Roll D4, D6, D8, D10, D12 & D20
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The D4, or four-sided die, is a regular tetrahedron — one of the five Platonic solids first described by the ancient Greeks and proven to be among the most geometrically perfect objects in mathematics. Every face is an equilateral triangle, every edge is identical in length, and the four vertices are spaced as far from each other as geometry allows on a sphere.

Unlike every other polyhedral die, the D4 has no natural "top face" when it comes to rest. Instead it balances on a triangular face with a single vertex pointing skyward. Two reading conventions exist in the hobby: some dice show the result at the bottom edge of each visible face, while others show it at the top vertex. Both are valid; what matters is consistency within a set.

The humble D6 is a regular hexahedron — a perfect cube — and it is unquestionably the most recognised die on earth. Six square faces meet at right angles; twelve edges are all identical; eight vertices each join exactly three faces. This beautiful symmetry means the cube can tile three-dimensional space perfectly, filling every gap without overlap — something no other Platonic solid can do alone.

The opposite-faces-sum-to-7 rule is not arbitrary. It emerges from the geometry: the cube has three axes of symmetry through opposite face centres. Assigning opposite faces to sum to (n+1) — where n is the number of faces — is the convention adopted thousands of years ago, and it guarantees the most uniform distribution of weight across every axis, making the die as fair as possible.

The D8 is a regular octahedron — exactly two square-based pyramids joined at their equatorial plane, creating eight identical equilateral triangular faces. It belongs to the same family of Platonic solids as the cube, and the two are actually mathematical duals of each other: if you connect the centres of a cube's six faces, you draw a perfect octahedron inside it, and vice versa.

This dual relationship means the D8 and D6 share the same axes of rotational symmetry. Every face of the D8 is identical, every edge is the same length, and every vertex is surrounded by exactly four triangles. The result is one of the fairest dice in the polyhedral set — its low, wide rolling profile gives it exceptional stability and tumbling characteristics.

The D10 is the odd one out among polyhedral dice: it is a pentagonal trapezohedron, not a Platonic solid. Its ten faces are kite-shaped (deltoid) quadrilaterals arranged in two interleaved rings of five, meeting at top and bottom vertices. This geometry is sometimes described as a "twisted" antiprism, and it has no equivalent in classical Greek solid geometry.

Because 10 is not the number of faces of any Platonic solid, dice manufacturers historically used various approximations. The modern trapezohedron design — adopted across the hobby in the 1980s — is a beautifully engineered solution: the kite faces are carefully proportioned so the die rolls and lands fairly, even though the faces are not regular polygons.

The D10 is the only die in a standard polyhedral set with kite-shaped faces rather than regular polygons. Its vertices are deliberately not normalised to a perfect sphere during manufacture — a move that keeps each kite face mathematically planar, ensuring the numbers land cleanly.

The D12 is a regular dodecahedron — twelve regular pentagonal faces, thirty edges, twenty vertices. It is perhaps the most geometrically remarkable of all the Platonic solids: Plato himself associated it with the cosmos, writing in the Timaeus that the god used the dodecahedron "for arranging the constellations on the whole heaven."

The dodecahedron and icosahedron are mathematical duals: connect the centres of a dodecahedron's twelve faces and you draw a perfect icosahedron inside it. This means the D12 and D20 share a deep geometric relationship, even though their faces are entirely different shapes — pentagons versus triangles.

The D12's rolling characteristics are superb: it is large enough to handle comfortably, heavy enough to roll convincingly, and its twelve pentagonal faces give it excellent stability. Yet in most RPG systems it sees relatively light use, which has made it a die celebrated by those who play classes that actually need it.

The D20 is a regular icosahedron — twenty equilateral triangular faces, thirty edges, twelve vertices, with exactly five triangles meeting at every vertex. It is the largest and arguably the most beautiful of the five Platonic solids, and it has become the single most recognisable symbol of tabletop roleplaying games worldwide.

Icosahedral dice are not a modern invention. A D20 carved from serpentine stone was found in Egypt, dating to between 2nd century BCE and 4th century CE. Greek and Roman examples exist in museums across the world, suggesting that humans have been fascinated by this shape — and using it for games and divination — for over two millennia.

The modern D20's twenty faces spread probability evenly across the widest range of any standard polyhedral die. Each face is guaranteed equal area, equal edge length, and equal angular relationships with its neighbours — the mathematical definition of a fair die. The opposite-faces-sum-to-21 rule is the highest-n version of the universal polyhedral convention and holds without exception on every properly manufactured D20.