What’s the Plural of Vertex?

The English language has many words that are derived from Latin, and these often follow specific rules for pluralization. One such word is “vertex,” which has a Latin origin. Understanding how to pluralize “vertex” correctly is essential, especially for those working in fields like mathematics, geometry, computer graphics, and even anatomy.

In this article, we’ll explore the correct plural form of “vertex,” explain why it follows the rule it does, provide examples of its usage, and address common questions and misconceptions. By the end, you will feel confident in using “vertex” and its plural form in any context.

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What Does “Vertex” Mean?

Before we dive into the plural form of “vertex,” let’s first clarify its meaning. A vertex is a point where two or more lines, edges, or curves meet. The word is commonly used in various fields:

• Geometry: A vertex is where two or more lines meet to form an angle, or where the edges of a polygon or polyhedron converge.
• Graph Theory: A vertex (or node) is a fundamental unit in a graph, representing a point that can be connected to other vertices via edges.
• Computer Graphics: In 3D modeling, vertices are the points that make up the corners of polygons, which are used to define the shape of an object.
• Anatomy: The vertex refers to the highest point of the head or skull.

Examples of “Vertex” in Singular Form:

• In a triangle, each corner is called a vertex.
  (Here, “vertex” refers to one of the three points where the edges of the triangle meet.)
• The graph consists of several edges connecting different vertex points.
  (In this sentence, “vertex” refers to individual nodes in a graph.)
• The highest point on the human skull is known as the vertex.
  (Here, “vertex” refers to the anatomical location on the head.)

In all of these examples, “vertex” is used in its singular form. But what happens when you need to talk about more than one vertex?

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What’s the Plural of “Vertex”?

The plural of “vertex” is “vertices.” This follows the typical Latin-based pluralization rule for words ending in “-ex.” In Latin, many nouns that end in “-ex” form their plural by changing “-ex” to “-ices.” This rule applies to other words like “index” (plural: “indices”) and “appendix” (plural: “appendices”).

Why “Vertices”?

The word “vertex” comes from the Latin word vertex, which means “whirl” or “top.” In Latin, the plural form of vertex is “vertices.” When the word was borrowed into English, it retained this plural pattern. Therefore, the correct plural form in English is also “vertices.”

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Examples of “Vertices” in Sentences

Now that we know the correct plural form, let’s look at some examples of “vertices” in different contexts. These examples will help you see how to use the word in real-world situations.

Geometry:

• A pentagon has five vertices, where each pair of adjacent sides meet.
  (Here, “vertices” refers to the five points where the edges of the pentagon join.)
• In a cube, there are eight vertices where the edges converge.
  (In this sentence, “vertices” refers to the eight corner points of a cube.)
• Calculating the angles at the vertices of a polygon is an important part of geometry.
  (Here, “vertices” refers to the points in a polygon where the angles are formed.)

Graph Theory and Computer Science:

• The graph has ten vertices, each representing a city connected by roads.
  (In this sentence, “vertices” refers to the nodes in a graph representing different cities.)
• In computer graphics, 3D models are made up of polygons, and the corners of these polygons are called vertices.
  (Here, “vertices” refers to the points that define the shapes of polygons in 3D models.)
• The shortest path between two vertices in a graph is calculated using Dijkstra’s algorithm.
  (In this example, “vertices” refers to the points in a graph between which the shortest path is determined.)

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Singular vs. Plural: “Vertex” vs. “Vertices”

It’s important to know when to use “vertex” and when to use “vertices.” The distinction is simple: “vertex” refers to a single point, while “vertices” refers to multiple points.

Let’s clarify this with some additional examples:

Singular (“Vertex”) in Sentences:

• Each corner of a pyramid is called a vertex.
  (Here, “vertex” refers to a single point at a corner of the pyramid.)
• A parabola has only one vertex, which is its highest or lowest point.
  (In this sentence, “vertex” refers to the point that marks the extremity of the parabola.)

Plural (“Vertices”) in Sentences:

• To calculate the surface area of a polyhedron, you need to consider all its vertices and edges.
  (In this sentence, “vertices” refers to multiple points where the edges of the polyhedron meet.)
• A cube has six faces, twelve edges, and eight vertices.
  (Here, “vertices” refers to the eight corner points of the cube.)

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Why Do Some People Confuse the Plural of “Vertex”?

The confusion around the plural form of “vertex” often stems from a lack of familiarity with Latin-based pluralization rules. In English, most words form their plural simply by adding “-s” or “-es” (e.g., “dog” → “dogs” or “box” → “boxes”). However, words that come from Latin, such as “vertex,” often retain their original plural forms based on Latin grammar.

