The Married Burr disassembled. Three is pieces A B C with C as the ready to slide piece. Six is pieces 1 - 6 with 1 as the ready to twist rounded piece. The twist pieces are triangular rounded with one edge aligned with the uncut corner of the piece. Naturally the puzzle works without rounding too. The actual copy in the story:
A perfect semi symmetrical solid slide version. A and 1 can be obscure rounded to make the working together version:
These pictured Married Burr solutions with or without rounding are copyright Erik Johansson.
When it comes to rectilinear burrs it is all about intersecting connections and how to slide out from a connection. It is the designer's choice to use twist or slide alone or both to open the burr.
Is it also possible to design other 9-piece burrs with internal voids to allow sequential moves to open? Or to have combined twist and slide pieces?
The solid symmetrical Eight-Square and Nine-Block burrs uses sequential twist moves to open. And the symmetrical shaped Five-Star and Seven-Star burrs uses combined twist and slide pieces.