Nets, Vertices, Edges and Faces - Exploration+Practice
The applet above shows the number V of vertices, E of edges and F of faces of the solid that you obtain using the displayed net.
Calculate the value of V - E + F.
What is the result?
Select New net to show a new net of a solid. Explore the solid, and calculate the value of V - E + F for your new solid.
What is the result?
Change the number of sides of the base of the solid, using the related slider, and calculate V - E + F again.
What do you notice?
You have just shown by example an interesting property of polyhedrons, called "the Euler Formula for polyhedrons", that was discovered by the German mathematician Leonhard Euler in 1752.
It works for most solid shapes - except those with a hole in the middle.
Well done!