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Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?

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Cutting a Cube

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

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Instant Insanity

We have a set of four very innocent-looking cubes - each face coloured red, blue, green or white - and they have to be arranged in a row so that all of the four colours appear on each of the four long sides of the resulting cuboid.

Net Result

Stage: 3 Short Challenge Level: Challenge Level:1

$E$ is opposite $X$

When the shape is folded up, imagine $X$ is on top. This means $B$ is on the left hand face and $C$ is on the right hand face. This means $A$ is on the back face and $D$ is on the front face. This leaves $E$ on the bottom face, so opposite $X$.

This problem is taken from the UKMT Mathematical Challenges.