2D representations of 3D shapes

problem
Air nets

Age

7 to 18

Challenge level

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
problem
The perforated cube

Age

14 to 16

Challenge level

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?
problem
Picture a pyramid

Age

7 to 11

Challenge level

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
problem
Hamiltonian cube

Age

11 to 16

Challenge level

Weekly Problem 36 - 2007
Find the length along the shortest path passing through certain points on the cube.
problem
The spider and the fly

Age

14 to 16

Challenge level

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
problem
Building blocks

Age

7 to 11

Challenge level

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?
problem
Three cubed

Age

7 to 11

Challenge level

Can you make a 3x3 cube with these shapes made from small cubes?
problem
The third dimension

Age

5 to 11

Challenge level

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
problem
Christmas boxes

Age

11 to 14

Challenge level

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
problem
Icosian game

Age

11 to 14

Challenge level

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.