Maths Investigation 2

Today we looked at a bit of Geometry.
Firstly Polygons: How many diagonal lines are there inside polyhedral shapes? And is there a general rule? Can the number be predicted?
We found that for a four-sided shape the total is 2, five-sided it's 5, six-sided it's 9, seven-sided it's 14, and eight-sided it's 20. So obviously the number of diagonals increases. To find a rule, we looked carefully at each corner, and we found it useful to notice, for every shape, how many diagonals came from each corner.
In the end we did come up with a rule, and used it to predict that the number of diagonals in a 100-sided shape is 4850 (phew!).
Here's our rule, where "s" means the number of sides on the shape:
(s-3) x s / 2. We checked it and it works for all the smaller shapes, so we think it will work for the larger ones too.

Then we had some time to work with Polyhedra. We looked at three nets and noticed that although they are all called pyramids, they were quite different. We folded and made the shapes, then designed our own nets which were made from at least three different 2D shapes.