The Ternary Burr belongs to a group of puzzles that are known as "N-ary" puzzles. A very informative write-up with loads of photos about "N-ary" puzzles by Goetz Schwandtner can be found here.
Designed by well-known Singaporean puzzle designer Goh Pit Khiam, there are only 68 copies of the Ternary Burr that have been so far made and sold commercially; 30 copies from Brian Young in 2009 and 38 from Eric Fuller. Hence the rather expensive (but value for money) price of US$274.
The Ternary Burr has a "base-3" mechanism with inherent dead ends. What is this "base-3" mechanism? Here's what Goh had to say:-
In an n-ary puzzle, each stage can have n positions. In the Ternary burr, each stage consists of only one piece which can be in one of three different positions. If there are two stages, there would be 3 x 3 different positions of both pieces. If there are m stages, then there are n^m different positions. The mechanism of the puzzle tries to make the puzzle go through all these positions, thus creating plenty of moves before disassembly. In the Ternary burr mechanism, it doesn't really go through every possible combination of piece positions. Some of them are dead-ends. In the later designs like the NumLock, it really does go through every piece positions before dis-assembly occurs.
The Ternary Burr from Eric is made from Cherry and Walnut. It consists of a total of 22 pieces including a 17-piece cage which can be dismantled fully. The cage houses 5 Walnut interlocking burr pieces which have to be shifted in a particular sequence requiring a total of 75 moves to remove the first piece. A total of 98 moves is needed to fully take apart the entire burr. And there is only one solution!
Construction fit and finish is excellent and the pieces all move smoothly after some dry-box de-humidification.Given its size, the Ternary Burr is very heavy and solid and quite a large handful to hold for average size hands.
Needless to say, a burr at this level is well beyond me. I tried to figure out the N-ary sequence but this proved way to difficult and confusing, resulting in me getting stuck a number of times mid-way. A very good memory would certainly help, since there are repeating moves.
Even with the aid of Burr Tools which I needed, it took a fairly long time for me to get through the entire sequence and extract the first piece. And then to disassemble the remaining 17 pieces of the cage. Putting back the whole thing together took me even longer as I grappled with the 22 pieces, first forming the rectangular cage and then going though the reverse N-ary moves to insert the 5 burr pieces back into the cage. For a really amazing feat of the Ternary Burr's re-assembly (without any aids), check out Brian Young's video on YouTube. Incredible!
The Ternary Burr is no doubt for hardcore burrists. Yes, today there are some higher level burrs around but none made in the fashion of the Ternary Burr, with most of its pieces dissimilar, as you can see from the photo. Unfortunately its not commercially available and the only way to get one is through private sale or auction. Given that they are also very difficult to make (Eric said "crafting this design took all (his) abilities"), we are unlikely to see any new copies on the market anytime soon.