Cuboid / Rectangular Prism (3D) — free printable diagram

How many faces, edges and vertices a cuboid has

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

Solid

Cuboid (rectangular prism)

Faces

6

Edges

12

Vertices (corners)

8

Shape of each end

Rectangle

Joining faces

4 rectangles

Volume

V = l × w × h

Surface area

SA = 2(lw + lh + wh)

• A prism has the same cross-section all the way along. This one has a rectangle at each end joined by 4 rectangles, so 4 + 2 = 6 faces altogether.
• Every cuboid has 12 edges (3 × 4) and 8 vertices (2 × 4), whatever size it is drawn at and whichever way up it is standing.
• The six faces come in three matching pairs — opposite faces are always congruent — which is where the 2(lw + lh + wh) in the surface-area formula comes from.
• A cube is a cuboid whose three dimensions happen to be equal, so every cube is a cuboid but most cuboids are not cubes.
• “Cuboid” and “rectangular prism” are the same solid under two names; UK and Australian curricula tend to the first, US curricula to the second.
• 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.