Ionic Order

Ionic order is one of various systems of architecture, in which the order is specific. In this structure above, the order is:
cornice-A horizontal molded projection crowning a building or structure
frieze-A broad horizontal band of sculpted or painted decoration
architrave-A main beam resting across the tops of columns
capital-The distinct, typically broader section at the head of a pillar or column
shaft-The body of a column; the cylindrical pillar between the capital and base 
and finally, base- the bottom, or foundation, of a structure- upholding structural elements like columns or pillars

Doric, Ionic, and Corinthian are the three orders of classic Greek architecture.
Ionic order was first used in mid-16th century BC in Ionia, the SW group of islands inhabited by Ionian Greeks. Here are some examples of buildings with ionic order:
Erectheion
Library at Ephesus
Roman Colosseum
Temple of Apollo
Temple of Artemis
Temple of Athena Nike
Roman Forum.
A complete list is available:
http://www.greatbuildings.com/types/styles/ionic.html