3D Shapes Worksheet Vertices, Edges, Faces

3D shapes, vertices, edges, faces at a glance

A three-dimensional shape (3D shape) has three dimensions, length, width and height. Students are expected to recognise solid shapes such as cubes, cuboids (or rectangular prisms) and triangular prisms. We live in a three-dimensional world, so students should be familiar with the real life examples of different 3D shapes around them.

3D shape properties include the number of faces, edges and vertices of 3d shapes. A face is a flat or curved surface. An edge is where two faces meet, and a vertex is a corner where edges meet. If the faces of a 3-dimensional shape are all polygons, it is called a polyhedron. If all faces are the same regular polygon, it is called a regular polyhedron. An example of a regular polyhedron is a tetrahedron which has four equilateral triangular faces. 

Euler’s formula links the number of faces, vertices and edges. It states that for any polyhedron, the number of faces plus the number of vertices minus the number of edges will always be 2. This is not examined at GCSE but can be a good enrichment task when studying properties of 3D shapes and is a great introduction to a very famous mathematician. 

A prism is a geometric shape that has a constant cross-section. If we cut a prism parallel to its end, we reveal an identical 2D shape. An example of a prism is a hexagonal prism; it consists of two hexagonal faces at either end, and six rectangular faces joining the hexagons. If we cut this prism through the rectangular faces, the 2D shape revealed inside would be a hexagon. 

There are different 3D shapes activities students can do to learn properties of 3D shapes. For example, it can be useful for students to create a set of revision flashcards with the name, diagram and properties of each 3D shape. Creating a 3D paper model or a net or using real life examples can help make 3D shapes interactive and allow students to identify and count faces, edges and vertices on the shape.

Looking forward, students can then progress to additional 3D shapes worksheets and more geometry worksheets for example an angles in polygons worksheet or volume and surface area of spheres worksheet.

For more teaching and learning support on Geometry our GCSE maths lessons provide step by step support for all GCSE maths concepts.