Isometric Projection of Solids

About this unit

This unit teaches you to show a solid object in a single pictorial view in which three faces are visible at once. In an isometric projection the three principal edges of the object (length, width and height) are drawn along three isometric axes that are 120° apart: one vertical and two inclined at 30° to the horizontal. Because every edge along these axes is equally foreshortened, all such lengths are drawn with the isometric scale. The unit builds from the scale itself to prisms, pyramids, curved solids and solids placed in different positions.

Key ideas

• Isometric axes: one vertical line and two lines at 30° to the horizontal, 120° apart from each other.
• Isometric lines (parallel to the axes) are measured with the isometric scale; non-isometric lines are not.
• Isometric length ≈ 0.816 × true length (ratio √2 : √3).
• Isometric projection uses the isometric scale; an isometric view (drawing) uses true lengths.
• Circles on isometric faces appear as ellipses, usually drawn by the four-centre method.
• Hidden edges are normally not shown in isometric projections.

How to prepare

Practise constructing the isometric scale neatly until it takes only a few minutes. Learn the box (enclosing rectangle) method for polygons and the four-centre method for ellipses. Typical questions ask for the ratio 0.816, the angles of the axes, how a sphere is drawn, and how the axis of a solid is placed for a stated position.