What Is a Vertex? Everything You Need to Know

Vertices are all around us, from the corners of your desk to the edges of a book. 

But what exactly is a vertex? Is it the same as an edge, or is there a difference after all? You are about to find out.

Whether you're just learning about vertices in school or brushing up for a test, this guide will make the concept easy to understand. 

We’ll break it down with simple definitions, visuals, and comparisons to similar geometry concepts—plus, we’ll answer some of the most common questions students have along the way.

Let’s get started!

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What Is a Vertex in Geometry?

A vertex (plural: vertices) is a special point in geometry where two or more line segments, rays, or edges meet.

• In polygons like triangles, squares, and pentagons, a vertex is where two sides, or line segments, connect. For example, a triangle has three vertices, one at each corner. 

• In rays and angles, a vertex is the starting point where two rays meet to form an angle. Think of the point where two sides of a "V" come together—that’s a vertex!

• In 3D shapes (like cubes and pyramids), a vertex is where three or more edges meet. Imagine the corner of a box—that’s a vertex in a three-dimensional space.

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Vertex vs. Faces vs. Edges - What’s the Difference?

When learning about shapes, especially 3D shapes like cubes, pyramids, and prisms, we often hear the terms edges, faces, and vertices mentioned together. 

Each of these describes a different part of a shape. Let’s have a look:

• Edges are the straight lines where two surfaces meet. If you look at a box, the edges are like the lines where the sides connect.
• Faces are the flat surfaces of a shape. A cube has six faces, just like the sides of a dice.
• Vertices (the plural of vertex) are the corner points where edges meet. If you touch the corner of a book or a pyramid, you’re touching a vertex!

Vertex in 2D Shapes

2D shapes (two-dimensional shapes) are flat figures that have only length and width but no depth. They are made up of straight sides that connect to form a closed shape.

Vertices of 2D shapes are the points where two sides meet. You can think of them as the corners of a shape. Every polygon (a closed shape with straight sides) has vertices, and the number of vertices matches the number of sides!

Let’s look at some of the common 2D shapes and the number of vertices they have:

• A triangle has 3 vertices.
• A square has 4 vertices.
• A rectangle has 4 vertices.
• A pentagon has 5 vertices.
• A hexagon has 6 vertices.
• An octagon has 8 vertices.

Shapes with curved edges, like circles and ovals, do not have vertices because they don’t have straight sides meeting at a point.

Vertex in 3D Shapes

3D shapes (three-dimensional shapes) have length, width, and depth, meaning they take up space. They are made up of faces (flat surfaces), edges (straight lines), and vertices (corner points).

Vertices of 3D shapes are the points where three or more edges meet. You can think of them as the sharp corners of the shape. 

Let’s look at some of the common 3D shapes and the number of vertices they have:

• A cube has 8 vertices.
• A rectangular prism has 8 vertices.
• A triangular prism has 6 vertices.
• A pyramid with a square base has 5 vertices.
• A triangular pyramid (tetrahedron) has 6 vertices.

However, not all 3D shapes have vertices—a sphere has no vertices because it has no straight edges. 

Practice Time: Test Your Knowledge of Vertices

Are you ready to put your vertex knowledge to the test? Take our quick quiz, then check your answers at the end of the guide!

Question 1: What is a vertex?

A vertex is…
A) A flat surface of a shape
B) A point where two or more line segments, rays, or edges meet
C) A line that connects two faces
D) A shape with straight sides

Question 2: Which shape has the most vertices?

A) Triangle
B) Square
C) Pentagon
D) Hexagon

Question 3: In a 3D shape, how many edges meet at a vertex?

A) 2
B) 3 or more
C) 4
D) 5

Question 4: How many vertices does this 2D shape have?

Question 5: How many vertices does this 3D shape have? 

FAQs About Vertex

We’ve put together a list of questions from students at Mathnasium of West Chester–along with answers to clear up any confusion.

1. Can a shape have more edges than vertices?

Yes! In 3D shapes, the number of edges is usually greater than the number of vertices. 

For example, a cube has 8 vertices but 12 edges. However, in 2D polygons, the number of vertices and edges is always the same (e.g., a pentagon has 5 vertices and 5 edges).

2. Do all polygons have the same number of vertices as sides?

Yes! In 2D shapes, the number of vertices always matches the number of sides. A triangle has 3 sides and 3 vertices, a square has 4 sides and 4 vertices, and so on. This rule applies to all polygons, no matter how big or small.

3. If two shapes have the same number of vertices, does that mean they are the same shape?

Not necessarily! 

Different shapes can have the same number of vertices but look very different. For example, a square and a rhombus both have 4 vertices, but they are not the same shape because their angles and side lengths differ.

4. Can a vertex exist without edges?

No, a vertex only exists where edges meet. Without edges, there is nothing to connect at a point, so it wouldn’t be a vertex. A single dot on a page isn’t a vertex—it’s just a point!

5. Do curved 3D shapes, like cylinders or cones, have vertices?

No, curved shapes don’t have vertices unless they have sharp corners. 

A cylinder has no vertices because it has no edges that meet. However, a cone has one sharp point at the top, which is sometimes called a vertex, even though it doesn’t have edges like a polygon or polyhedron.

Master Vertex at Mathnasium of West Chester

Mathnasium of West Chester is a math-only learning center for K-12 students in West Chester, OH.

Using a proprietary teaching approach called the Mathnasium Method™, our specially trained math tutors follow personalized, assessment-based learning plans and employ a variety of proven teaching techniques to build upon what the student already knows, close their knowledge gaps, and gradually expand their mathematical thinking. 

We provide face-to-face instruction in a supportive group environment, helping students master any math class and topic, including vertex, typically covered in elementary school.

Whether your student is looking to catch up, keep up, or get ahead in their math class, schedule an assessment, and enroll at Mathnasium of West Chester today! 

Schedule a Free Assessment at Mathnasium of West Chester 

Pssst! Check Your Answers Here

If you’ve given our exercises a try, check how you did below.

Question 1: What is a vertex?
B) A point where two or more line segments, rays, or edges meet

Question 2: Which shape has the most vertices?
D) Hexagon (A hexagon has 6 vertices).

Question 3: In a 3D shape, how many edges meet at a vertex?
B) 3 or more (In 3D shapes, a vertex is formed where at least three edges come together.)

Question 4: How many vertices does this 2D shape have?
An octagon has 8 vertices.

Question 5: How many vertices does this 3D shape have?
A rectangular prism has 8 vertices.