Counting Stacked Polyhexes
Since each solid hexagon has 8 faces the number of stacked hexagons is rising faster then the number of polycubes.
You can check the number of stacked tetrahexes by hand, but it seems to be difficult to count pieces with more hexagons
without a computer. My rather static program written in the last century produced the following numbers. In 2001
Brendan Owen counted 60020 stacked polyhexes with 8 hexagons.
||5 ||6 ||7|
|Number of Stacked Polyhexes
|Number of Flat Polyhexes
|Number of Polycubes