Icosidodecahedral Star

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

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

Classical form: f(z) = H(z)^3 / T(z)^2 (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

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	20 points: 20 of order 3
poles	30 points: 30 of order 2
degree	60
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 dodecahedron, side by side: E001 atlas sheet.
• Printability and the cut plane: P001 and P002.

Status: listed. Generated from the catalog entry icosidodecahedral-star.