three congruent equilateral triangles can be arranged in a nice symmetric pattern in two ways: the Zelda Triforce and (approximately) the radioactivity symbol (radiation hazard symbol). (alternative construction for the latter: dissect a regular hexagon into 6 congruent equilateral triangles. color the triangles two alternating colors.)
tell a story that someone has been doing it wrong. characters in the Zelda universe discover that assembling the Triforce the other way unlocks the devastating power of the atom. or, nuclear scientists discover the Triforce.
less symmetry (because chiral): vertex touches midpoint of edge.
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