The Mysteries of Many-faced Mathematical Parrots Quiz

Answer: Any three-dimensional geometric solid with flat sides and straight edges

The word comes from the Greek "poly" = many, and "hedron" = face or base. Modern mathematicians, being the complicated individuals that they are, find this definition imprecise, and not at all satisfactory - but it's the one your maths teacher would probably have taught you.

Answer: Corner

If you're talking about more than one corner, they're called vertices. The word "vertex" comes from a Latin word meaning "turning point".

Answer: Tetrahedron

If you've ever played with polyhedral dice, you'll know the tetrahedron as the d4, the four-sided die (also known as the caltrop - even those who haven't played will probably wince at the thought of accidentally standing on a little pyramid made of hard plastic resin!) The caltrop is in reality a nasty little device composed of four spikes pointing outwards into the corners of a tetrahedron. This meant that when a number were tossed into the path of oncoming cavalry, each had a spike that was pointing upwards - with painful consequences.

Answer: Equilateral triangles

Which explains why a tetrahedron is sometimes called a triangular pyramid. The tetrahedron is also seen in chemistry, in a myriad of covalent molecules, starting with CH4, methane - which has a carbon atom in the centre and four hydrogen atoms in the vertices of a regular tetrahedron.

Answer: Cube

The cube has six faces, which are all squares, making it a regular hexahedron. It gives us the familiar six-sided dice, and numerous other common everyday objects. In chemistry, the cubic system is one of the most common shapes found in minerals - including crystals of sodium chloride.

Answer: Octahedron

The octahedron looks like two square-based pyramids with their bases stuck together. All the faces are equilateral triangles. It is found in nature as the form of crystals of fluorite or alum (you can easily grow crystals of potash alum to see this).

Answer: Kites

A pentagonal trapezohedron has ten congruent kite-shaped faces, five on top and five below, shifted so they fit together. It's called a pentagonal trapezohedron because it's the dual polyhedron to the pentagonal antiprism. (And what that means is far easier explained with diagrams - so feel free to look it up!)

Answer: Pentagons

The dodecahedron has twelve pentagonal faces, and twenty vertices. Not that you're likely to come across this one outside of a set of polyhedral dice (where it is the D12), playing with a Megaminx - a dodecahedral version of the Rubik's Cube, or a model in a Mathematics classroom! A few quasi-crystals form this shape.

Answer: Icosahedron

The icosahedron gets its name from the Greek "eikosi" which means twenty. The icosahedron turns up in nature - the herpes virus is an icosahedron, as are some of the amoeboid protozoa called Radiolarians. In gaming, besides being the shape of the iconic D20 polyhedral die, it is also the die used in Scattergories to choose one of twenty letters of the alphabet.

Answer: Platonic solids

Plato wrote about the five Platonic solids in his dialogue "Timaeus" in which he linked four of the five platonic solids with the four classical elements. The solid cube was earth; the tetrahedron with its upward point was fire; the octahedron was air; the icosahedron that rolls so easily was water; and the dodecahedron with its twelve faces (like the twelve signs of the zodiac) was the fifth element - "used for arranging the constellations on the whole heaven".