After having spent time doing analysis of the Barcode Burr geometry inspiration, I came up with this design for a puzzle piece shape which was based on my idea of having the core octahedral blocks each having an arm extending around to the other side of the core cluster in order to hold the cluster in position. These arms replaced the need for the hexagonal gluing jig base and cap components that were keeping things together in that previous inspiration.

Overall, I was extremely pleased to have come up with what seemed to me at the time (and in the 20 years since, has proven to be true) a totally new and exciting form of interlocking geometry which not only has the novel property that each piece is freely able to move along a diagonal axis of the underlying cubic structure, but also that each piece is that same shape and that the structure itself holds together and maintains its properties even when multiple pieces have been removed! Big celebration time!

Although those traits I just mentioned are very special, the overall appearance of the assembled structure left something to be desired from an aesthetic standpoint, so I spent some time with scrap blocks of geometry and masking tape, experimenting with how I could augment/truncate this piece shape into something that had a more appealing external shape once assembled; this led up to the Barcode Burr piece geometry prototype.