Carlo H. Séquin

Prof. Emeritus

EECS Department, University of California, Berkeley

Berkeley, CA, 94720, USA


I am using mathematical knots as an inspiration for making abstract geometrical sculptures. Recently, I have started with simple knots and have then increased their complexity by following the knot curve with a “cable” with several parallel strands. Before the cable is closed into a loop, it is given an appropriate amount of torsional twist, so that we obtain cyclic connectivity among all the strands, resulting in a single closed-loop strand and thus in a valid mathematical knot.


Image for entry 'Cable-Knots & Knotted Braids'

Cable-Knots & Knotted Braids

16.0 x 24.0 x 14.0 cm

3D-prints in PLA


On the left is the 4-crossing “Figure-8 knot” outlined with a 4-strand cable. The cable is given a 90° torsional twist to connect the four strands into a single closed loop. Wherever the Figure-8 knot had a simple crossing, there are now 16 crossings; and there are three more crossings due to the quarter twist of the cable. Thus, the resulting knot has 67 crossings. On the right is "Knot-5_2" outlined with a 4-strand cable. This leads to a knot with 5×16=80 crossings. In addition, the four strands are woven into a classical braid, adding another 129 crossings, since there are 10.75 braid periods, and each period has 12 crossings. This leads to a knot with a grand total of 209 crossings.