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| ![Symmetric lattice trefoil knot][1] **Symmetric Minimality** After I posted [_Minimal_][5] on [Mathstodon][2], [David Eppstein asked about][3] and then [found][4] a minimal lattice trefoil with 3-hedral symmetry. Here are the... |
| ![Rotating minimal lattice trefoil knot][1] **Minimal** This shows the trefoil knot lying on the simple cubic lattice with the fewest possible number of edges (it's [a theorem of Yuanan Diao][2] that the lattice stick number of the trefoil is... |
| These are very cool! Thanks! |
| Hi Karram, All my animations are covered by a Creative Commons [Attribution-NonCommercial-NoDerivatives license][1], which basically says you can use them for non-commercial purposes as long as you credit me. Best, Clay [1]:... |
| ![Histogram of Dirichlet-distributed barycentric coordinates on the square][1] **Dropped Call** The Dirichlet distributions are a family of distributions on the $n$-simplex $x_1 + \dots + x_{n+1} = 1$. For example, the Dirichlet$(1,\dots , 1)$... |
| ![Stereographic projection of optimal packing of 124 circles on the sphere][1] **Fitting In** For various reasons I've spent some time recently playing around with [Neil Sloane's tables of putatively optimal packings of points on spheres and... |
| ![Chladni figures for a square drum][1] **Dance** Speaking of [vibration modes of a square drum][2], here are the Chladni figures for linear combinations of the $(20,21)$ and $(21,20)$ vibration modes of the square. This is entirely in the... |
| ![Circles rolling inside a circle][1] This one is pretty simple: take two circles of radius 1/2 rolling inside a unit circle and track a point on each circle's perimeter. The points turn out to follow straight lines, and the challenge is to make... |
| ![Projected rotating 16-cell][1] **Double Projection** This is a similar idea to [_J34_][3]: starting with the vertices of the 16-cell (a.k.a. cross polytope, a.k.a. orthoplex) and thinking of them as points on the 3-sphere, I'm applying a... |