While reading a paper (citation omitted to protect the "guilty"), I came across a reference to an "n-dimensional tetrahedron", meaning the subset of Rn given by
x1, ..., xn ≥ 0 and x1 w1 + ... xn wn ≤ τ
for positive constants w1,..., wn and τ.
Of course this is an n-simplex. But calling it a "tetrahedron" is etymologically incorrect -- that means "four faces", while an n-simplex has n+1 faces. This probably occurs because most of us tend to visualize in three dimensions, not in arbitrary high-dimensional spaces.
I'm not saying that "tetrahedron" shouldn't be used here -- I'm just pointing out an interesting linguistic phenomenon.