Five of the seven dice are the five Platonic solids, which are the only five shapes where every face is identical. Those give you the d4, d6, d8, d12, and d20.

The sixth, the d10, isn't a Platonic solid at all, because a ten faced one cannot exist. It's a different shape entirely, invented much later.

The seventh is a second d10, marked differently so the two can be rolled together to produce a number from 1 to 100.

Five perfect solids, one workaround, and one copy of the workaround. That's seven.

Now the interesting part.

Somewhere around 400 BC, Greek mathematicians became fascinated by a particular kind of shape. One where every face is the same regular polygon, every edge is the same length, and every corner meets at exactly the same angle. Perfectly regular, in every direction, with no side more special than any other.

They found five.

The tetrahedron. Four triangular faces. The simplest solid that can exist in three dimensions, and the only one of the five that doesn't have a face parallel to the ground when you roll it. This is why a d4 famously refuses to roll and instead just sits there, judging you.

The cube. Six square faces. The one shape here that everybody already owned, thanks to several thousand years of board games.

The octahedron. Eight triangular faces, like two square pyramids joined at the base.

The dodecahedron. Twelve pentagonal faces. Roman bronze versions have been dug up across Europe and nobody is entirely sure what they were for, which is its own excellent rabbit hole.

The icosahedron. Twenty triangular faces. The most sphere-like of the five, and the one that would eventually become the most recognisable object in tabletop gaming.

Plato wrote about these in the Timaeus and believed they were the building blocks the universe was assembled from, one shape per element. That's why they carry his name, even though he didn't discover them.

This is the part that makes the whole thing satisfying.

There is no sixth Platonic solid. Not undiscovered, not waiting to be found with better maths. There cannot be one.

Euclid proved it in the Elements, around 300 BC, and the proof is simple enough to follow. To form a solid corner you need at least three faces meeting at a point, and their angles have to add up to less than 360 degrees. If they add to exactly 360 the shape lies flat, and any more than that and it cannot close up at all.

Work through the regular polygons and you run out almost immediately. Triangles work with three, four, or five meeting at a corner. Squares work with three. Pentagons work with three. Hexagons have 120 degree angles, so three of them make exactly 360, and the shape stays flat forever. Everything beyond a hexagon is worse.

Three plus one plus one. Five solids. That's the entire list, and it always will be.

A die needs to be fair, and fairness is harder to guarantee than it looks.

The Platonic solids solve it completely. Because every face is identical and the shape is symmetrical in every direction, there is no physical reason for any one face to come up more often than another. You don't need to test it. You don't need to roll it ten thousand times and check. The geometry rules it out.

That's a rare and lovely property, and it's why these five shapes became dice rather than any of the thousands of other shapes available.

It's also why cheap dice sometimes aren't fair. The shape guarantees fairness only if the manufacturing is accurate. Bubbles in the material, uneven faces, or a sloppy mould will all reintroduce bias that the geometry was supposed to eliminate. Dice collectors test for this by floating dice in salt water and watching which face keeps rotating upwards. If the same number surfaces every time, something inside is off balance.

What each die actually does

Here's where the neat mathematical story breaks down.

Ten is how humans count. We have ten fingers, we use base ten, and any game with percentages needs a die that produces ten outcomes.

There is no Platonic solid with ten faces.

For years, this was worked around rather than solved. Early dice sets shipped with a d20 numbered zero to nine twice, and you rolled it for anything needing a number out of ten. It worked, but nobody loved it.

The solution eventually arrived in the form of a shape most people have never heard of: the pentagonal trapezohedron. Ten kite shaped faces, meeting in a zigzag seam around the middle, with a point at the top and bottom. It looks like two five sided pyramids that have been twisted against each other.

It is not a Platonic solid. The faces are kites rather than regular polygons, so it fails the definition.

But it is still perfectly fair, because all ten faces are identical to one another and the shape is symmetrical in the way that counts. It turns out you don't need Platonic perfection to make a fair die. You just need every face to be the same as every other face.

The modern d10 became standard around 1980, and it's the newest thing in the box by roughly 2,300 years.

The last die is a second d10, marked 00, 10, 20, and so on up to 90.

Roll it alongside the normal d10 and you read them together as tens and units. A 30 and a 7 gives you 37. Two zeroes conventionally read as 100.

That's a percentile roll, or d%, and it's why the seventh die exists. It isn't a new shape or a new idea. It's the same workaround, printed differently, so the set can produce any number from 1 to 100 without anyone needing a hundred sided die.

Those do exist, incidentally. They roll like a golf ball and take an uncomfortably long time to stop.

Why the d20 became the star

Of the seven, one has escaped the table entirely. The d20 is on t-shirts, tattoos, and shop signs, and people who have never played a game recognise it instantly.

Partly that's because it does the most work. In most modern systems the d20 decides whether you hit, whether you dodge, whether you notice the trapdoor, and whether the lie you just told landed. Rolling a natural 20 is the best moment in the game, and rolling a 1 is the funniest.

The rest is geometry. Twenty triangular faces is the closest any of the five gets to a sphere, which makes it the most pleasing to hold and the most satisfying to roll. It tumbles rather than clatters. It looks engineered.

Two and a half thousand years after Greek mathematicians proved it was one of only five perfect shapes, it's a keyring.

We didn't set out to make dice.

CMY Cubes has always been about the geometry of light: translucent objects in cyan, magenta, and yellow that mix colour as you turn them and hold them up to a window. Somewhere along the way we worked our way through the Platonic solids, because if you're making objects out of pure geometry you eventually end up there.

The Original Cube is a hexahedron. The Aether is an octahedron. The Motus is an icosahedron.

A d6, a d8, and a d20.

We had been making dice for years. We just hadn't put numbers on them.

Which, in hindsight, explains why our comment sections filled up with people asking us to.

What are the 7 dice in a D&D set? A d4, d6, d8, d10, d12, d20, and a percentile d10 marked in tens.

Why is a d20 shaped the way it is? It's an icosahedron, one of the five Platonic solids. Twenty identical triangular faces, symmetrical in every direction, which makes it fair to roll by geometry rather than by testing.

Is the d10 a Platonic solid? No. There is no Platonic solid with ten faces, and there cannot be. The d10 is a pentagonal trapezohedron with ten kite shaped faces. It's still fair, because all ten faces are identical.

What is the percentile die for? Rolled with a standard d10, it produces a number from 1 to 100. The percentile die supplies the tens, the standard d10 supplies the units.

Are all dice actually fair? Only if they're well made. The shape guarantees fairness in theory, but bubbles, uneven faces, or an inaccurate mould will bias a die in practice. Floating one in salt water and watching which face rises is the usual home test.

Why are there five Platonic solids and not more? Because the angles at each corner have to add up to less than 360 degrees to close into a solid. Work through the regular polygons and only five combinations satisfy it. Euclid proved this around 300 BC.