In the Greek Doric order the abacus is a plain square slab. In the Roman and Renaissance Doric orders it is crowned by a moulding. In the Archaic-Greek Ionic order, owing to the greater width of the capital, the abacus is rectangular in plan, and consists of a carved ovolo moulding. In later examples the abacus is square, except where there are angle volutes, when it is slightly curved over the same. In the Roman and Renaissance Ionic capital, the abacus is square with a fillet on the top of an ogee moulding, but is curved over angled volutes. In the Greek Corinthian order, the abacus is moulded, its sides are concave and its angles canted (except in one or two exceptional Greek capitals, where it is brought to a sharp angle); and the same shape is adopted in the Roman and Renaissance Corinthian and Composite capitals, in some cases with the ovolo moulding carved.
In Romanesque architecture the abacus is square with the lower edge splayed off and moulded or carved, and the same was retained in France during the medieval period; but in England, in Early English work, a circular deeply moulded abacus was introduced, which in the 14th and 15th centuries was transformed into an octagonal one.
Examples:
In Saxon work it is frequently simply chamfered, but sometimes grooved as in the crypt at Repton (fig. 1) and in the arcade of the refectory at Westminster. The abacus in Norman work is square where the columns are small; but on larger piers it is sometimes octagonal, as at Waltham Abbey. The square of the abacus is often sculptured, as at the White Tower and at Alton (fig. 2). In Early English work the abacus is generally circular, and in larger work a continuation of circles (fig. 4), sometimes octagonal, and occasionally square. The mouldings are generally rounds, which overhang deep hollows. The abacus in early French work is generally square, as at Chateau Blois (fig. 3)
The diminutive of abacus, abaciscus, is applied in architecture to the chequers or squares of a tessellated pavement.