It is known that the area of the largest equilateral triangular
section of a cube is 140sq cm. What is the side length of the cube?
The distances between the centres of two adjacent faces of another
cube is 8cms. What is the side length of this cube? Another cube
has an edge length of 12cm. At each vertex a tetrahedron with three
mutually perpendicular edges of length 4cm is sliced away. What is
the surface area and volume of the remaining solid?
Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the relationship between Euler's formula and angle deficiency of polyhedra.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?