The Trapentrix with even deeper cuts, a doctrinaire puzzle with two threefold turns.

• Inventor: Ian Henriksen
• Mechanism: Doctrinaire puzzle with limited axis system
• Patents: Unknown
• Producer: Customly 3D printed
• Year: 2023
• Original Price: $0.00 USD
• Current Price: No Data

The Photonic Crystal is what happens if you take the cuts for the Trapentrix (see the seperate entry) and make them a bit deeper. All the piece types from the trapentrix are present as well as two new additional ones that form the small stars all around the puzzle.

An alternative way to view this puzzle is as the idea of Evgeniy's bingo cube (where you're only allowed to turn adjacent to a specific edge) applied to a radiolarian 9 or 10. The trapentrix is the result of applying this idea to a radiolarian 11 or later. The deeper cuts correspond to a shallower "enabler edge" version. Equivalents for earlier puzzles in the radiolarian series are also possible, but the "enabler edge" idea doesn't apply quite as cleanly to those versions.

The name "photonic crystal" was inspired by the fact that it's a relative of both the trapentrix and the radio crystal (radiolarian 9). The inventor thought: it's a crystal and also a trap... what can be trapped in crystals? Maybe light? Specifically this works with photonic crystals—an ongoing research area in physics.

This was part of the Puzzle Advent Calendar 2023.

It's a bit unclear what to call the "diameter" here. The large center pieces cut closer to the center of the puzzle, but it seems wrong to use those for the measurement since a lot of the pieces are further out. The radius from the face in the middle of each grip to the center point of the puzzle is 60mm.
Diameter: 120 mm
Weight: 645 grams

The puzzle has 28470899486765297936972434636800000000000000000=28.5*10^45 permutations if all pieces are considered distinguishable and their orientations visible.
Compared with the number available if the puzzle can be disassembled and reassembled there are these restrictions:
-The rhombi allow only even permutations.
-The large pentagons allow only even permutations.
-The first three large pentagons determine the orientation of the fourth.
-The large triangles (which fall into two subsets) are restricted by a factor of 172800.
-The small triangles fall into two subsets.
-The small triangles allow only even permutations for both subsets.
-The small pentagons are restricted by a factor of 1200.
-The orientation of the second face (aka unmovable triangle) determines the permutations of the last three triangles and last three pentagons. (Factor=9)
Stickered as shown here the puzzle has 19771457976920345789564190720000000=19.8*10^33 permutations.

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