Pyramid
SŠ12 minConstruct both views of a pyramid step by step – the apex falls inside the base in plan and sets the height in the front view.
Solid
The base is formed as for the prism – every point is one of its vertices. The apex sits above the base centroid at height h.
A pyramid needs at least 3 points.
Points · 2
max 12Each further point gives the base another vertex – a triangle becomes a quadrilateral, a pentagon…
Planar section
3D view
Perspective
Bring the eye closer and parallel edges rush together toward a vanishing point; move it away and perspective tends to parallel projection.
Theory
A pyramid projects like a prism – vertex by vertex – but with one special point added: the apex V. The whole solid is fixed by its base plus this one extra point, so it is enough to construct the views of the base and the views of V.
When a pyramid stands on π₁ its apex is above the base. In the top view it therefore projects inside the base and the lateral edges split it into triangles; the whole pyramid is seen from above, so every edge is solid in plan. The apex carries the height, and only the front view reads it.
Visibility in the front view uses the same rule as for a prism: the lateral edge to the farthest base vertex lies behind the body, so it is dashed – together with the rear base edge. The other lateral edges face you and are solid.
Step-by-step construction
Practice
Build the construction yourself
What is the next step?
1 / 4Choose the step that comes next. The drawing only advances on a correct choice.
Check your understanding
Where does the apex of a pyramid standing on π₁ project in the top view?
From which view do you read the pyramid’s height?
How many lateral edges of a triangular pyramid are usually dashed in the front view?
Downloadable material
A PDF for this lesson is in preparation.
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