A Spacefilling Trefoil Knot
نویسنده
چکیده
This note describes a (polyhedral) prototile which is topologically equivalent to a trefoil knot and admits a (monohedral) tiling of 3-space.
منابع مشابه
The ideal trefoil knot
The most tight conformation of the trefoil knot found by the SONO algorithm is presented. Structure of the set of its self-contact points is
متن کاملA Symmetric Motion Picture of the Twist-Spun Trefoil
A 2-knot will be a 2-sphere embedded into R locally flatly. Although we cannot see a 2-knot directly with our eyes, there are several ways to visualize it. A motion picture is one of the ways. Roughly speaking, a motion picture is a CT scan (Computed Tomographic scan) of a 2-knot. It is a one-parameter family of slices of a 2-knot, that are 0or 1-dimensional objects in R. The n-twist-spun trefo...
متن کامل1 The ideal trefoil knot
The most tight conformation of the trefoil knot found by the SONO algorithm is presented. Structure of the set of its self-contact points is analyzed.
متن کاملTopological Semimetals carrying Arbitrary Hopf Numbers: Hopf-Link, Solomon’s-Knot, Trefoil-Knot and Other Semimetals
We propose a new type of Hopf semimetals indexed by a pair of numbers (p, q), where the Hopf number is given by pq. The Fermi surface is given by the preimage of the Hopf map, which consists of loops nontrivially linked for a nonzero Hopf number. The Fermi surface forms a torus link, whose examples are the Hopf link indexed by (1, 1), the Solomon’s knot (2, 1), the double Hopf-link (2, 2) and t...
متن کاملMinimal Flat Knotted Ribbons
This paper gives mathematical models for flat knotted ribbons, and makes specific conjectures for the least length of ribbon (for a given width)) needed to tie the trefoil knot and the figure eight knot. The first conjecture states that (for width one) the least length of ribbon needed to tie an open-ended trefoil knot is
متن کامل