What an odd name. It sure sounds interesting, like some sort of exotic fruit tree. Alas; argyle apple is a eucalyptus; to be specific, Eucalyptus cinerea. Compared to most other eucalypti, it stays rather low. It barely gets as tall as a two story house, even if it gets broad enough to shade most of the backyard. The rusty brown bark becomes roughly furrowed. The irregular branch structure can be quite sculptural.
The main attraction of argyle apple is the aromatic silvery foliage. Young trees are outfitted with circular juvenile leaves that are attached directly to the stems without petioles (leaf stalks). Lanceolate adult leaves are as silvery as juvenile foliage is. (Juvenile foliage of most other eucalypti is more colorful than adult foliage is.) Aggressive pruning of small trees keeps foliage juvenile for a long time.
Actually, those who know how to work with it might pollard or coppice argyle apple. Pollarding eliminates all foliated stems at the end of winter, but for the rest of the year, allows vigorous arching canes of very silvery juvenile foliage to spread outward from a few stout limbs on top of a trunk. Coppicing allows the same sort of growth from stumps just above grade.