2-Piece Pyramid, 4-piece Pyramid

Tasks
Combine the two blue pieces to make a pyramid. Hint: What happens to the square face of each piece?
Combine the four red pieces to make a pyramid. Hint: Two small red pieces can be put together to form a piece of the blue pyramid.
With the 4-piece puzzle we can see one cross-section of the tetrahedron is a square. What is the other cross section?
Maths

The 2-piece pyramid is made from two identical pieces. Since a tetrahedron only has triangular faces, the square faces of the 2-piece pyramid have to vanish. This can be achieved by putting the square faces together. In other words, the square is hidden inside the tetrahedron. In fact, it is a cross-section of the tetrahedron. The four edges of the square lie on each of the four faces of the tetrahedron.
The 4-piece pyramid is made from four identical pieces. However, we can put two red pieces together to form an object which looks like a blue piece, and solve as before. In this case we can see one cross-section of the tetrahedron is a square, and another cross-section of the tetrahedron is a triangle.
History

The tetrahedron is called a Platonic solid. These solids have identical regular polygon faces, (such as triangles, squares and pentagons), and the same number of faces at each corner. There are only five Platonic solids, the tetrahedron, cube, octahedron, icosahedron and dodecahedron. They are named after the ancient Greek philosopher Plato, who associated these solids with the classical elements of fire, earth, air, water and a fifth element called “quintessence”.
People
Plato c. 428BC-348BC
Plato was a philosopher from Ancient Greece. He was a student of Socrates and the teacher of Aristotle. Plato set up the first institution of higher learning in the Western world, called the Academy. While not a mathematician himself, Plato associated the five regular solids (tetrahedron, cube, octahedron, icosahedron, dodecahedron) with the four classical element (fire, earth, air, water) and a fifth element, quintessence.
Applications

The tetrahedron shape can be often found in chemistry when looking at the shape of molecules. For example, methane is a central carbon atom surrounded by four hydrogen atoms. The hydrogen atoms repel each other and want to be as far apart as possible, so form a tetrahedron shape.An irregular volume in space can be approximated by an irregular triangulated surface, and irregular tetrahedral volume elements. This has applications in aerodynamics and engineering.
Maths at Home

Make the 2-piece puzzle at home by printing this net onto thin card. Cut out the two shapes and glue the tabs to make the 2-pieces.