3D Shapes: Faces, Edges and Vertices

G63D Shapes

Faces, edges and vertices.

3D shapes have faces (flat surfaces), edges (where faces meet) and vertices (corners).

Count faces, edges, vertices.

Cuboid

6 faces · 12 edges · 8 vertices

Square-based pyramid

5 faces · 8 edges · 5 vertices

Sphere

1 curved surface · 0 edges · 0 vertices

Face = flat surface · edge = where two faces meet · vertex = corner point.

Learn the Counts

1Cube and cuboid.

Both: 6 faces, 12 edges, 8 vertices. The cube's faces are all squares.

6 · 12 · 8

2Pyramids.

Square-based pyramid: 5 faces (4 triangles + 1 square), 8 edges, 5 vertices.

5 · 8 · 5

3Prisms.

Triangular prism: 5 faces, 9 edges, 6 vertices. A prism has the same cross-section all along.

5 · 9 · 6

💡 Key IdeaA prism keeps the same cross-section all the way through — slice it anywhere and you see the same shape.

Worked Example

Name the shape from its counts.

6 identical square faces

cube

1 curved surface, 1 flat circular face, 1 vertex... apex

cone

2 circular faces + 1 curved surface

cylinder

Watch Out! Common Mistakes

Counting hidden faces wrong.

Careful! Drawings hide the back faces. Count systematically: a cuboid has 3 pairs of opposite faces = 6.

Edges vs vertices muddle.

Remember: an edge is a line where two faces meet; a vertex is a point where edges meet. A cube: 12 edges, 8 vertices.

Calling a sphere's surface a face.

Not quite! A face is flat. A sphere has one curved surface, no faces, no edges, no vertices.

⬇ Cheat Sheet

3D SHAPES

Face = flat surface · edge = where faces meet · vertex = corner.
Cube/cuboid: 6 faces, 12 edges, 8 vertices.
Square-based pyramid: 5, 8, 5. Triangular prism: 5, 9, 6.
Prism = same cross-section all along.

Example: 6 square faces → cube · 2 circles + curve → cylinder

📄 Free printable: Download the 3D Shapes cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Face = flat surface; edge = line where faces meet; vertex = corner point.
Cube and cuboid: 6 faces, 12 edges, 8 vertices.
Square-based pyramid: 5 faces, 8 edges, 5 vertices; triangular prism: 5, 9, 6.
Spheres have a curved surface — no faces, edges or vertices.

Frequently asked questions

What are faces, edges and vertices?

Faces are the flat surfaces of a 3D shape, edges are the lines where two faces meet, and vertices are the corner points where edges meet.

How many faces, edges and vertices does a cube have?

6 faces, 12 edges and 8 vertices — exactly the same counts as a cuboid.

What is a prism?

A 3D shape with the same cross-section all the way through, like a triangular prism (Toblerone shape) or a cylinder's circular cousin.

3D Shapes