3-dimensional solids
Click to explore refreshed revision resources for GCSE Maths: 3D shapes, with step-by-step slideshows, quizzes, practice exam questions, and more!
Some 3D solids have faces, edges and vertices.
- A face is a flat surface.
- An edge is where two faces meet.
- A vertex is a corner where edges meet. The plural is vertices.
A prism is a 3D solid with a uniform cross-section. The two end faces of a prism are identical in shape and size. If you make a cut parallel to the ends, the cross-section exposed will be the same shape and size as the ends.
A pyramid has a polygon as its base and the rest of its faces are triangles that meet at the same vertex.
Here are some common 3D solids.
| Name | Faces | Edges | Vertices |
| Cube | 6 (all squares) | 12 | 8 |
| Cuboid | 6 (all rectangles) | 12 | 8 |
| Square-based pyramid | 5 | 8 | 5 |
| Triangular-based pyramid | 4 | 6 | 4 |
| Name | Cube |
|---|---|
| Faces | 6 (all squares) |
| Edges | 12 |
| Vertices | 8 |
| Name | Cuboid |
|---|---|
| Faces | 6 (all rectangles) |
| Edges | 12 |
| Vertices | 8 |
| Name | Square-based pyramid |
|---|---|
| Faces | 5 |
| Edges | 8 |
| Vertices | 5 |
| Name | Triangular-based pyramid |
|---|---|
| Faces | 4 |
| Edges | 6 |
| Vertices | 4 |
Some 3D solids, such as the cone and the cylinder, have faces and curved surfaces.
Some 3D solids, like the sphere, just have a curved surface.
More guides on this topic
- NEW: Angles
- NEW: Angles in parallel lines
- NEW: Polygons
- NEW: Line and rotational symmetry
- NEW: Constructing triangles
- NEW: Ruler and compass constructions
- NEW: Loci
- NEW: Bearings
- NEW: Perimeter
- NEW: Area
- NEW: Volume of a prism
- NEW: Surface area of a prism
- NEW: Pyramids, cones and spheres
- NEW: Nets, plans and elevations
- NEW: Circumference and arc length
- NEW: Area of circles and sectors
- NEW: Higher – Circle Theorems – Calculating angles using circles
- NEW: Higher – Using the alternate segment theorem, tangents and chords
- NEW: Reflection
- NEW: Rotation
- NEW: Translation
- NEW: Enlargement
- NEW: Higher − Negative enlargements
- NEW: Higher – Combined transformations and invariant points
- NEW: Congruent and similar shapes
- NEW: Higher – Similarity in 2D and 3D shapes
- NEW: Pythagoras' theorem
- NEW: Solving 2D and 3D problems using Pythagoras' theorem
- NEW: Right-angled trigonometry
- NEW: Exact trigonometric values
- NEW: Higher – Sine rule – OCR
- NEW: Higher – Cosine rule
- NEW: Higher – 2D and 3D trigonometry problems
- NEW: Vectors
- NEW: Higher – Geometric problems using vectors
- Angles, lines and polygons - OCR
- Loci and constructions - OCR
- 2-dimensional shapes - OCR
- Circles, sectors and arcs - OCR
- Circle theorems - Higher - OCR
- Transformations - OCR
- Pythagoras' theorem - OCR
- Units of measure - OCR
- Trigonometry - OCR
- Vectors - OCR
