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Torso of a Young Girl, onyx on a stone base by Constantin Brancusi, 1922; in the Philadelphia Museum of Art, Pennsylvania, U.S.Courtesy of Philadelphia Museum of Art, the A.E. Gallatin Collection

It is not possible to see the whole of a fully three-dimensional form at once. The observer can only see the whole of it if he turns it around or goes around it himself. For this reason it is sometimes mistakenly assumed that sculpture must be designed primarily to present a series of satisfactory projective views and that this multiplicity of views constitutes the main difference between sculpture and the pictorial arts, which present only one view of their subject. Such an attitude toward sculpture ignores the fact that it is possible to apprehend solid forms as volumes, to conceive an idea of them in the round from any one aspect. A great deal of sculpture is designed to be apprehended primarily as volume.

A single volume is the fundamental unit of three-dimensional solid form that can be conceived in the round. Some sculptures consist of only one volume, others are configurations of a number of volumes. The human figure is often treated by sculptors as a configuration of volumes, each of which corresponds to a major part of the body, such as the head, neck, thorax, and thigh.

Holes and cavities in sculpture, which are as carefully shaped as the solid forms and are of equal importance to the overall design, are sometimes referred to as negative volumes.

The surfaces of sculpture are in fact all that one actually sees. It is from their inflections that one makes inferences about the internal structure of the sculpture. A surface has, so to speak, two aspects: it contains and defines the internal structure of the masses of the sculpture, and it is the part of the sculpture that enters into relations with external space.

The expressive character of different kinds of surfaces is of the utmost importance in sculpture. Double-curved convex surfaces suggest fullness, containment, enclosure, the outward pressure of internal forces. In the aesthetics of Indian sculpture such surfaces have a special metaphysical significance. Representing the encroachment of space into the mass of the sculpture, concave surfaces suggest the action of external forces and are often indicative of collapse or erosion. Flat surfaces tend to convey a feeling of material hardness and rigidity; they are unbending or unyielding, unaffected by either internal or external pressures. Surfaces that are convex in one curvature and concave in the other can suggest the operation of internal pressures and at the same time a receptivity to the influence of external forces. They are associated with growth, with expansion into space.

Unlike the painter, who creates light effects within the work, the sculptor manipulates actual light on the work. The distribution of light and shade over the forms of his work depends upon the direction and intensity of light from external sources. Nevertheless, to some extent he can determine the kinds of effect this external light will have. If he knows where the work is to be sited, he can adapt it to the kind of light it is likely to receive. The brilliant overhead sunlight of Egypt and India demands a different treatment from the dim interior light of a northern medieval cathedral. Then again, it is possible to create effects of light and shade, or chiaroscuro, by cutting or modeling deep, shadow-catching hollows and prominent, highlighted ridges. Many late Gothic sculptors used light and shade as a powerful expressive feature of their work, aiming at a mysterious obscurity, with forms broken by shadow emerging from a dark background. Greek, Indian, and most Italian Renaissance sculptors shaped the forms of their work to receive light in a way that makes the whole work radiantly clear.

The colouring of sculpture may be either natural or applied. In the recent past, sculptors became more aware than ever before of the inherent beauty of sculptural materials. Under the slogan of “truth to materials” many of them worked their materials in ways that exploited their natural properties, including colour and texture. More recently, however, there has been a growing tendency to use bright artificial colouring as an important element in the design of sculpture.

In the ancient world and during the Middle Ages almost all sculpture was artificially coloured, usually in a bold and decorative rather than a naturalistic manner. The sculptured portal of a cathedral, for example, would be coloured and gilded with all the brilliance of a contemporary illuminated manuscript. Combinations of differently coloured materials, such as the ivory and gold of some Greek sculpture, were not unknown before the 17th century; but the early Baroque sculptor Gian Lorenzo Bernini greatly extended the practice by combining variously coloured marbles with white marble and gilt bronze. Principles of design

It is doubtful whether any principles of design are universal in the art of sculpture, for the principles that govern the organization of the elements of sculpture into expressive compositions differ from style to style. In fact, distinctions made among the major styles of sculpture are largely based on a recognition of differences in the principles of design that underlie them. Thus, the art historian Erwin Panofsky was attempting to define a difference of principle in the design of Romanesque and Gothic sculpture when he stated that the forms of Romanesque were conceived as projections from a plane outside themselves, while those of Gothic were conceived as being centred on an axis within themselves. The “principle of axiality” was considered by Panofsky to be “the essential principle of classical statuary,” which Gothic had rediscovered.

The principles of sculptural design govern the approaches of sculptors to such fundamental matters as orientation, proportion, scale, articulation, and balance.

For conceiving and describing the orientation of the forms of sculpture in relation to each other, to a spectator, and to their surroundings, some kind of spatial scheme of reference is required. This is provided by a system of axes and planes of reference.

An axis is an imaginary centre line through a symmetrical or near symmetrical volume or group of volumes that suggests the gravitational pivot of the mass. Thus, all the main components of the human body have axes of their own, while an upright figure has a single vertical axis running through its entire length. Volumes may rotate or tilt on their axes.

Planes of reference are imaginary planes to which the movements, positions, and directions of volumes, axes, and surfaces may be referred. The principal planes of reference are the frontal, the horizontal, and the two profile planes.

The principles that govern the characteristic poses and spatial compositions of upright figures in different styles of sculpture are formulated with reference to axes and the four cardinal planes: for example, the principle of axiality already referred to; the principle of frontality, which governs the design of Archaic sculpture; the characteristic contrapposto (pose in which parts of the body, such as upper and lower, tilt or even twist in opposite directions) of Michelangelo’s figures; and in standing Greek sculpture of the Classical period the frequently used balanced “chiastic” pose (stance in which the body weight is taken principally on one leg, thereby creating a contrast of tension and relaxation between the opposite sides of a figure).

Proportional relations exist among linear dimensions, areas, and volumes and masses. All three types of proportion coexist and interact in sculpture, contributing to its expressiveness and beauty. Attitudes toward proportion differ considerably among sculptors. Some sculptors, both abstract and figurative, use mathematical systems of proportion; for example, the refinement and idealization of natural human proportions was a major preoccupation of Greek sculptors. Indian sculptors employed iconometric canons, or systems of carefully related proportions, that determined the proportions of all significant dimensions of the human figure. African and other tribal sculptors base the proportions of their figures on the subjective importance of the parts of the body. Unnatural proportions may be used for expressive purposes or to accommodate a sculpture to its surroundings. The elongation of the figures on the Portail Royal (“Royal Portal”) of Chartres cathedral does both: it enhances their otherworldliness and also integrates them with the columnar architecture.