Quantity   Component name
12 × LEDs Two per edge segment
1 × Microcontroller ATtiny45 for tetraheron, probably ATtiny4313 for larger polyhedra
1 × IC socket Optional, to protect the Microcontroller while soldering
1 × Wires to suspend the microcontroller in the center
1 × (Base) Optionally use my parametric 3D-printable base