What do you call a triangle with three equal sides?

Equilateral, and equal sides force equal angles, so all three are 60 degrees. That rigidity is why triangles are everywhere in structures: a four-sided frame can be pushed into a parallelogram without changing the length of anything, while a triangle cannot deform at all unless a member actually stretches or breaks. Bridges, roof trusses and scaffolding are triangles for that reason alone.

It is the first proposition of Euclid's Elements - given a line, construct an equilateral triangle on it - and it is the opening move of the most successful textbook ever written, in use for more than two thousand years.

Its most famous appearance is a shape that cannot exist. The Penrose triangle, drawn by Oscar Reutersvard in 1934 and popularised by Roger Penrose in the 1950s, looks like a solid equilateral object and could not be built in three dimensions - each corner is locally consistent and the whole is impossible. Escher built several of his best-known prints on it.