The standard Burr is made of six pieces, each 2 by 2 by 6. A planar Burr is made of six pieces, each 1 by 4 by 6. Why not make a Burr from six pieces, each 2 by 3 by 4? An example, non-trivial, is shown below.
start with red and black
add yellow
add blue (opposite yellow)
add white (opposite black)
adding green completes the puzzle