By default, dice shapes are organised by category. The categories are:
- Platonic
Shapes which are Platonic Solids; where all faces, edges, and vertices share full symmetry - these are therefore the most fair dice shapes.
- Catalan
Shapes from the Catalan Solids, duals of the Archimedean Solids - each is isohedral and therefore a fair die shape.
- Bipyramids & Trapezohedra
Two sets of fair dice shapes, each can be squashed/stretched. Sophie's Dice has all possible bipyramids & trapezohedra up to 30 faces.
- Antiprism (Crystal) Dice
Antiprisms are fair dice when discounting the top and bottom faces, crystal dice have points on those faces to prevent settling on them. Sophie's Dice includes every possible crystal dice up to 20 faces
- Prism (Barrel) Dice
Prisms are fair dice when discounting the top and bottom faces, barrel dice have points on those faces to prevent settling on them. Sophie's Dice includes every possible barrel dice up to 20 faces
- Coins
Flat shapes with only two faces
- Curved-Face Solids
Shapes which are isohedral but don't have flat faces. These are fair dice shapes, but are impracticle to manufacture fairly in real life.
- Anisohedral
Shapes with multiple different faces - these are not isohedral and so could not be considered fair shapes when rolled in real life (despite what some might say). When rolled in Sophie's Dice however, these will be fair as long as "Realistic Bias" is not enabled.
- Sphericons
Shapes constructed by twisting half of a bicone or bipyramid. All but the 1-sided sphericon are anisohedral (though their faces are the same, the symmetries between them are not).
- Novelty
Novelty shapes, most will not produce fair random numbers under any condition.
- Sets
There are several 'sets' of shapes which share a common theme, most contain dice to be used with RPGs which use standard polyhedral dice (d4, d6, d8, d10, d12, d20) but some may include extras, such as the framed sets.
- Framed
Shapes which have a secondary 'frame' which can be customised with a second material
- Frame Only
Shapes which have only a frame, and are otherwise hollow
- Rounded Faces
Shapes which are curved across their entire faces.
- Rounded Corners
Shapes which have have had their corners rounded
- Truncated
Shapes which have their vertices truncated
- Mine Shapes
Shapes which have spikes at their vertices.
- Sliced
Shapes made up of multiple flat slices
- Anti-gravity shapes
Shapes where the faces are not connected by edges, instead floating independantly.
- Spinners
Shapes which are essentially bipyramids or trapezohedra, but instead are spun around a spindle.
- Skewed
Shapes where faces are made up of edges of different lengths. (These are still isohedral, and therefore fair die shapes)
- Seed
Shapes which are essentially very smooth antiprisms
- Spikey Solids
Shapes which have sharper-pointing vertices
- Compound Cylinders
Shapes made from cylinders (and cones, in the case of the tetrahedron) which intersect
- Cosmic Geometry
These shapes are not real, do not look at them, they are ancient lies which warp existence.
- Fidgies
Concave shapes made of one or two kinds of triangle, whose convex hull forms a fair die.
- Other Shapes
A variety of other shapes which don't fit into other categories are here (these are all also fair dice)