3D shapes

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

How many edges of a cube need to be coloured black to mean every face has at least one black edge?

A blue cube has blue cubes glued on all of its faces. Yellow cubes are then glued onto all the visible blue facces. How many yellow cubes are needed?

A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?

A solid 'star' shape is created. How many faces does it have?

A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?

An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?

The net shown here is cut out and folded to form a cube. Which face is then opposite the face marked X?

How many cubes can you see?

Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?

Weekly Problem 20 - 2010
You have already used Magic Squares, now meet a Magic Octahedron...

Weekly Problem 37 - 2010
An ant is crawling around the edges of a cube. From the description of his path, can you predict when he will return to his starting point?

Can you make the numbers around each face of this solid add up to the same total?

A tetrahedron has each corner cut off to produce a solid. What is the total length of the edges of this solid?

What is the smallest number of colours needed to paint the faces of a regular octahedron so that no adjacent faces are the same colour?

The base of a pyramid has n edges. What is the difference between the number of edges the pyramid has and the number of faces the pyramid has?

The diagram shows the net of a cube. Which edge meets the edge X when the net is folded to form the cube?

Four cubes are placed together to make a cuboid. What is the surface area of this cuboid?

A cube is rolled on a plane, landing on the squares in the order shown. Which two positions had the same face of the cube touching the surface?

What is the surface area of the solid shown?

The edges of a cube are stretched, can you find the new surface area?

Which of these can be obtained by rotating this shape?

Which faces are opposite each other when this net is folded into a cube?

What is the total surface area of this shape?

The net shown is folded up to form a cube. What is the largest possible vertex product?