The number of chromosomes in one of the mutually-homologous sets is called the monoploid number (x). This is the same number for every set in every cell of a given organism.
Euploidy is the state of a cell or organism having an integral multiple of the monoploid number, possibly excluding the sex-determining chromosomes. For example, a human cell has 46 chromosomes, which is an integer multiple of the monoploid number, 23. A human with abnormal, but integral, multiples of this full set (e.g. 69 chromosomes) would also be considered as euploid. Aneuploidy is the state of not having euploidy. In humans, examples include having a single extra chromosome (such as Down syndrome), or missing a chromosome (such as Turner syndrome). Aneuploidy is not normally considered -ploidy but -somy, such as trisomy or monosomy.
In humans, the monoploid number (x) equals the haploid number (the number in a gamete, n), that is, x = n = 23. In some species (especially plants), these numbers differ. Commercial common wheat is an allopolyploid with six sets of chromosomes, two sets coming originally from each of three different species, with six copies of chromosomes in each cell. The gametes of common wheat are considered as haploid since they contain half the genetic information of somatic cells, but are not monoploid as they still contain three complete sets of chromosomes from the original three different species (n = 3x).
Most fungi and a few algae are monoploid organisms, and male bees, wasps, and ants are haploid because of the way they develop from unfertilized, haploid eggs. The Australian bulldog ant, Myrmecia pilosula, a haplodiploid species has n = 1, the lowest known (and lowest theoretically possible) n. A monoploid cell is likely to be identical to the cell it was copied from however in haploid cells one of two differing copies of the same chromosome is in the haploid set.
Plants and some algae switch between a haploid and a diploid or polyploid state, with one of the stages emphasized over the other. This is called alternation of generations. Most diploid organisms produce monoploid sex cells that can combine to form a diploid zygote, for example animals are primarily diploid but produce monoploid gametes. During meiosis, germ cell precursors have their number of chromosomes halved by randomly "choosing" one homologue, resulting in haploid germ cells (sperm and ovum).
A laboratory procedure called haploidisation forces a normal cell to expel half of its chromosomal complement. In mammals this renders this cell chromosomally equal to sperm or egg. This was one of the procedures used by Japanese researchers to produce Kaguya, a fatherless mouse.
Haploidisation sometimes occurs in plants when meiotically reduced cells (usually egg cells) develop by parthenogenesis.
Polyploidy is the state where all cells have multiple pairs of chromosomes beyond the basic set. These may be from the same species or from closely related species. In the latter case these are known as allopolyploids, amphidiploids or allotetraploids. Allopolyploids can be formed from the hybridisation of two separate species followed by their subsequent chromosome doubling. A good example is the so-called Brassica triangle where three different parent species have hybridized in each pair combination to form three different allopolyploid species. Polyploid plants are probably most often formed from the pairing of meiotically unreduced gametes (Ramsey and Schemske, 2002).
Polyploidy occurs commonly in plants, but rarely in animals. Even in diploid organisms many somatic cells are polyploid due to a process called endoreduplication where duplication of the genome occurs without mitosis (cell division).
The extreme in polyploidy occurs in the fern-ally genus Ophioglossum, the adder's-tongues, in which polyploidy results in chromosome counts in the hundreds, or in at least one case, well over one thousand. Interestingly, these plants seem to have simplified structures in their phenotype.
Dihaploids (which are diploid) are important for selective breeding of tetraploid crop plants (notably potatoes), because selection is faster with diploids than with tetraploids. Tetraploids can be reconstituted from the diploids, for example by somatic fusion.
The term “dihaploid” was coined by Bender (1963) to combine in one word the number of genome copies (diploid) and their origin (haploid). The term is well established in this original sense (e.g., Nogler 1984; Pehu 1996), but it has also been used for doubled monoploids or doubled haploids, which are homozygous and used for genetic research (Sprague et al, 1960).