An allopolypoid is a species that is formed by the mating of two separate species. While this isn't a common occurrence in nature, it has been used in breeding experiments to create new organisms. When diploid organisms have the same number of chromosomes, and thus the same number of gametes, scientists have been able to successfully interbred them in laboratory and field experiments. Very often however, the offspring tend to be are sterile.
It's easy to see how this could be useful, particularly in regards to agriculture. By mating different plant species one might be able to create a new, more productive species. A new species that could enable farmers to increase their productivity and yield. In 1928 a Russian biologist by the name of Georgii Dmintrievich Karpechenko accomplished this goal by breeding a radish and a cabbage.
The product of this marriage is known as Raphanobrassica [a combination of radish (Raphanus) and cabbage (Brassica)]. Radishes and cabbages each have a diploid (2n) number of 18 chromosomes, and thus (n) 9 gametes. But, when these plants were mated it produced a sterile amphidiploid hybrid. Karpechenko's insight was to create a autopolyploid, that is a tetraploid (4n) with 36 chromosomes. This new species, nicknamed the Rabbage, was able to reproduce and produce fertile offspring.
There was however one downside, the rabbage consisted of the top half of the radish and the bottom half of the cabbage. Needless to say, there's a good reason why no one grows rabbages.