Prisms and pyramids

The essentials

Prisms and pyramids are drawn in isometric projection by first drawing their base and then the height along the axis. A polygon base is drawn inside an enclosing rectangle (the box method): the rectangle's sides are isometric lines, so they can be measured with the isometric scale, and the corners of the polygon are located on them. For a prism, the base is repeated at the other end of the axis and corresponding corners are joined. For a pyramid, the apex is located on the axis at the given height from the centre of the base, and joined to every base corner.

Key points

• Cube: three isometric axes from one corner, each edge = isometric length of the side.
• Triangular base: enclosing rectangle of side a × (√3/2)a; apex of the triangle at the midpoint of the far side.
• Square base: the square itself is drawn as a rhombus (isometric square) when its sides are along the axes.
• Hexagonal base of side a: enclosing rectangle 2a × √3 a (corner-to-corner × flat-to-flat). For a = 25 mm this is 50 × about 43.3 mm true, i.e. about 40.8 × 35.4 mm isometric.
• Pentagonal base: draw the true pentagon in an enclosing rectangle and transfer offsets (distances measured along isometric directions) to the isometric rectangle.
• Pyramid slant edges and polygon sides that are not parallel to an axis are non-isometric lines; never measure them with the scale.

Exam tips

• Draw the base and the axis first with thin lines; darken only the visible edges at the end.
• Always find the centre of the base by joining diagonals of the enclosing rectangle before raising the axis of a pyramid.

Common mistakes

• Measuring a pyramid's slant edge along the 30° line.
• Forgetting to foreshorten the height of the solid.
• Showing hidden edges, which are normally omitted.