Sunday, December 24, 2017

stained glass triakis icosahedron

It was hand-made 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.

On the Making

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 poor-man's golden ratio).
  1. Bind all their edges in copper foil tape, solder the borders
  2. Solder them all together so internal dihedral angles are all exactly 138.189685°
  3. I made a little jig out of coat hangers and hot glue to help get the angles right.
  4. Before closing it up, shove an LED light strip in there.

coat hanger jig calibrated to exactly 138.189685°

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 three-dimensional 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
Tetrahedron.svg
Hexahedron.svg

Octahedron.svg
Dodecahedron.svg
Icosahedron.svg

Video of lights in action


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