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Rhombicuboctahedron (R4, vertex–edge)

A Phase 1 recipe applied beyond the Platonic solids.

Recipe R4ve on the rhombicuboctahedron (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.

Note

The alternative recipe on the same symmetry: degree 48.

Zeros and poles

The rhombicuboctahedron with the zeros (blue) and poles (red) of its function

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 portrait of f in the plane

Phase on the Riemann sphere

Phase on the Riemann sphere

The printed shape, colored by phase

The printed shape, colored by phase

The printed shape

The printed shape

The function and the print

zeros 24 points: 24 of order 2
poles 48 points: 48 of order 1
degree 48
printed not yet
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

Status: exported. Generated from the catalog entry r4ve-rhombicuboctahedron.