There are over 300 dice shapes which can be customised in Sophie's Dice, this page describes how they are listed.

• Listing
• Categories
• Fairness Type

Listing

Each button in the Shape Select menu has different parts

• a. Face Count
How many faces the shape has.
• b. Inverted Collider
If visible, this icon indicates that the shape's collision mesh is different to its display mesh. When rolled in real life, these shapes would not settle with a single face pointing upwards, and would need their results read from the base.
• c. Anisohedral
If visible, this icon indicates that the shape is not isohedral - not all of its faces are the same. Anisohedral shapes do not roll fair in real life (and will roll less fair in the app if "Realistic Bias" is enabled).
• d. Standard Deviation
Displayed as a percentage, this shows how much deviation the shape presented after (10000*Face Count) rolls of testing. Whilst lower values do indicate fairer shapes, it is expected that even perfectly fair shapes have a deviation of around 1% after this many rolls. Be assured that all dice (apart from Novelty shapes, or Anisohedral shapes with "Realistic Bias" enabled) will roll fair.
• e. Shape Name
The name of the shape.
• f. Shape Icon
A preview of what the shape looks like. If the icon has golden elements, it indicates that parts of the shape can be customised with a second material.

Categories

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
• Prism
Unlike the barrel-type prism dice, these have their faces on the top/bottom sides counted. This makes them anisohedral.
• Framed Barrel
Shapes which have an inside part rotated so that their colliders need not be inverted
• Truncated
Shapes which have their vertices truncated
• Trunkis
Shapes which have had their vertices truncated and the new faces raised with a pyramid
• Rounded Faces
Shapes which are curved across their entire faces.
• Rounded Corners
Shapes which have have had their corners rounded
• Bevelled Shapes
Shapes which have their edges truncated.
• Faceted Shapes
Shapes which have been faceted in a gem-cut style.
• Recessed Shapes
Shapes which have a polygonal depression in each face.
• Protruding Shapes
Shapes which have a polygonal protrusion from each face.
• 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.
• 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.
• Linear Framed
Shapes which a single bent frame that traces the full convex hull without intersecting itself.
• Spinners
Shapes which are spun around a spindle on a vertical axis, rather than rolled. Spinners are normally flat with the result read from the top, but there are also teetotums (results read from the side), fall-flat teetotems (shaped to fall completely flat after spinning), and spinahedra (bipyramid/trapezohedra shapes with a spindle).
• Weighted-Void Spheres
Spheres with an interior void and loose weight moving within it. Because the void is a fair die shape, these spheres also make fair dice.
• 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)

Fairness Type

Shapes can also be sorted by their "Fairness Type". (Without "Realistic Bias" enabled, all dice will be fair, but this is a way I have of classifying dice shapes that you might find interesting if you've read this far!)

• General/True Fairness
Dice shapes in this category are fair in all circumstances (assuming they are solid with consistent density).
• Specific/Circumstantial Fairness
Dice shapes in this category can be fair only in one particular circumstance (changes to the circumstance that make the shape unfair include things like changing how many dice are rolled, how they are rolled, the material of the dice or the surface they are rolled on, the shape of the surface, atmospherics, and so-on).
In all realistic use, you can consider these shapes to be unfair and at least somewhat biased. Sometimes people may claim they have found a shape in this class that is fair - but really they simply tweaked the shape until it tested fairly for their specific circumstance.
• Physically Unfair
Dice shapes in this category are never fair in reality. They lack the required symmetry and will always present bias (though some more or less than others)
• Unknown
Okay this is mostly just a joke category for novelty shapes. They are actually either unfair or they are one-sided.