Octahedral Crown

One of the original Klein-invariant ornaments (the baseline, R0).

Recipe R4ve (reciprocal) on the octahedron (how the recipes work): zeros at the edge points (feet of the perpendiculars from the centre), each of order 2; poles at the vertex directions, each of order equal to the vertex's valence.

Classical form: f(z) = E(z) / V(z)^2.

Note

Completes the baseline set.

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

Phase portrait of f in the plane

Phase on the Riemann sphere

The printed shape, colored by phase

The printed shape

The function and the print

zeros	12 points: 12 of order 1
poles	6 points: 6 of order 2
degree	12
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 octahedron, side by side: E001 atlas sheet.
• Printability and the cut plane: P001 and P002.

Status: listed. Generated from the catalog entry octahedral-crown.