# Impossible Dovetails

Logic Level 5

The impossible dovetail is, originally a woodworking, puzzle. It is a cube consisting of two pieces connected to each other. On each of the four verticals sides, identical looking dovetail joints are visible, as shown in the image below. The earliest known reference was a picture in the May 1902 edition of Woodworker magazine.

How many different ways are there to achieve the impossible dovetail illusion?

By this I mean: how many different ways are there to achieve the illusion where two rigid solid pieces that can not flex or bend are connected to each other to form a completely solid cube (without voids inside), such that they show four identical dovetails, one on each vertical side, and can still be assembled and disassembled.

Note that solutions where the assembling and disassembling are just mirrored versions of each other (symmetrically identical), or that only differ in the direction of translation(s) and/or rotation(s) and/or size are considered the same.

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