Thank you ian. It's genuinely interesting though I do fear you may be slipping into developer speak. (what sort of developer is another question)
Well, we are diploid, which means we have two sets of chromosomes (and we make haploid cells, in the down-belows). There are human tissues that can have more than two sets of chromosomes (so are polyploid) but they're somatic exceptions. Most animals are diploid, though a lot of a fish and amphibians are tetraploid. Mutations that affect meiosis often lead to polyploidy, in most cases it leads to infertility or is fatal to any zygote.
Plants are a bit more flexible, more so when we breed them – wheat, for instance, is effectively three different organisms crammed into the same package, hence hexaploid (three diploids).
To put things back on track, most commercial potatoes (like the kind you find in tins) are tetraploid (but not diploidized, oh no, so have four alleles at each gene locus, frankly a bit greedy but there you go, anything for a crisp sandwich), but potato is quite a good species in which to stupid polyploidy in as they're quite variable in the wild.
Once upon a time botanist and molecular geneticist – I am available for stimulating after-dinner speaking engagements, and ladies (and gents), alas, I'm spoken for.