Variants to a product

I need a product listing where there are multiple color variants. We are a yarn shop. Within one product like an organic cotton yarn, we carry 18 different colors. In another yarn we stock 38 different colors of one yarn weight. I had hoped one could create a product page, and then click through to variant thumbnails with inventory within that variant.  Most of what I see on variants has color as one option, and then different fields like size. I don't see a way to create a product and then show the "same" variant across one product. It's going to matter to someone making a garment that they can pick the color in the weight of yarn they need.