Back to interactive cinquefoil knots
The cinquefoil knot is a 5-2-torus-knot, 5 times around the torus axis, 2 times around
the central circle of the torus (see the anaglyph picture). usually the cinquefoil knot
is drawn as the much nicer looking 2-5-torus-knot, which, in its standard position,
has only 5 crossings. this is the minimal number of crossings for the cinquefoil knot.
in the
Clifford Torus
page we show how a torus can be turned inside out, with
only one point of the torus passing through infinity. if the knot avoids this point,
we have a deformation of the 5-2-torus-knot into the 2-5-torus-knot.
The cinquefoil knot is a torus knot. Meaning, it can be drawn as a curve winding around a torus.
Cinquefoil knot, rotating around the torus's axis of revolution.
knot2 5to5 2 001
We can deform a torus m_n_knot with the help of the inside-out-deformation
of the Clifford torus
[see Clifford Torus]
into a torus n_m_knot. We only need to place the knot in such a way on the torus
that the torus point, which passes through infinity under the inside-out deformation,
does not lie on the knot.
In the animation the knot is realized as a strip on the torus by restricting a suitable
parametrization to a narrow band.
The cinquefoil knot in its 5-2 version looks confusing without the torus,
we show a cross-eye stereogram of this knot on the torus.
the cinquefoil knot in its 5-2 version looks somewhat confusing without the torus,
we show two stereo images of this knot on the torus.
