Positions of solids

The essentials

The same solid looks different depending on how it is placed relative to the horizontal plane (HP) and vertical plane (VP). In isometric projection, the position decides which isometric axis the solid's axis follows and which isometric plane holds its base. The vertical isometric axis represents lines perpendicular to the HP. The two 30° axes represent horizontal lines: one is perpendicular to the VP, the other is parallel to both the HP and the VP.

Key points

• Axis perpendicular to HP: the solid stands (or hangs) vertically; the axis is drawn along the vertical isometric axis and the base lies on a horizontal isometric plane.
• Axis perpendicular to VP: the axis is horizontal and is drawn along the 30° axis that represents lines perpendicular to the VP; the base lies on a vertical isometric plane parallel to the VP.
• Axis parallel to both HP and VP: the axis is horizontal and drawn along the other 30° axis; the base lies on a vertical plane parallel to the profile plane.
• Base sides parallel or perpendicular to HP/VP: this decides how the polygon sits inside its enclosing rectangle, for example whether a hexagon has two sides or two corners facing the observer.
• Lying solids: a prism "lying on a rectangular face" has its axis horizontal; a cone "lying" usually means its axis is horizontal with the base vertical.

Exam tips

• Read the question carefully and write down: which plane the base is on, and along which isometric axis the axis lies.
• A quick thin-line sketch of the box (enclosing prism) in the correct orientation avoids most errors.

Common mistakes

• Treating "axis parallel to VP" as automatically vertical; a horizontal axis can also be parallel to the VP.
• Drawing a horizontal-axis solid with its base ellipse on a horizontal plane.