### Rolling trefoil

This is the trefoil knot, printed out in a shape that will smoothly roll across the table!

##### Tags:
Mathematical Art
cm: 10.544 w x 6.362 d x 6.344 h
in: 4.151 w x 2.505 d x 2.498 h

#### Comments

@Jenson @ttoinou Ah, I see. That's interesting. That might work to make another rolling knot, although the mathematical question people are interested in is about "triple tangencies", planes which are tangent to the knot in three places. If there are no triple tangencies then the knot will roll, but the converse isn't necessarily true - the plane might be tangent in three places, but crash through other parts of the knot, so the table could never be that plane. I'll have to think about this!
@henryseg I think he means the part in the middle of the knot where it is twisted. If you look at it from the correct angle it looks a bit like a double helix. (Look at the rotating 3d model gif with 'shapeways' in the corner)
@ttoinou What do you mean by "double helices"?
Awesome! Thanks for the link I'll print myself one. Maybe your trefoil can be made higher by adding length to double helices ?
@ttoinou I'm not sure what the state of the art is in this. I think very little is known about this property for knots. "Sphericons" are related: http://www.pjroberts.com/sphericon/index.php
This is such a good idea! Do you happen to know if there is others curves like this in 3D ? ("with only two points of contacts"..)

• ##### White Strong & Flexible

White nylon plastic with a matte finish and slight grainy feel.

\$10.00