Today’s Rhymes With Orange:
A marmaxi is a giant martini — the word resulting from a playful reanalysis of martini as mar + tini (though the Martini of Martini e Rossi, the vermouth makers, is an Italian patronymic from the personal name Martino, i.e. Martin, so that historically martin is a unit). Compare the martini variants the appletini and the okratini, portmanteaus in which the -tini is contributed by martini.
In the cartoon, the -tini of martini has been associated with the adjective teeny; from OED2:
dial. and colloq.
An emphasized form of tiny adj. and n.; orig. in childish use.
[cites from 1825 on]
What’s the opposite of -tini ‘little’? Well, no obvious suffixal element comes to mind, but there is a well-attested prefixal element, the libfix maxi-. From Quinion’s affix site on maxi-:
Very large or long.
[English maximum, from Latin maximus, the superlative of magnus, great.]
This form was created on the model of mini- at the beginning of the 1960s. Some early terms related to clothing (maxi-coat, maxi-skirt, maxi-dress). Others are maxi-single, a record with two songs on each side instead of just one; maxi-CD, an audio CD of extended duration or number of tracks; maxi-yacht, in Australian usage, a yacht of about twenty metres length or more. Many terms are written without the hyphen (maxiskirt); maxi single is often seen written thus as two words; maxi alone is an abbreviated form of maximum, or sometimes of maxi-skirt.
So you get the peculiar sort of playful portmanteau marmaxi, with the mar- of martini plus -maxi (the opposite of -tini ‘little) from prefixal maxi-.
Two bonus discussions, on the drink name martini (or Martini), and on a reanalysis similar in some ways to the one in mar-tini, giving monokini as a counterpart to bikini (and trikini as well).
History of the Martini. From OED3 (Dec. 2000) under Martini n.2:
Etymology: As the name of a cocktail, perhaps < the name of Martinez, a city in western California, subsequently reinforced by and remodelled after the proprietary name, which is < the name of Martini and Rossi, Italian manufacturers of vermouth (application for U.S. trade mark incorporating the words Martini e Rossi filed March 16 1882, although earlier use is claimed, and the product is reported to have been exported earlier by the parent company of Martini and Sola).
The earliest examples of the name of the cocktail have the form Martinez, and a number of anecdotes associate the name of the cocktail with the name of the Californian city Martinez. For further details see: P. Tamony in Western Folklore (1967) 26 124.
a. More fully Martini cocktail. A cocktail containing (esp. dry) vermouth combined with gin or (less frequently) with vodka.
b. A proprietary name for: a type of vermouth, manufactured in varying degrees of sweetness.
dry Martini n. (a) a Martini cocktail consisting of more gin than vermouth, sometimes with the addition of orange bitters, etc.; (b) (a drink of) the dry variety of Martini.
[cites from 1884, for Martinez cocktail]
Note the OED‘s “perhaps” in the etymology, and the suggestion of multiple contributions to the name for the drink. Today’s Wikipedia entry (reproduced below, complete with its run-on sentence) is even more speculative:
The exact origin of the martini is unclear however the most likely explanation is that it was simply a shortening of the main ingredient, Martini branded vermouth. One popular alternative suggests it evolved from a cocktail called the Martinez served at the Occidental Hotel in San Francisco in 1862, which people frequented before taking an evening ferry to the nearby town of Martinez. Another theory links the origin of the martini to the name of a bartender who concocted the drink at the Knickerbocker Hotel in New York City in 1911.
(The earliest martinis seem to have been made with sweet vermouth, in what is sometimes known these days as a Martini gin — Martini for the sweet vermouth, gin for the principal ingredient.)
The monokini. The story starts immediately after World War II. From OED2 under bikini n.:
Etymology: < Bikini, the name of an atoll in the Marshall Islands where an atomic bomb test was carried out in July, 1946.
a. A large explosion. (? Obs.)
[1947 cite only]
b. [ < French, apparently < sense a.] A scanty two-piece beach garment worn by women.
[cite in French 1947; first English cite 1948]
Draft additions Jan. 2002:
In sing. and pl. Chiefly N. Amer. A pair of short, close-fitting men’s swimming trunks. [and in bikini briefs, which are (of course one-part) underpants; cites from 1957 on, including an entertaining one from Time Out in 1998 with nutsack bikinis referring to the swimming suit]
And then in OED3 (Dec. 2002) under monokini n. [from bikini, as if bikini were a formation in bi- ‘two’]:
French monokini and bikini were both apparently coined by Louis Réard and patented by him in 1946: see Femmes d’Aujourd’hui (1972) 12 July.
A one-piece beach garment or swimming costume worn usually by women and girls, esp. one equivalent to the lower part of a bikini.
[cites from 1964 on; also known as a unikini]
And then from OED2 under trikini n.:
Any of various designs of ladies’ swimsuit which consist of three main areas of fabric (as pants and a separate covering for each breast).
[cites from 1967, when Rudi Gernreich created the garment and coined the name, on]
Other innovations in -kini (see the Wikipedia page on bikini variants): microkini (super small), tankini (with tank top), pubikini (exposing pubic hair), veilkini (for modesty). The element -kini ‘(women’s) bathing suit’ seems to be on its way to becoming a libfix (and -tini ‘kind of martini’ might be as well).