Two-sided Rounded Polyhexes with 3 or 4 Hexagons
The area of an hexagon is 3n(n-1)+1 = 1 mod 6. Therefore we can't cover an
hexagon with pieces of order 4 and I decided to use a combined set with pieces of
order 3 and 4. Then I constructed a hexagon of size 9 and with
the remaining pieces a triangle of size 3. Naturally I started with the triangle.
Two-sided Rounded Polyhexes with 2 up to 4 Hexagons
Adding pieces of order 2 even two hexagons are possible to make.
One-sided Rounded Polyhexes with 3 or 4 Hexagons
The 99 one-sided pieces of order 3 and 4 with an area of 386 = 217+169 allow for
two hexagons of size 8 and 9.
One-sided Rounded Polyhexes with 2 up to 4 Hexagons
If we add the pieces of order 2 the total area is 390, which is divisible by 6 without remainder.
Therefore figures with hexagonal symmetry but without a center piece can be constructed and I chose two
hexagonal rings. The second one is shown with the real pieces.