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.
On-curve anchor— a point the strand passes through (each curve segment joins here).
Control vertex— the off-curve handle each segment bends toward.
Handle— links each anchor to its control vertex.
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.
Knot Editor
PROJECT
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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.
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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.