# 3D Geometry, Shape and Space - June 2004, Stage 2&3

## Problems

### Building Blocks

##### Stage: 2 Challenge Level:

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

### Right or Left?

##### Stage: 2 Challenge Level:

Which of these dice are right-handed and which are left-handed?

### A Chain of Eight Polyhedra

##### Stage: 2 Challenge Level:

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

### Cut Nets

##### Stage: 2 Challenge Level:

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

### Painted Cube

##### Stage: 3 Challenge Level:

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

### Triangles to Tetrahedra

##### Stage: 3 Challenge Level:

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

### Tetrahedra Tester

##### Stage: 3 Challenge Level:

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?