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Polyhedra

Started: 2017-12-03 16:25:13

Submitted: 2017-12-03 18:20:12

Visibility: World-readable

In which the intrepid narrator reverse-engineers an elaborate Lego polyhedra to serve as a Christmas tree topper

My relationship with Christmas decorations is best described as ambivalent. I don't feel compelled to decorate for the holiday. Kiesa, however, has several boxes in storage dedicated to Christmas decorations. She pulled out the decorations as soon as we got back from Thanksgiving, complete with a modestly-sized artificial Christmas tree.

Three years ago, Kiesa built a Lego snowman to sit on top of our Christmas tree. This year, she wanted some sort of Lego-based star to sit on top of the Christmas tree. She had some trouble finding what she was looking for online because a Google search for "Lego star" would find results for Star Wars and Star Trek. She eventually found a flickr feed using a promising-looking star as the feed's avatar. I squinted at the avatar, and tried to figure out if I could discern enough detail to get something I could work with out of the avatar, and lucked out when I found a complete picture of the star, titled Rhombic Hexecontahedron. (Go look at the entire feed, which is quite impressive. The artist's designs were used in The Lego Movie as background decoration, hanging from the ceiling in the live-action basement set.)

I studied the picture until I recognized enough of the pieces to try to build it myself. We pulled out Calvin's Legos, spread them out on the floor of the living room, and I set to work. Each edge uses a Hinge Plate 1 x 4 Swivel to form the arbitrary corner angles, and a Plate, Modified 1 x 2 with Handle on Side to connect to a Plate, Modified 1 x 2 with Clips Horizontal. I had enough pieces to build a partial mock-up of each corner to prove to myself that I knew how to build it.

My next challenge was ordering the pieces I needed, in the colors I wanted. I gave Kiesa the choice of any (Lego) color she wanted and she thought the original colors would be fine. I counted 60 faces in the completed design, with four edges each, so I needed 240 of most pieces. I added 10% to my order to make sure I had some extra to work with. I searched for the pieces on Bricklink and eventually found what I needed from three vendors (combined with the pieces for an ornament Kiesa wanted Calvin to make as Christmas gifts).

I ordered the pieces before Thanksgiving, and they arrived at my office on the first day after Thanksgiving. I stayed home sick on Monday (recovering from a nasty cold I picked up over Thanksgiving), and picked up the pieces on Tuesday. I sat down with Calvin after supper to put the polyhedra together.

Calvin assembles a Lego polyhedra
Calvin assembles a Lego polyhedra

I started by assembling groups of three faces into the acute pointed edge sections, then assembling them in groups of five.

Lego polyhedra section
Lego polyhedra section

By the time I had most of the polyhedra assembled, I was starting to run out of pieces.

Mostly-assembled Lego polyhedra
Mostly-assembled Lego polyhedra

I eventually concluded that I had received fewer pieces than I had ordered (possibly because the sellers did not exhaustively count the 264 individual pieces I ordered, and rather packed based on weight), but the 10% extra I ordered gave me just enough pieces to finish the construction.

Calvin holds the assembled Lego polyhedra
Calvin holds the assembled Lego polyhedra

I let Kiesa put the completed polyhedra on top of the Christmas tree. It fits perfectly, though it appears that it's a bit more yellow than the rest of our tree decorations

Lego polyhedra on the Christmas tree
Lego polyhedra on the Christmas tree
... if Mr. Greenspan should happen to die, I would do like they did
in the movie Weekend at Bernie's. I'd prop him up and put a pair of
dark glasses on him.
- John McCain, presidential candidate