portapiatti s.m.inv.
1 (scolapiatti) plate-rack, dish-rack, dish drainer.
2 (vassoio) tray, plate tray. [Sansoni]

Infatti dal dizionario monolingua (Oxford) risulta che:
tray 1 a flat piece of wood, metal or plastic with raised edges, used for carrying or holding things, especially food:
Ex. He brought her breakfast in bed on a tray.
She came in with a tray of drinks.
a tea tray
2 (often in compounds) a shallow plastic box, used for various purposes:
Ex. a seed tray (= for planting seeds in)
a cat’s litter tray

rack 1(often in compounds) a piece of equipment, usually made of metal or wooden bars, that is used for holding things or for hanging things on:
Ex. a vegetable / wine / plate / toast rack
I looked through a rack of clothes at the back of the shop.




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Note added at 1 ora (2008-05-11 16:43:00 GMT)
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su Google immagini ho trovato:

a triple-triered tray
http://images.google.it/images?um=1&hl=it&q=triple-triered t...

a three layer rack
http://images.google.it/images?um=1&hl=it&q=a three layer ra...

a tiered plate rack
http://images.google.it/images?um=1&hl=it&q=a tiered plate r...