Thursday, April 23, 2026

Joining up link components to form knotted deltahedra

›
The tetrahedral graph is a Tait graph of a 3-component link. Many interesting deltahedra, foremost among them the triangle-faced Platonic ...
Friday, April 17, 2026

The stupendous abundance of unicursal polyhedral triangulations

›
Since the last post I have been using Gilles Schaeffer's C program planarmap to randomly sample larger polyhedral triangulations (3-v...
Thursday, April 2, 2026

Why are unicursal planar graphs so common?

›
The number of polyhedral triangulations of the sphere having n vertices, starting at n=3 , is given by OEIS A000109: 1, 1, 1, 2, 5, 14, 50,...
Tuesday, March 24, 2026

Stay in your lane: 1 in 3 spherical triangulations are z-knotted

›
In a triangulation of the sphere, a triangle strip can be seen as sort of topological geodesic, an attempt to travel as straight as possible...
Thursday, March 19, 2026

Weaving deltahedra without knotology

›
The 9-vertex z-knotted tetrahelix realized as a road code basket. This is the same deltahedron, Plantri 9-12, whose dual was illustrated in...
Friday, March 6, 2026

Some tetrahelixes are knotted (unicursal)

›
Any tetrahelix on 3+6n vertices is unicursal, 9 vertices in this example. Any tetrahelix on 5+6n vertices is unicursal, 11 vertices in thi...
Thursday, March 5, 2026

"House of n gables," the operation dual to "t3...n4"

›
The result of "house of n gables" operating on Johnson solid J20. Johnson solid J20 A view of dt3n(3,0.5,0.3)n(4,0.5,0.3)dJ20 ...