Many words derived from Latin have two (and occasionally three or more) possible plural forms. The distinction is usually between popular usage based on English plural endings grafted onto Latin terms and scientific or technical form based on a traditional reading of the original language. Here are discussions of alternatives for plural forms of six types of word endings.
-as or -ae
Antennas are devices for carrying radio signals; antennae are sensory organs attached to the heads of certain creatures. Formulas might be used in a comparison of beverage mixtures for infants (and for other popular usage and even business contexts), while formulae is the formal term for mathematical or scientific expressions.
-eaus or -eaux
French words borrowed into English that end in -eau usually take the English plural form -s. The form ending in -x is likely to be seen as pedantic unless it is clearly used in a mocking sense (as when a writer facetiously sympathizes with a billionaire who has felt compelled to sell one of several chateaux.)
-exes/-ixes or -ices
Words ending in -ex or -ix (appendix, index, matrix, vertex) are generally followed by the plural form -es in all but the most technical contexts, though in scholarly publishing, appendices is the norm to refer to two or more pieces of additional text following the main section of a book.
-mas or -mata
Few words derived from Greek that end in -ma are in general usage, at least in plural form. (Anathema, for example, is common in singular form but not in plural form.) Dogma and schema, however, take an -s plural ending in popular usage; -mata is the formal alternative.
-ums or -a
Words ending in -um sometimes take an -s as a plural ending in popular usage and -ia in scientific or technical contexts — consortium, criterion, forum, spectrum, and symposium come to mind — but several notable exceptions exist:
Mediums applies informally to multiple objects such as garments labeled as medium size, or to two or more spiritualists, while forms of communication are almost invariably referred to as media; that form is also prevalent in digital technology. (In relatively obscure scientific contexts, media is the singular form, and mediae is the plural form.)
Memoranda and millennia are the preferred plural forms even in popular usage. Phenomena is prevalent over phenomenons, but the latter form (or the truncation phenoms) might be used as slang to refer to more than one particularly talented person.
us- or -i
The singular form of octopus is used to refer collectively to specimens used as food. (“The main course was sautéed octopus.”) Octopuses is the most sensible plural form in general; octopi is incorrect because octopus is from Greek, not Latin, and -i is a Latin plural suffix, but the Greek form, octopodes, employing the Greek plural suffix -odes, is rare.
The same is true, generally, of the plural form of platypuses, though the singular form frequently does double duty. Cactus, however, is Latin (albeit botanical, rather than classical, Latin), not Greek. Cacti is the prevalent plural form, though cactus and cactuses are also common.
Other words ending in -us vary in their plural form: focus, fungus, and radius become, depending on formality, focuses, funguses, and radiuses or foci, fungi, and radii, while corpus and genus take an -era ending (corpera, genera) in scientific contexts. The only correct plural form for census and prospectus is the English plural ending -es (and campi is a rare plural form for campus), but alumnus becomes alumni; alumnuses is incorrect.