Rotating a relatively simple shape by 120 degrees adds a node to the path. The shape is a kind of like the letter V. The original has six nodes but when rotated 120 degrees another node gets added resulting in seven nodes. Rotating by 90 or 135 does not add a new node. This problem occurred by selecting the shape, clicking on it again which shows the rotation arrows. Mouse down on a corner rotation arrow and move the mouse to rotate the object, release the mouse button when 120 degree and a node will be added. This happens both when the constrained rotate, that is when the ctrl key is held down, and in the normal non-constrained rotate. In the non-constrained rotate the rotation does not have to be exactly 120 degrees.
The extra node was causing me confusion because the new node is in the same position as another node so it is not easily visible.
Attached is a file showing the original shape and rotated duplicates.