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Four square panels of the same grid of octagons and squares, its edges dashed and their midpoints marked in terracotta. From each midpoint two lapis lines leave at a set angle, 45, 56.25, 67.5 and 78.75 degrees, and meet in stars that sharpen as the angle grows; each panel is cut along the pattern's mirror lines.
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The Pattern Atlas

Hankin’s Method

No. 25 of 100 · free · 300 dpi

What you seeFour square panels of the same grid of octagons and squares, its edges dashed and their midpoints marked in terracotta. From each midpoint two lapis lines leave at a set angle, 45, 56.25, 67.5 and 78.75 degrees, and meet in stars that sharpen as the angle grows; each panel is cut along the pattern's mirror lines.

What it meansThe British scientist E. H. Hankin, studying Islamic ornament in India, proposed that many star patterns can be drawn on a hidden grid of polygons in contact, by lines that cross at the midpoints of their edges. His method is widely used today to analyse and redraw historical patterns.

Where it worksA clear teaching plate for a studio, a classroom or a design office.

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2:3 · 7200 × 10800 px4×6 · 8×12 · 12×18 · 16×24 · 20×30 · 24×36 in
3:4 · 5400 × 7200 px6×8 · 9×12 · 12×16 · 18×24 in
4:5 · 7200 × 9000 px4×5 · 8×10 · 16×20 · 24×30 in
11:14 · 3300 × 4200 px11×14 in
A-series · 7023 × 9933 pxA5 · A4 · A3 · A2 · A1

Everything is one ZIP: every shape and size, the phone wallpaper, the SVGs and a printing guide.

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More from The Pattern Atlas

All 100 prints
A tiling of deep green octagons and brown squares on pale sage, each octagon set with a gold eight-pointed star and each square with a smaller square, with one corner opened out in a roundel to show its angles of 135, 135 and 90 degrees.Octagon and SquareNo. 26
A field of cream eight-pointed star tiles, each centred with a lapis or red star and an ochre octagon, interlocking with deep green crosses that carry four small ochre dots, all within dark joints on warm saffron.Star and CrossNo. 27
A panel on soft rose of burgundy hexagons, each holding a pale six-pointed star, and gold and blue triangles pointing up and down, so that a star of triangles rings every hexagon; one corner is circled where triangle, hexagon, triangle and hexagon meet at 60 and 120 degrees.TrihexagonalNo. 28
A Solomon's knot on deep teal: a gold loop and a coral loop, two even bands crossing at right angles and passing alternately over and under, inside a dark roundel ringed with fine gold lines.Solomon’s KnotNo. 29
A rectangular interlace knot on aubergine: a single gold strand runs on the diagonal, turns at the edges of a grid and crosses itself over and under, with the spaces between filled in pink and violet and set with small gold and cream diamonds.Endless KnotNo. 30
A field of six-pointed stars on deep teal, coloured gold, coral and cream in a repeating three-colour order, each with a smaller star inside, joined by small hexagons and woven through by a pale mint strap that runs over and under.Hexagram TilingNo. 31
Four brick panels on saffron, each labelled: basket weave of paired bricks, herringbone with diagonal bands of green glazed brick, and two banna'i walls in running bond whose blue and green glazed bricks trace lozenges and chevrons.HazarbafNo. 32
An octagonal plan of a muqarnas vault on aubergine: rings of gold, cream, pink and teal squares and rhombi growing out tier by tier from an eight-pointed star of rhombi at the centre, every unit the same edge length.Muqarnas PlanNo. 33

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Two bands, one lapis and one turquoise, weave over and under each other, enclosing blossoms and split palmettes.InterlaceArabesque · No. 9
Large ivory twelve-pointed stars with red star centres sit in a framed field on a triangular grid, with small gold stars between them and green pieces around, all tied together by interlaced dark bands with a pale core.Twelve and SixIslamic Art · No. 14
A large composite blossom in red, white and turquoise rises on its stem against cobalt, held between two arching saz leaves with small tulip buds.HatayiIznik · No. 7
A pointed arch framed in ten-fold girih tilework in cobalt and sky blue, whose pattern loosens beyond the frame and drifts away in separate tiles, a few of them gold.Gate of MercyBab · No. 1
A single cream ring of inward-turning ram's horns around a small red centre, on a quiet moss-green field framed by a fine stitched line.Moss WreathFelt & Horn · No. 4
A flower-filled boteh whose tip grows into a long stem, carrying leaves and blossoms in saffron, indigo and teal.UnfurlingPaisley · No. 10
A full chest panel on a dark dress ground. A double frame with star-filled corners holds bands of hooked zigzags and chains of small diamonds around a diamond medallion with a star at its heart, with borders of gold diamonds above and below.QabbehTatreez · No. 3
Paired spiralling horns in saffron and cream on deep indigo, alternating upright and inverted in staggered rows.Ram's HornKilim · No. 3