stained glass triakis icosahedron
It was handmade from cut glass (score and snap), bound in copper foil (rather than lead came), and soldered with 60/40 (tin/lead) solder.The lighting is provided by strip of LED lights  it consumes little power, and could be supplied by a wall adapter or computer’s USB port.I find the shape to be both aesthetically and mathematically pleasing.
First make a a lot of uniform isosceles triangles (at least 60, probably more if any turn out badly). I made mine about 2.5 inches tall and 1.5 inches wide (a very poorman's golden ratio).On the Making
 Bind all their edges in copper foil tape, solder the borders
 Solder them all together so internal dihedral angles are all exactly 138.189685°
 I made a little jig out of coat hangers and hot glue to help get the angles right.
 Before closing it up, shove an LED light strip in there.

On the Triakis Icosahedron
The shape can be seen as a platonic icosahedron with triangular pyramids augmented to each face.Icosahedron:
An icosahedron is a polyhedron with 20 faces, 30 edges and 12 vertices. There are many kinds of icosahedra, with some being more symmetrical than others.The best known (and the one this star builds from) is the Platonic, convex regular icosahedron, which has five equilateral triangular faces meeting at each vertex.Triakis:
Adding a triangular pyramid to each face of a polyhedron, making a particular Kleetope.Platonic:
In threedimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size) regular (all angles equal and all sides equal) polygonal faces with the same number of faces meeting at each vertex. Five solids meet those criteria:
Four faces

Six faces

Eight faces

Twelve faces

Twenty faces

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