to indicate six-sided shapes or structures. A hexagon is a polygon with six sides and six angles. It is one…

The Koch pentagon is a fractal shape that starts with a regular pentagon. Here, we divide each side of the pentagon into three equal parts. Then, we replace the middle with two sides of an outward-pointing equilateral triangle. We repeat this process for every new…

In geometry, “tangent” refers to a scenario where a line, curve, or surface touches another at exactly one point without crossing or leaving a gap. A tangent line to a circle is a straight line that touches the circle at only one point, and it…

The geometric shapes constructed using only a compass and straightedge have significantly influenced the development of reasoning and logic that underpin modern science. This non-numerical approach is also known as the Synthetic Geometry. Before René Descartes introduced Analytic Geometry, this method was widely studied and…

The practical geometry of the ancient Egyptian “rope-stretchers” delineated land after the annual flooding of the Nile River. Thus, the term “geometry” derives from the Greek words “gaia” (earth) and “metria” (measurement). Greek mathematicians used compass and straightedge to perform similar calculations on paper. This…

A spiral is a curve that begins at a central point and continuously moves outward, either getting larger (in an outward spiral) or smaller (in an inward spiral). It often revolves around a central point or axis. Spirals are fascinating because they appear in many…

A fractal is a complex geometric shape that we can split into parts, each of which is a reduced-scale copy of the whole. This property is self-similarity. Fractals often exhibit patterns that repeat at different scales. We can find fractals in nature, such as in…

In mathematics, “curve” describes one-dimensional objects or line shapes, regardless of their curvature. Straight lines, polylines, and curved lines all fall under the category of “curves.” You may remember working with equation graphs in high school math classes. For instance, a first-degree equation produces straight-line…

The Flowsnake, or Gosper curve is a space-filling fractal. It is also known as the Peano-Gosper curve. There are other similar space-filling fractals such as the Dragon curve, or the Hilbert curve. A space-filling fractal is a special type of curve, that fills a plane…

In computer-aided design (CAD), a polyline is a series (or a chain) of straight lines. Each straight section of a polyline is a “segment,” and the points where the segments connect are “vertices.” If a polyline’s starting and ending vertices coincide, it is a “closed…