Bezier point key

Corner cusp — arc–arc cusp on a 45° bisector.
U-turn cusp — arc–arc cusp on an axis-aligned bisector.
Apex — mid-strand apex of a 180° arc.
Arc continuation — two arcs with parallel chords (not a cusp).
Diag–arc joint — one diagonal piece meets one arc piece.
Diag–diag joint — two diagonal pieces meet.
Open boundary — end of an open strand.
Control points & handles — bezier handles and control-point dots.

Symmetry diagram key

2-fold rotation — order-2 centre (180°).
3-fold rotation — order-3 centre (120°).
4-fold rotation — order-4 centre (90°).
6-fold rotation — order-6 centre (60°).
Mirror axis — solid line; reflection.
Glide axis — dashed line; glide reflection.
PROJECT
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KNOTS
PALETTES
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Open a knot from the Library on the left, or create a new one with the New button.

Size (Grid units before pattern repeats)

10
10

Boundary

Turn strand ends back at the boundary so the knot has no loose ends. Also toggles the frame, which can then be overridden on the Colour tab.

Repeat

Repeat the design across the canvas.
1
1
Rotations
Mirrors
Glides
o
p1

Found Symmetries

Selected Orbifold Strand layout
Found Orbifold of Selected Cell Strand layout
Image
Found Orbifold of Minimal Cell Strand layout
Image
Found on selected cell Found on minimal cell
Unsupported (hex lattice)

Profile

50%
0.20

Crossing

0%
0.40
0.40

Cross-section

✎

Strand colour variation (Vary colour of striped band(s))

From: → To: ⓘ

Background

Frame

2.0%

Export

Each export definition is a fully configured way to produce an output file — modify the knot, then re-export it the same way in one click. An empty list is fine: you only define exports when you want them.
When ticked, every Bezier-segment endpoint is drawn as a small blue dot on top of the knot (and is included in the export).
Overlay the wallpaper-group symmetry elements (rotation centres, mirror and glide axes) on the knot.
Mark the inbetween dots (centres of cells of the crossing-point grid) as small grey circles, and connect each pair whose intervening orbit edge is in a delete or contract state with a thin grey dotted line.
10s
100%
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Paste special

Edit Strand Profile

Cross-section
The strand is symmetrical. The left edge of the cross-section is the edge of the strand; the right edge is the middle of the strand.
Strand preview
Knot preview

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