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 ...
Wednesday, March 4, 2026

A polyhedron operation that preserves unicursality for general face spectra

›
In polyHédronisme, this is t3 n(10,0.5,0.3) n(5,0.5,0.3) n(3,0.5,0.3) n(4,0.5,0.3) J20 . It is unicursal just like its base polyhedron, John...
Tuesday, March 3, 2026

Why teafork works

›
The graphical Reidemeister moves (from Jiang, Jin and Deng, "Determining the component number of links corresponding to triangular and ...
Monday, March 2, 2026

Teafork: a polyhedron operation that preserves cursality on {3, 4}-face regular polyhedra

›
The teafork operation (t4k) applied to Johnson solid J8 Expressed in polyHédronisme algebra, the polyhedron-building operation t4k (teafor...