Vertex figure facts for kids

A vertex figure is a special shape you get when you "slice off" a corner of a 3D shape (like a polyhedron) or a higher-dimensional shape (a polytope). Imagine you have a cube, and you cut off one of its corners. The flat surface you create by cutting is the vertex figure for that corner. It helps us understand what the shape looks like right around that corner.

What is a Vertex Figure?

Think of a 3D shape, like a cube or a pyramid. These shapes have corners, which we call vertices (one corner is a vertex). A vertex figure is like a tiny cross-section or slice taken right through one of these corners.

To find a vertex figure:

• Pick one corner (vertex) of your shape.
• Imagine cutting through all the edges that meet at that corner.
• Make sure your cut goes through each edge at the same distance from the corner.
• The new flat shape you create by making this cut is the vertex figure.

For example, if you slice off a corner of a cube, the new face you see is a triangle. So, the vertex figure of a cube is a triangle. This triangle tells us that three faces and three edges meet at each corner of a cube.

Why are Vertex Figures Useful?

Vertex figures are important in geometry because they help scientists and mathematicians understand and classify complex shapes.

• They show how many faces and edges meet at a single corner.
• They can help us figure out if a shape is regular (meaning all its faces and corners are the same).
• They are especially useful for studying shapes that repeat, like patterns in crystals or honeycomb structures.

Examples of Vertex Figures

Let's look at a few examples:

• Cube: As we mentioned, if you cut off a corner of a cube, you get a triangle. This means three square faces meet at each corner of a cube.
• Pyramid: For a square pyramid, the vertex figure at the top (apex) is a square. This is because four triangular faces meet at that point. The vertex figures at the base corners would be different, usually triangles.
• Truncated Cubic Honeycomb: This is a very complex 3D pattern made of different shapes fitting together. Its vertex figures help mathematicians understand how all these shapes connect at each point. The images below show parts of such a complex structure.

Images for kids

• 

  A part of a truncated cubic honeycomb.

• 

  This image shows how different shapes like truncated cubes and octahedrons connect in a complex pattern. The way they meet at a point can be described by a vertex figure.

See also

In Spanish: Figura de vértice para niños