A Symmetric Motion Picture of the Twist-Spun Trefoil

Abstract

With the aid of a computer, we provide a motion picture of the twist-spun trefoil that satisfactorily exhibits the periodicity.

2000 AMS Subject Classification::

• Primary 57Q45
• Secondary 68U05
• 68U07

Keywords:

• 2-knot
• motion picture
• diagram
• visualization
• 3D modeling

Notes

¹An animation of this diagram can be seen at http://www.youtube.com/watch?v=BB1B6hDJga8 .

²An animation of this diagram can be found at http://www.youtube.com/watch?v=-obouoE3DVA .

³See also the animation at http://www.youtube.com/watch?v=-OEMiR43iIs for more detail.

⁴The animation at http://www.youtube.com/watch?v=u1j8JLP4bUU is color-coded to show connected components.

⁵See also the animation at http://www.youtube.com/watch?v=6lIM9p6XOKo for further details.

⁶Blender is a quite powerful free open-source 3D content-creation suite, available at http://www.blender.org/ .