After solving Cover a single cube with FIVE identical cube nets I had the idea for this puzzle, which may be regarded as a natural generalisation to triangular grids.
Find two different nets, A and B, of a regular octahedron such that these two collections of nets can each be folded into the surface of a single regular octahedron with seven times the surface area of the original octahedron:
- 3 copies of A and 4 of B
- 6 copies of A and 1 of B
Restrictions from the five-cubes-to-cube puzzle apply analogously:
- A and B must be formed by cutting along the original octahedron's edges (so they are octiamonds). All small nets are of the same size.
- The nets are one-sided. Suppose one side of each net is painted, then all copies of A must be identical without flipping when the painted side is up, and similarly for B. The large octahedra formed by both net collections must show only painted faces.
- The large octahedra must have no gaps or overlaps in them.
As a hint, A and B differ by only one triangle.
A and B are also totally asymmetric (not rotation/reflection-symmetric).
If one triangle is removed from net A the remaining heptiamond has the symmetries of a triskelion. Net B can be decomposed into two Pac-Man-shaped tetriamonds.