First and Second Year of Secondary Education


- Elements, Euler's polyhedral formula.
Regular polyhedra
- Tetrahedron.
- Octahedron.
- Icosahedron.
- Cube or hexahedron.
- Dodecahedron.
- Tetrahedron 2, compound. 
- Cube-Octahedron, compound.
- Dodecahedron-Icosahedron, compound.
Surface areas of prisms and pyramids.
- The net of a prism.
- The surface of a prism.
- The net of a pyramid.
- The surface area of a pyramid.
Volumes of prisms and pyramids.
- Volume of a cuboid.
- Volume of a prism.

- Formula of the volume of pyramid.
- Volume of a pyramid.
A curiosity.
- A very strange polyhedron.


These activities are designed to be viewed on a 17-inch screen and with a resolution of
1024 x 768 pixels because some windows show measurements in centimetres and millimetres that, when viewed with another configuration, will not correspond with reality; and the size of some windows can even be too big.

The design of these activities allows autonomous learning, but they also raise questions for students to investigate using the windows and to do their own deductions. Therefore, students should take notes in their notebooks so that they can share ideas afterwards.


  • To recognise the different polyhedral shapes in the objects in our surroundings.
  • To distinguish the elements of a polyhedron.
  • To know Euler's formula, that is, the relation among the faces, edges and vertices of a non-toroidal polyhedron. 
  • To investigate the symmetries and relations between regular polyhedra.
  • To practise the measurement of short distances in centimetres and millimetres, finding accuracy in the measurement and the correct expression of the values. 
  • To calculate the area of the base and the lateral area of prisms and pyramids.
  • To calculate the volume of a prism.
  • To deduce the equation of the volume of a prism and to apply it.
  • To get into the habit of writing down the corresponding measurement unit in the outcome of an exercise.
  Eduardo Barbero Corral
Spanish Ministry of Education , Social Afairs and Sport. Year 2007

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