Why spheres, why a tetrahedron.
Spheromino isn't decorated with maths — it is the maths. Here's the short tour of what your hands are actually solving.
Close packing — twelve neighbours
Stack oranges and each one settles against twelve others, not the six of a square grid. That is face-centred cubic (FCC) packing. Spheromino lives on this lattice: positions carry coordinates [x, y, z] in a 60° skew basis, and two balls touch exactly when the quadratic form
Q(Δ) = Δx² + Δy² + Δz² + ΔxΔy + ΔxΔz + ΔyΔz = 1.
That single rule decides which balls are neighbours, whether a segment is a valid connected shape, and how tightly two pieces interlock.
Triangular & tetrahedral numbers
A tetrahedron of edge 5 is built from five triangular layers of 1, 3, 6, 10, 15 balls. They sum to 35 — the 5th tetrahedral number. Segments are made of 1–5 balls, so an edge of exactly 5 is the smallest board where the whole family of pieces fits.
Rare by design — 435 in ~32,164
A set is a subset of the 21 segments whose sizes add to 35. Most subsets that add up can't actually tile the tetrahedron. Of roughly 32,164 size-valid combinations, at least 435 are known to truly pack — about 1.4% — and the solver keeps finding more. Finding a packable set is the hard, beautiful part.
Twelve orientations, one solution
The tetrahedron's rotation group (A₄) has 12 orientations. One solved object, shown from different angles and with different pieces hidden, becomes a whole family of puzzles — which is how a handful of sets yields thousands of tasks.
Why it's a good puzzle
Spatial reasoning, planning, and the satisfying click of a unique solution. Difficulty is honest: it grows with how many segments are hidden (4 → 7 = Beginner → Genius) and how many pieces cross at right angles. Every task ships with a colourblind-safe letter on each segment, so it's readable for everyone.