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Attributes of 3D Shapes

This lesson explains the attributes of 3D shapes, faces, edges, and vertices, and shows how to identify and count them for solids like cubes, prisms, pyramids, cones, cylinders, and spheres using labeled diagrams and worked examples.

What Are the Attributes of 3D Shapes?

Every solid, or 3D shape, can be described using three key attributes: its faces, its edges, and its vertices. Learning to spot and count these parts helps you tell shapes apart, even when they look similar at first glance. This builds directly on what you already know from 3D shapes, where you first met solids like cubes, cones, and spheres.

Here is what each attribute means:

Face: a flat or curved surface on the outside of a shape.
Edge: a line segment where two faces meet.
Vertex (plural: vertices): a point where two or more edges meet, often called a corner.

Labeling a Solid

Look at the cube below. It has flat square faces, straight edges where the faces meet, and sharp corner points called vertices.

A cube has 6 flat faces, 12 straight edges, and 8 vertices.

Counting Attributes of Common Solids

Different solids have different combinations of faces, edges, and vertices. Some, like spheres and cylinders, have curved surfaces and no sharp corners at all. Comparing these attributes side by side makes the differences easy to see, and connects to what you learned in Comparing 2D and 3D shapes.

Solid	Faces	Edges	Vertices
Cube	6	12	8
Rectangular prism	6	12	8
Triangular prism	5	9	6
Square pyramid	5	8	5
Cone	2	1	1
Cylinder	3	2	0
Sphere	1	0	0

Worked Example 1: Counting Attributes of a Rectangular Pyramid

A square pyramid has a flat square base and four triangular sides that meet at a single point on top.

Faces: the 1 square base plus the 4 triangular sides gives \( 1 + 4 = 5 \) faces.

Edges: 4 edges run around the base, and 4 more edges run up the sides to the top point, giving \( 4 + 4 = 8 \) edges.

Vertices: there are 4 corners on the base plus 1 point at the top, giving \( 4 + 1 = 5 \) vertices.

So a square pyramid has 5 faces, 8 edges, and 5 vertices.

Worked Example 2: Comparing a Cylinder and a Cone

A cylinder has 2 flat circular faces (top and bottom) plus 1 curved face wrapping around them, for 3 faces total. It has 2 curved edges where the flat and curved faces meet, and 0 vertices, since a curved surface never comes to a sharp point.

A cone has 1 flat circular face plus 1 curved face that narrows to a point, for 2 faces total. It has 1 curved edge and exactly 1 vertex, the pointed tip at the top.

Even though both shapes have curved surfaces, only the cone has a vertex, because only the cone's surface comes to a single point.

Why Attributes Matter

Describing a solid by its faces, edges, and vertices lets you classify and compare shapes without relying on pictures alone. It also helps you notice patterns, such as why every prism has two matching end faces, or why any shape with a curved surface, like a sphere or cylinder, has no true vertices. These same ideas of sides and corners first appear with flat shapes in Sides and corners of 2D shapes, so recognizing the pattern in 3D is a natural next step.

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