Trefoil knot

Trefoil knot
Trefoil knot

In knot theory, the trefoil knot is the simplest nontrivial knot. It can be obtained by joining the loose ends of an overhand knot. A trefoil knot is the unique prime knot with three crossings.

Mathematically, it can be described in many variants.


The symbol of the trefoil knot has known from ancient times as triquetra. Triquetra is a work derived from Latin tri- (three) and quetrus (cornered). Its original meaning was simply "triangle" and it has been used to refer to various three-cornered shapes.

Triquetra in blue as part of an interlaced Christian Trinitarian decorative symbol.

An interlaced double Triquetra.

Triquetra interlaced with circle as Christian Trinitarian symbol (a "Trinity knot").

The triquetra has been found on rune stones in Northern Europe and on early Germanic coins. (See also images of Borromean rings on rune stones)

Triquetra on one of the Funbo Runestones, located in the park of Uppsala university.

Also, the triquetra is often found in Celtic art. While it is uncertain what the symbol may have meant to the Celts, it is often found as a design element in larger drawings of triskeles or triple spirals. Later, the symbol was used by Christians as a symbol of the Trinity (Father, Son and Holy Spirit).

Nowadays, the triquetra has been used in various logos. A triquetra is one of the four symbols on the cover of the Led Zeppelin album, "Led Zeppelin IV", where it used as the personal symbol of bassist John Paul Jones.


Trefoil knots has frequently used in art. Dutch artist M.C. Escher shown three versions of the knot on his lithograph "Knots". On of them is a kind of Möbius strip.

M.C. Escher

There's sculpture of the trefoil knot the Hollander York Gallery, on Toronto's Yorkville Avenue.

Trefoil knot sculpture
Trefoil knot near Hollander York Gallery

Derived variations

Trefoil knot can be easely transformed into Möbius strip as you can see on the photo of sculpture by Carlo H. Séequin.

Double trefoil knot
Double trefoil knot by Carlo H. Séequin

The smooth shape of the trefoil knot can be transormed into the figure with straight lines and formed into impossible figure like Penrose tribar.

Impossible trefoil knot
Impossible trefoil knot

Appendix. Artistic examples of the trefoil knot

Möbius-Trefoil Knot Gears
by Tom Longtin