3D shapes and their properties

Are these statements always true, sometimes true or never true?

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

Make a cube out of straws and have a go at this practical challenge.

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?

What 3D shapes occur in nature. How efficiently can you pack these shapes together?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?