The player is faced with an array of numbered dots and connects them with segments.

How to play

• Draw lines between points to create triangles.
• Connect vertices to create triangles and assemble an image.
• The number on a vertex shows its remaining connections.
• Triangles will fill in if they are correct.
• Double tap a vertex to clear its connections.

I should add that the finished puzzle is a connected network of triangles and every segment is part of a triangle.

Question: is a solvable Vertex puzzle guaranteed to have a unique solution?

I tried a few Vertex puzzles on the NYT site.  None of them had triangles only connected by corners.   I didn't think of this, but as far as I'm concerned, it counts.