_Were Plato with us today, these would most certainly be on both his ideal and real Christmas trees!_
This ornament consists of a dodecahedron whose faces are held in place by a wireframe spherical icosahedron. The dodecahedron faces come in two variations, a star, and a slightly modified pentaflake (second iteration).
The concept of using an icosahedron as a support frame for a dodecahedron was inspired by the split polyhedra in Rinus Roelofs’s project "Dynamic Tilings" (original version: http://www.rinusroelofs.nl/projects/dyn-tilings/pr-dyn-tilings-00.html , archived version: https://web.archive.org/web/20210509140606/http://www.rinusroelofs.nl/projects/dyn-tilings/pr-dyn-tilings-00.html ).