How to join surfaces together for converting to T-Splines

I want to join the attached 5 pieces together and then convert to T-spline surface / mesh.
I tried “join” directly to an open polysurface. However, It couldn’t be converted to T-splines.
Any other method?How to join.3dm (84.3 KB)

Try converting the sides separately then join together by merging or bridging edges or faces.

I used Mergesrf to create 3 sides successfully, but the other 2 sides could not be connected.
One more thing, the object type of the attached merged surface was open surface. I converted it to T-splines and then converted it back to Rhino object. It changed to open polysurface. What is the difference between open surface & open polysurface?
PS: Open polysurface cannot be converted to T-Splines again, nor using boolean union!First step.3dm (90.9 KB)

Buid the 5 separate surfaces, convert all of them to t-splines and then use TSMerge to weld the edges. Smooth=no if the options is there, I didn’t pay attention.

First step_answer.3dm (114.2 KB)