Hexagon draws a regular six-sided shape outwards from its center. It stands with one corner at the top and one at the bottom, its left and right sides upright, and it is made of six equilateral triangles meeting in the middle.
What it does
Choose ‘Hexagon’ on the rail (on a phone, under ‘Shapes’); the cursor carries a small hexagon beside the crosshair. It has no keyboard shortcut.
Press at the center and drag outwards. The drag sets the distance from the center to each corner, and in a regular hexagon that distance is also the length of each side, so the hexagon comes out twice as tall as the drag and about 1.7 times as wide. The drag’s direction does not turn it. A 30° turn with Move, two Shift-steps, lays it on a flat side instead. A click with no drag makes nothing.
Once the drag has begun, Shift takes the size from the longer of the horizontal and vertical distances rather than the diagonal (the tooltip’s ‘⇧ pins the size’, the hint line’s ‘Pin the size’), and Space moves the hexagon without changing its size. Option does nothing, since the hexagon already grows from its center, and the hint line does not offer it. Held before the press, Shift, Option and Command lend you Curves, Points and Move.
The result is six corner anchors joined by straight lines, ready for Points and Curves like any other path.
Why it works this way
The hexagon is here because it is the most sociable of the regular shapes. Only three regular polygons fit together edge to edge to cover a flat surface with no gaps: the triangle, the square and the hexagon, whose corners of 60°, 90° and 120° divide a full turn exactly. Of the three the hexagon is the roundest, and the one whose tiles meet their neighbors most evenly: each touches six others along a whole side, and none at a single point.
It is drawn from the center and kept upright for the same reasons as the triangle. A regular shape has no corner to start from, and a drag that also turned it would never quite hold still.
The metaphor
Set a compass to any width and draw a circle. Then walk the compass around the rim without changing its width. It comes back to where it started in exactly six steps, and the six marks are the corners of a regular hexagon; Euclid gives the construction in the fourth book of the Elements. The hexagon is what a compass makes when it is left alone.
The natural image is the bee’s cell, and it holds: a honeycomb is a hexagon repeated until it fills a space. It breaks where one hexagon is all you have. A single cell says little; the hexagon shows its nature in company, which is why Copies is its natural partner.
A history
In art
Hexagons run through Japanese design. The repeat of hexagons called kikkō, tortoiseshell, after the plates of a tortoise’s shell, appears on textiles and in family crests, and the same name was given to the small hexagonal plates sewn into samurai armor. Islamic geometric art builds many of its most intricate star patterns on a hidden grid of hexagons and triangles, the six-fold symmetry making room for stars of six and twelve points.
In printing
The link to printing is thin, but it runs through cut paper, which is close to home. In Japan, patterns were printed onto kimono cloth through katagami: stencils cut by hand from layers of Japanese paper bonded and hardened with persimmon tannin, a craft centered on Suzuka in Mie Prefecture. Paste was spread through the cut openings to resist the dye, so what the cutter removed and what the cutter left both carried the design, much as the hole and the piece do in a notan. Geometric repeats, hexagons among them, belong to the katagami cutter’s repertoire.
In technology
The hexagon’s economy was noticed early. The Roman scholar Varro, in the first century BC, and later Pappus of Alexandria, in the fourth century AD, reasoned that bees build hexagons because that shape divides a surface into equal cells with the least wall. It stayed a conjecture for two thousand years, until Thomas Hales proved it in 1999. In 1611 Johannes Kepler wrote a short book as a New Year’s gift to a patron, asking why snowflakes always have six corners; he could not settle it, and left the question to those who came after. At the Giant’s Causeway in Northern Ireland, about forty thousand basalt columns, most of them hexagonal, cracked into shape as the lava cooled and shrank, the way drying mud cracks.
Engineers use hexagons for the same reason bees do. On 11 December 1947 Douglas Ring of Bell Labs wrote a memorandum, building on an idea of his colleague W. Rae Young, proposing that a city be covered in hexagonal cells, each with its own low-power radio transmitter, so that the same frequencies could be used again a few cells away. The electronics to build it arrived in the 1970s, and cellular telephones are named after those cells. Game boards and map grids use hexagons because every neighbor is the same distance away, with no diagonals to argue about.
In professional software
A hexagon is a polygon tool set to six sides, and the question that matters is one CAD asks outright: is the size measured to the corners, or across the flat sides? Across the flats is how nuts, bolt heads and the spanners that fit them are measured.
- Adobe Illustrator. The Polygon tool, grouped with the Rectangle tool, draws a hexagon until you change it; drag out from the center, or click to type a radius. Hold Shift to keep one side level, which leaves the hexagon lying on a flat side, 30° around from the one here. For a honeycomb, the ‘Pattern Options’ panel offers ‘Hex by Column’ and ‘Hex by Row’ tile types.
- Adobe Photoshop. The Polygon tool (
U) takes a number of sides; set it to 6. Lower its ‘Star Ratio’ below 100% and the same tool draws a six-pointed star. - Autodesk AutoCAD.
POLYGONwith six sides makes the choice explicit: ‘Inscribed in circle’ puts the corners on the circle you size, and ‘Circumscribed about circle’ puts the middles of the sides on it, which is the across-flats measurement a nut is drawn to. - Autodesk Fusion (formerly Fusion 360). Inscribed Polygon, Circumscribed Polygon and Edge Polygon make the same choice as three separate tools, with the number of sides typed as you draw.
- Inkscape. The Star/Polygon tool (
*) draws a hexagon with its corners set to 6, and its star mode makes a six-pointed star from the same count.
What carries over. Decide what a size means before you type it. The drag here measures from the center to a corner, so a hexagon dragged out to 20 is 40 from corner to corner and about 34.6 across the flats. And because hexagons tile, learn each program’s way to repeat one alongside the tool itself.
Try this
- Drag a hexagon, then turn it with Move by two Shift-steps of 15° so that it lies on a flat side.
- Take Curves and drag outwards from every other corner: three smooth points and three sharp ones share one outline.
- Draw a small hexagon and repeat it with Copies.