Octagonal Prism (3D) — free printable diagram

How many faces, edges and vertices an octagonal prism has

An octagonal prism is a 3D solid with 10 faces, 24 edges and 16 vertices. Every face is flat, so it is a polyhedron and Euler's formula applies to it.

Solid

Octagonal prism

Faces

10

Edges

24

Vertices (corners)

16

Shape of each end

Octagon

Joining faces

8 rectangles

Volume

V = area of the octagonal end × length

Surface area

SA = 2 × (area of the octagon) + (perimeter of the octagon × length)

• A prism has the same cross-section all the way along. This one has an octagon at each end joined by 8 rectangles, so 8 + 2 = 10 faces altogether.
• Every octagonal prism has 24 edges (3 × 8) and 16 vertices (2 × 8), whatever size it is drawn at and whichever way up it is standing.
• 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 10 + 16 − 24 = 2.