Polyhedron with Net for School Maths Lab

Quick Answer: Polyhedron with Net is a solid geometry teaching aid that pairs a polyhedron, a solid bounded by flat polygon faces, with the net that folds to make it. Students compare each polyhedron with its net to count faces, edges and vertices and to see how a flat pattern becomes a solid.

Solid and Net Side by Side

A polyhedron has only flat faces, straight edges and sharp vertices, so cubes, prisms and pyramids qualify while cylinders, cones and spheres do not. Seeing the solid next to its net answers questions that a single drawing leaves open: which face ends up opposite which, how many edges meet at each vertex, and why the net of a square pyramid has one square surrounded by four triangles.

Counting on the model leads to Euler’s formula for convex polyhedra, F + V − E = 2. A cube has 6 faces, 8 vertices and 12 edges; a tetrahedron has 4, 4 and 6; an octahedron has 8 faces, 6 vertices and 12 edges. Each set of numbers satisfies the formula, and students can test it on every solid they handle. The five regular polyhedra, or Platonic solids, are the special cases in which every face is the same regular polygon and the same number of faces meet at each vertex.

Which polyhedra are included, and whether the nets are fixed to the solids or loose, varies between versions; check the list with LabEquip if a lesson depends on a particular solid.

Care & Handling

• Store each polyhedron with its own net so that the pairs stay matched.
• Handle the solids by their faces rather than their vertices, which take knocks most easily.
• Wipe with a dry cloth and keep loose nets flat in a folder.

Specifications

Applications

• Counting faces, edges and vertices and tabulating them for several solids
• Verifying Euler’s formula F + V − E = 2
• Matching nets to solids and predicting which faces of the net become opposite faces
• Finding surface area as the total area of the net

Why Choose LabEquip

Schools that give students Paper Nets of Solid Shapes to fold often keep one polyhedron-with-net set at the front of the class as a durable reference, and the Formation of Tetrahedron model extends the work to the simplest polyhedron. All three are in LabEquip’s Mathematics School Lab Products range.

Frequently Asked Questions

What makes a solid a polyhedron?

A polyhedron is bounded entirely by flat polygonal faces that meet along straight edges. Cubes, cuboids, prisms and pyramids are polyhedra. Cylinders, cones and spheres are not, because they have curved surfaces.

What is Euler’s formula for polyhedra?

For any convex polyhedron, the number of faces plus the number of vertices minus the number of edges equals 2. A triangular prism has 5 faces, 6 vertices and 9 edges, and 5 + 6 − 9 gives 2. Students can confirm it on each solid in the set.

What are the Platonic solids?

They are the five regular convex polyhedra: the tetrahedron, cube, octahedron, dodecahedron and icosahedron. In each one, every face is the same regular polygon and the same number of faces meet at every vertex. No other convex solid meets both conditions.

Can a solid have more than one net?

Yes. A cube has eleven different nets, and other polyhedra have several too. The net supplied with a model is one of them; students can draw others on squared or isometric paper and test whether they fold into the same solid.

How does the net help find surface area?

The net contains every face of the polyhedron laid flat, so the surface area equals the sum of the face areas measured on the net. For a triangular prism, adding the two triangular ends and the three rectangular sides gives the total surface area.

How is this different from paper nets that students fold?

Paper nets are meant to be cut, folded and sometimes glued, so they are used up over time. A polyhedron with net keeps a rigid solid alongside its pattern for repeated demonstrations, which suits teacher-led lessons and revision.

Last Updated: September 2026