Naked curves despite being snapped

Im new to Rhino and would be grateful for some help.

I built the attached file, being careful to snap everything together. But I still have naked edges, even though it appears they are touching. What am I missing here?

Please help, and thanks so much!

MatthewHelpMe.3dm (4.4 MB)

you have overlapping or near coincident surfaces

and also some gaps between polysurfaces

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Thanks so much for your response Diego!

I thought at some point in combing overlapping surfaces, the program would understand one or more were redundant. Would the solution be to explode those areas and deleting one of the two overlapping surfaces?

As for the pyramid shapes, I created one side and then copy pasted the others, osnapping to the tippy top for each as I rotated them. I assumed this would mean they were seamless. Any thoughts on why that small gap remains?

Truly grateful for the response!