Common Mistakes

Mistake 1: Adding “-es” to Form the Plural
Some people may try to pluralize “vertex” by adding “-es,” resulting in “vertexes.” While this is understandable, it is incorrect. The correct plural form is “vertices.”

Mistake 2: Using “Vertice” as the Singular
Another common mistake is using “vertice” as the singular form and “vertices” as the plural. This is incorrect because “vertex” is the singular form, and “vertices” is the plural. There is no such word as “vertice” in standard English.

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How to Use “Vertices” Correctly in Sentences

Whether you’re writing about geometry, computer science, or graph theory, knowing how to use “vertices” correctly is crucial. Let’s look at some specific contexts where the plural form is used.

In Geometry:

• A hexagon has six vertices, and each vertex forms part of an internal angle.
  (Here, “vertices” refers to the six points where the sides of the hexagon meet.)
• To find the area of a polygon, you need to know the coordinates of all its vertices.
  (In this sentence, “vertices” refers to the points that define the shape of the polygon.)

In Computer Graphics:

• When rendering a 3D model, each vertex is assigned a position in space, and multiple vertices form the shape of the object.
  (Here, “vertices” refers to the points that make up the shape of a 3D model.)
• The more vertices a model has, the more detailed its shape will be.
  (In this example, “vertices” refers to the points that contribute to the complexity of a 3D object.)

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Common Questions and Misconceptions About “Vertices”

Let’s address some common questions and misconceptions people often have about the plural form of “vertex.”

Question 1:

Is “vertexes” ever correct?

Answer:
No, “vertexes” is not the correct plural form. The only accepted plural form of “vertex” is “vertices.”

Example:

• The polygon has five vertices, not five vertexes.

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Question 2:

Why isn’t the plural of “vertex” just “vertexes”?

Answer:
The word “vertex” comes from Latin, and in Latin, many words that end in “-ex” form their plural by changing “-ex” to “-ices.” In English, we retain this rule for certain Latin-derived words, including “vertex” (plural: “vertices”), “index” (plural: “indices”), and “appendix” (plural: “appendices”).

Example:

• The graph has multiple vertices connected by edges.

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Question 3:

Which plural form should I use in formal writing: “vertices” or “vertexes”?

Answer:
Always use “vertices” in formal writing. “Vertexes” is incorrect and should be avoided.

Example (Correct for formal writing):

• The 3D model consists of numerous vertices that define its structure.

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Question 4:

Which sentence is correct?

a) The pyramid has five vertexes at its base.
b) The pyramid has five vertices at its base.

Answer:
*b) The pyramid has five vertices at its base.

Explanation: The correct plural form of “vertex” is “vertices.” “Vertexes” is incorrect.

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Practice Questions: Vertex or Vertices?

Let’s test your understanding of when to use “vertex” and its plural form with some practice questions.

Question 1:

Which word is correct in the following sentence?

• The triangle has three _.

a) vertex
b) vertices

Answer:
b) vertices

Explanation: A triangle has three corners or points where the sides meet, so the plural “vertices” is the correct choice.

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Question 2:

Fill in the blank with the correct word:

• Each angle of the polygon is formed at a _.

Answer:
Vertex

Explanation: The sentence refers to a single point where two sides meet, so “vertex” is the correct singular form.

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Question 3:

True or False:
“Vertexes” is an acceptable plural form of “vertex.”

Answer:
False

Explanation: The correct plural form is “vertices.” “Vertexes” is incorrect.

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Question 4:

Which sentence is correct?

a) The cube has eight vertices.
b) The cube has eight vertexes.

Answer:
*a) The cube has eight vertices.

Explanation: The correct plural form of “vertex” is “vertices,” not “vertexes.”

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Conclusion

In summary, the plural form of “vertex” is “vertices.” This follows the Latin-based rule for words ending in “-ex,” in which the plural changes to “-ices.” Understanding and using the correct plural form is important, especially in fields like geometry, graph theory, and computer graphics.

Key Takeaways:

• “Vertex” is singular, referring to one point where edges or lines meet.
• “Vertices” is the correct plural form, and should always be used when referring to more than one vertex.
• Avoid using “vertexes” as it is incorrect.

By mastering the correct plural form of “vertex,” you can confidently use “vertices” in a variety of contexts, whether you’re discussing mathematical shapes, 3D models, or graphs.