A 3D link between maths, D&T,science and kids. Adrian Oldknow 8 December 2004

The regular polyhedra The regular polyhedra are sometimes known as the Platonic solids. There are only five of them. The faces of the tetrahedron, octahedron and icosahedron are equilateral triangles. The faces of the cube are ???? The faces of the dodecahedron are ????

Here are the triangular three.

A cube and a dodecahedron

Accounting For each of the regular polyhedra can you count the number of faces (F), edges (E) and vertices (V)? Tetrahedron: F = V = E = Cube:F = V = E = Octahedron:F = V = E = Dodecahedron: F = V =E = Icosahedron:F = V = E =

Leonhard Euler Dates: Swiss – from Basel F + V = E + 2 True for all polyhedra Try a square based pyramid F = V = E =

Semi-regular polyhedra There are 14 semi-regular polyhedra They are also known as the Archimedean solids. Their faces are a mixture of regular polyhedra. The same number of each type of face meet at every vertex. The truncated icosahedron has two hexagons and a pentagon at each vertex.

The truncated icosahedron

Accounting again How many hexagons H How many pentagons P How many edges E How many vertices V Does (H+P) + V = E + 2 Is Euler satisfied?

Buckminster Fuller Who was Buckminster Fuller? What is a Bucky Ball? What does “geodesic” mean? Where can you see Bucky Balls?

A Bucky Ball – familiar?

Black and blue should be what?

Carbon 60 Who is Harry Kroto? What is Buckminster Fullerine? What shapes do Carbon molecules have? Diamond? Graphite? What shape is C-60? Where do kids come across this shape?

So solid shapes are one link! Polyhedra in maths Molecular and crystal structures in science Shapes used in the built environment, shapes used to package objects,..in D&T Shapes met in the world outside school