118. The Cylinder's Blueprint · 3 faces, 2 edges, 0 vertices—always

Try to break it

Drag R to widen or narrow the cylinder and H to make it tall or short. Try to change the number of faces, edges, or corners — you can't. Every cylinder has 2 flat circular faces, 1 curved surface, 2 circular edges, and 0 vertices, whatever its size.

How you build it

Construct a cylinder.

• Draw the TOP face — a flat ellipse. Click two opposite corners of its bounding box so the circle looks tilted toward you.
• Draw the BOTTOM face directly below the top. The ellipse tool has locked the size, so it will come out the same as the top face automatically.
• Draw the LEFT side — a vertical segment from the leftmost point of the top ellipse straight down to the leftmost point of the bottom ellipse.
• Draw the RIGHT side — a vertical segment from the rightmost point of the top ellipse straight down to the rightmost point of the bottom ellipse. Cylinder complete.

The proof, step by step

Prove that the cylinder has 3 faces, 2 edges, and 0 vertices.

• A cylinder has two flat circular faces (top and bottom).
• It has one curved rectangular face that wraps around.
• The flat faces meet the curved face at two circular edges.
• There are no sharp corners or vertices because all boundaries are curved or parallel.

Worked example

A cylinder is a 3D solid with a curved surface and two identical flat circular ends. How many vertices does a cylinder have?

A cylinder has 0 vertices. Its surfaces are either flat circular faces or a curved face, and they meet at smooth edges, leaving no sharp corners.

• 1
• 2
• 0 — correct
• 4