Wednesday, November 16, 2022
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geometry – Seven octahedral nets to cowl an octahedron

After fixing Cover a single dice with FIVE similar dice nets I had the concept for this puzzle, which can be considered a pure generalisation to triangular grids.

Find two totally different nets, A and B, of an everyday octahedron such that these two collections of nets can every be folded into the floor of a single common octahedron with seven instances the floor space of the unique 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 should be fashioned by chopping alongside the unique octahedron’s edges (so they’re octiamonds). All small nets are of the identical measurement.
  • The nets are one-sided. Suppose one facet of every web is painted, then all copies of A should be similar with out flipping when the painted facet is up, and equally for B. The giant octahedra fashioned by each web collections should present solely painted faces.
  • The giant octahedra should present no gaps or overlaps in them.

As a touch, A and B differ by just one triangle.



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