Dodecahedron–Icosahedron Dual¶
One of the original Klein-invariant ornaments (the baseline, R0).
Recipe R2 on the icosahedron (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) = V(z)^5 / H(z)^3 (icosahedral forms).
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 | 12 points: 12 of order 5 |
| poles | 20 points: 20 of order 3 |
| degree | 60 |
| printed | yes |
| cut | two identical halves: print the half file twice |
| print files | coming to 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 icosahedron, side by side: E001 atlas sheet.
- Printability and the cut plane: P001 and P002.
Status: printed. Generated from the catalog entry dodecahedron-icosahedron-dual.