The objects

Each object is the modulus relief of one rational function on the Riemann sphere: poles are spikes, zeros are pits, and the color is the function's phase. The recipes that place them are explained under The question. Each object has its own page with its views, its function, how it is printed, and where to get the files.

Printed

Cube–Octahedron Dual R2 on the octahedron, degree 24

Dodecahedron–Icosahedron Dual R2 on the icosahedron, degree 60

Icosidodecahedral Star R4ve on the dodecahedron, degree 60

Icosahedral Crown R4ve (reciprocal) on the icosahedron, degree 60

Tetrahedral Dual R2 on the tetrahedron, degree 4

Octahedral Crown R4ve (reciprocal) on the octahedron, degree 12

Deltoidal Icositetrahedron (R2) R2 on the deltoidal icositetrahedron, degree 96

In the print queue

Rhombicuboctahedron (R4, vertex–edge) R4ve on the rhombicuboctahedron, degree 48

Triakis Tetrahedron (R2) R2 on the triakis tetrahedron, degree 12

Irregular Solid (R2) R2 on the irregular-mixed, degree 36

Irregular Solid, Separated (R2) R2 on the irregular-separated, degree 36

Digital only

Hexagonal Pyramid (R2) R2 on the hexagonal pyramid, degree 8