PS:But among v.3 nodes on the bottom edges of the vault, there are 2 different nodes that meet their members with different angles(so they should be different nodes). And of course among v.6 and v.4 nodes, there are many different nodes in terms of meeting angles.

For example, if the condition of the same node are…

Same Valence count

Same angle of the members to be connected

Then, similar node types are enlarged from 5 to 16.

Adding more conditions (such as the length of the members to be connected) may result in more numbers.
Anyway, in this case, I use Weaverbird’s Mesh From Lines and Mesh Topology Vertexin Sandbox.

As usual, that’s some very helpful stuff HS_Kim!
that’s really appreciated.

I understand what the first definition is doing, and although it doesn’t identify all the identical nodes, it actually helped me to spot an issue with the geometry (I shouldn’t have any v.2.

Sorry I should have better defined what I mean by identical.
As per your second post, the number of elements connecting to the node’s not the only requirement, there’s also the angle of the members connecting to the node (in 3d).

I am struggling to understand what part of your second definition is doing.
You are evaluating the angle between vectors from the node to the adjacent nodes (see first snapshot below) & the plane deconstructed Xdirection vector?
Is this similar to flattening the lines connecting at each node on a plan and evaluating the angles on that plane?
How can I take into account the 3dimensional features of each node?

See example on the last snapshot below.
Several nodes are identified as ‘type7’ but most of them are not identical (as per the definition above).

I’m also not sure how you are using the mass addition, to combine angles and lengths?

I’ve already mentioned and you probably noticed that it’s difficult to filter out all the differences when the conditions are simple. It would be better to consider some tolerances and add new conditions. (I knew the measured angles are 2d projections, so add vector deviations from the base plane this time and yields 27 different node-set)
I haven’t fully verified whether this is really the right way in this case. sorry. It will take some experimentation and validation to see which conditions would be better to add.