The Hypercube Paradigm

Hello!

I’m having sort of a hard time trying to think this through.

TL;DR i need to build a tree with multiple tags each tree

I need to make a catalog for a client’s website, the context being:

They have several product types:
-Type1 -Type2 -Type3

And each product have their attributes:
-Type1 -Type2 –Type3
–Size –Color –Width
–Color –Weight –Dimensions
–Shape –Size –Color

The products within each type COULD or COULD NOT share some of the attributes

I need to build a tree structure that can hold different tags each one and be able to cross search across them.

Know of a plugin and/or template that could help me do this?

Thanks in advance!