In short: A 3D shape has faces (flat sides), edges (where two faces meet) and vertices (corners). Prisms have the same shape all the way through, and pyramids come to a point. A net is the flat pattern that folds into the solid, and the top, front and side views are what you see from each direction.
Before you start
- The names of 2D shapes: triangle, square, rectangle, pentagon, hexagon, circle (see Triangles and Quadrilaterals).
Faces, edges and vertices
Prisms and pyramids
A prism has two matching ends joined by rectangles. Cut it anywhere parallel to the end and you get the same shape. A pyramid has one base, and triangles that meet at a point called the apex.
Both are named after their base.
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | 6 | 12 | 8 |
| Rectangular prism | 6 | 12 | 8 |
| Triangular prism | 5 | 9 | 6 |
| Hexagonal prism | 8 | 18 | 12 |
| Square pyramid | 5 | 8 | 5 |
| Triangular pyramid | 4 | 6 | 4 |
Curved solids
- A cylinder has two flat circle faces and one curved surface, like a can.
- A cone has one flat circle face, one curved surface and one point at the top, like an ice cream cone.
- A sphere has one curved surface and no flat faces, like a ball.
Nets
A net is a flat shape that folds up into a solid. A cube has 11 different nets. Here is one.
A triangular prism's net has 2 triangles and 3 rectangles. A square pyramid's net has 1 square and 4 triangles.
Views from the top, front and side
Imagine looking straight at a solid from one direction. You see a flat shape called a view.
| Solid | Top view | Front view | Side view |
|---|---|---|---|
| Cylinder standing up | Circle | Rectangle | Rectangle |
| Cone standing on its base | Circle with a dot in the middle | Triangle | Triangle |
| Square pyramid | Square with lines to the centre | Triangle | Triangle |
| Sphere | Circle | Circle | Circle |
A shadow works the same way. Shine a torch straight down on a standing can and its shadow is a circle. Shine it from the side and the shadow is a rectangle.
A cross-section is the face you get by cutting straight through a solid. Cut a prism parallel to its end and the cross-section is the same shape as the end.
- Faces are flat
- Edges where faces meet
- Vertices are corners
- Prisms: same all through
- Pyramids: come to a point
- Cylinder, cone, sphere
- F + V - E = 2
- Name by the base
- Fold into the solid
- One apart in a row: opposite
- Top, front, side
- Shadows and cross-sections
Quick summary
- Faces are flat, edges are where faces meet, vertices are corners.
- Prisms and pyramids are named after their base.
- For prisms and pyramids, faces vertices edges .
- A cube has 6 faces, 12 edges and 8 vertices.
- A net folds into a solid. In a row of squares, faces one apart are opposite.
- The top, front and side views are what you see looking straight at each side.
Quiz
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Try 3 questions now
How many faces does a cube have?
- A 4
- B 6
- C 8
- D 12
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B: 6
A cube has 6 square faces, like a dice.
Which solid has one curved surface and no flat faces?
- A Cylinder
- B Cone
- C Sphere
- D Cube
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C: Sphere
A sphere, like a ball, has only a curved surface.
Which solid has 4 faces, 6 edges and 4 vertices?
- A Square pyramid
- B Triangular pyramid
- C Triangular prism
- D Cube
Show answer
B: Triangular pyramid
A triangular pyramid has a triangle base and 3 triangle sides.