tacnode

noun

1. A point of a curve where two or more osculating circles to the curve at that point are tangent, so that two branches of the curve have ordinary tangency at the double point.

   “A tacnode is defined to be a singularity equivalent to the origin in the curve y²-x²#61;0, that is, the union of two smooth arcs meeting with contact of order two. Similarly, an oscnode is a singularity equivalent to y²-x⁶#61;0, i.e., consisting of two smooth branched with contact of order three, and so on.”