Tetrahedral Dual¶
One of the original Klein-invariant ornaments (the baseline, R0).
Recipe R2 on the tetrahedron (how the recipes work): zeros at the vertex directions, each of order equal to the vertex's valence; poles at the polar face directions, each of order equal to the face's number of sides.
Classical form: f(z) = Φ(z) / Ψ(z).
Note
Not chiral (six mirror planes); the phase rotates by cube roots of unity under three-fold rotations.
Zeros and poles¶
zeros (pits) poles (spikes). Markers grow with order. Drag to rotate, scroll or pinch to zoom, hover or tap a marker for details.
Views¶
The function and the print¶
| zeros | 4 points: 4 of order 1 |
| poles | 4 points: 4 of order 1 |
| degree | 4 |
| printed | yes |
| cut | two identical halves: print the half file twice |
| print files | on Printables: whole, cut halves, and a hanging-ornament version; 80 and 130 mm |
Where it comes from¶
- How the recipes work and how the constant is fixed: The recipes.
- Every recipe on the tetrahedron, side by side: E001 atlas sheet.
- Printability and the cut plane: P001 and P002.
Status: listed. Generated from the catalog entry tetrahedral-dual.