Prism
SŠ12 minBuild a prism from your own points and watch which edges are visible and which are dashed.
Solid
All points are snapped onto their best-fit plane, ordered into the base ring and extruded perpendicular to it. Each point you add gives the base another vertex.
Points · 4
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.
Measurements
- Volume
- 16.18
- Surface
- 38.93
- Vertices V
- 8
- Edges E
- 12
- Faces F
- 6
- V − E + F
- 2
V − E + F = 2 holds for every simple polyhedron (Euler’s formula) – a quick check that the body is closed.
Theory
A solid projects like everything else – vertex by vertex. Project the vertices, join the edges and you have both views. Only one thing is new: you must decide which edges are visible.
The visibility rule for a convex solid is short: an edge is visible when at least one of its faces turns toward the viewer. If both faces turn away, the edge is behind the body and is drawn dashed.
Careful – visibility is decided independently in each view. The same edge can be solid in one view and dashed in the other, because the observer stands somewhere else each time.
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
When is an edge of a convex solid drawn dashed?
Can the same edge be visible in the top view and hidden in the front view?
For which solid does Euler’s formula V − E + F = 2 hold?
Downloadable material
A PDF for this lesson is in preparation.
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