Building with 3D shapes

We have been investigating 3D shapes for our problem solving session this week.  We had pictures of some models built with 3D shapes and we had to finds out if they could be built or not.  If not, why not?

 There was lots of discussion about the properties of shapes - faces, edges, vertices, flat surface, rounded surface, as well as practising our reasoning skills ("That's because....)  It was good fun seeing if our predictions were right  - and there were a few surprises!  Some of us then drew our own models and predicted if they could be built or not.

Holly said straight away that model F couldn't be built -why?

We found out that if a shape had a flat shape it would balance on another shape with a flat face.

We couldn't balance a shape on top of the triangular prism because of the thin edge joining the vertices.
But what about if we turned the prism so the triangular face was flat on the bottom?

No shape could balance on top of a shape with one vertex, such as the cone or square based pyramid.

Abigail and Olivier thought this model wouldn't balance, but it did!  They reasoned that it must be because the cuboid could balance on top of the prism and the cuboid below!