Cube (3D) — free printable diagram

How many faces, edges and vertices a cube has

A cube is a 3D solid with 6 faces, 12 edges and 8 vertices. It is also called a regular hexahedron. Every face is flat, so it is a polyhedron and Euler's formula applies to it.

Solid

Cube (regular hexahedron)

Faces

6

Edges

12

Vertices (corners)

8

Shape of each end

Square

Joining faces

4 squares

Volume

V = s³, where s is the length of one edge

Surface area

SA = 6s²

• A prism has the same cross-section all the way along. This one has a square at each end joined by 4 squares, so 4 + 2 = 6 faces altogether.
• Every cube has 12 edges (3 × 4) and 8 vertices (2 × 4), whatever size it is drawn at and whichever way up it is standing.
• A cube is the one prism whose faces are all identical: six congruent squares, twelve equal edges and eight corners where three squares meet.
• Every cube is also a cuboid, and a square prism, and one of the five Platonic solids. Those are all correct descriptions of one solid rather than four different shapes — a point worth making explicitly, because a question that calls it a “square prism” throws students who have only ever heard “cube”.
• It has 11 distinct nets — eleven genuinely different ways to unfold it, not counting rotations and reflections of the same arrangement. Finding all eleven is a classic investigation.
• Euler's formula holds for every solid with flat faces: faces + vertices − edges = 2. It is the quickest way to check a count you are unsure of. Here that is 6 + 8 − 12 = 2.