Sphere Dice Set

The Sphere Dice are solid dice obtained by intersecting a regular polyhedron and a sphere.
They are "as fair as possible": the shape is fair but, as the numbering remove some material, there could be a little bias (but probably not more than commercial dice).
Here you have all the 7 Sphere Dice in one set:
 - D4 Sphere
 - D6 Sphere
 - D8 Sphere
 - D10 Sphere
 - D% Sphere
 - D12 Sphere
 - D20 Sphere
For dice collectors and RPG players.

Get all the dice from D3 to D20 plus the D% and D24 by gathering:
- the Sphere Dice Set
- the DCC Expansion Pack
- the Odd Spherical Dice Set
- the D18

You may also be interested into the brand new D22.

Truncated Sphere D11 with 3-fold symmetry.

This die is inspired by the repulsion force polyhedra. Nonetheless, the underlying polyhedron (not rounded) is very different from the shape that can be obtained through this technique with 11 points repulsing each others.

Actually, I calculated the positions of 11 points to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere with the following constraints:
- 2 poles (upper and lower face - parallel to the horizontal plane)
- 3 points around each pole
- 3 remaining points corresponding to 3 faces perpendicular to the horizontal plane

The result is a truncated sphere with 11 circular faces of same radius.

It is numbered from 1 to 11: 2 numbers are on faces (poles), 6 between vertices and face and  3 on edges. The sum of the numbers on the 3 upper vertices surronding the North pole is 18.  Same thing for the sum of the 3 numbers on the lower vertices surronding the South pole and the sum of the 3 numbers on the edges of the equator.

This die is made of a shell of 1.5mm that contains support material to make it heavier. The engraved numbers have a 0.75 mm depth. They are quite big since they overlap the surrounding faces and thus should be very easy to read.

See this thread for more informations.

Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.

Breaking news!
The KickStarter project has been sucessful!
Thank you all!
This die will be mass produced in March 2013!

Truncated Sphere D14 based on a cuboctahedron.
Numbered from 1 to 14.

A D14 numbered from 1 to 7 twice is also available.

This a new version with a better engraving and a new orientation that should give better results.

Truncated Sphere D15.

This die is inspired by the repulsive force polyhedra although in this case, the underlying polyhedron (not rounded) is very different from the shape that can be obtained through this technique with 15 points repulsing each others.
Actually, I calculated the positions of points (5 at each tropic, 5 at equator, none at the pole) to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere. The result is a truncated sphere with 15 circular faces of same radius.

It is numbered from 1 to 15: all numbers are on edges.
The sum of the numbers on each tropic is 40 and the same applies to the equator.
Except for 8, all the numbers go by pair summing to 16: on the tropic two numbers symmetric relatively to the plane of the equator sum to16 and on the equator circle itself two numbers symmetric relatively to number 8 sum to 16. 

This die is made of a shell of 1.5 mm that contains support material to make it heavier. The engraved numbers have a 0.75 mm depth.

More informations in this post.

Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.

Truncated Sphere D32, regular edition.
Based on an idea from Orangery.

The underlying polyhedron is a non-uniform icosidodecahedron (a kind of polyhedral soccer ball).

The distance between two faces is 30mm. The thickness is 1.5mm but it is full of support material to keep it heavy.

It is numbered from 1 to 32 with the difference between two numbers on opposite faces being always 16.
If you take the sum of a face surrounded by 5 neighbours (there are twelve of them, that corespond to pentagons on the underlying polyhedron i.e. before the intersection with a sphere) and its 5 surrounding faces you will always obtain 99.

More informations this post and this other post.

See also the Frosted Edition (20 mm only in Frosted Detail and Frosted Ultra Detail).

D4 Shell

It's a Truncated Sphere D4 without faces!
The idea of keeping only the round part of a truncated sphere die when the numbers are located on vertices or edges is from Clsn (check his D9 for instance).
The thickness is 2 mm. Since it does not contain a lot of material, this die is quite affordable.

All the D4: 
  - Truncated Sphere D4
 - Concave D4
 - D4 Shell

See also the D8 Shell.

D3 Shell

Available Truncated Sphere Dice: D3, D4, D6, D7, D8, D9, D10, D%, D11, D12, D13, D14, D15, D16, D17, D18, D19, D20, D24, D32, D33
Alternative shapes: alt D7 (2-fold), alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed), Alt D24 (snub)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D3 Shell, D4 Shell, D8 Shell.

D8 Shell

It's a Alternative D8 Sphere without faces!
The idea of keeping only the round part of a truncated sphere die when the numbers lie on vertices or edges is from Clsn (check his D9 for instance).
The thickness is 2 mm. Since it does not contain a lot of material, this die is quite affordable.

See also the D4 Shell and this thread for more informations.

Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.

Alternative D24 Sphere

This is a Truncated Sphere D24.

This die is inspired by the repulsion force polyhedra. In fact, the underlying polyhedron (not rounded) looks like the two shapes that can be obtained through this technique with 24 points repulsing each others (two Pentagonal Icositetrahedra).
Actually, I calculated the positions of those points to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere. The result is a truncated sphere with 24 circular faces of same radius.

See this thread for more informations.

Available Truncated Sphere Dice: D4, D6, D7, D8, D9, D10, D%, D11, D12, D13, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed), Alt D24 (snub)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.

D24 Sphere

This is a Truncated Sphere D24.
The underlying polyhedron is a deltoidal icositetrahedron.

The numbering proposed here is very classical (opposite faces sum to 25).
A less expensive version is available in Antique Bronze Glossy with an alternative numbering here.

Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.

D7 Sphere 2-fold

It's a Truncated Sphere 7-sided die.
Most of the 7-sided dice are based on a pentagonal prism. This one instead is based on an original polyhedron with nice symmetries (globally, it has a 2-fold symmetry).

See this thread for more informations.

Available Truncated Sphere Dice: D4, D6, D7, D8, D9, D10, D%, D11, D12, D13, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed), Alt D24 (snub)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.

Geared D6

This D6 has its pips replaced by gears. The gears should all turn when you move one.
Dimensions are 3 x 3 x 3 cm. The thickness is only 1 mm. Specially designed for Frosted Detail.

See also its shell available in a wider range of materials.

More information in this thread.

It arrived! Warning: NOT FULLY FUNCTIONAL! I found a problem in the design, so I will fix it quickly.

See a video in CG rendering.
See the video of the first prototype in Frosted Ultra Detail.

D19 Sphere

It is the intersection of a 19 sided polyhedron, inspired by the repulsive force polyhedra, with a sphere.

Available Truncated Sphere Dice: D1, D3, D4, D5, D6, D7, D8, D9, D10, D%, D11, D12, D13, D14, D15, D16, D17, D18, D19, D20, D24, D32, D33
Alternative shapes: alt D6 (3-fold), alt D7 (2-fold), alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed), Optimal D11, alt D24 (snub)
Coming soon: D21, D22, D23, D50
Related dice: Concave D4, Concave D6, D3 Shell, D4 Shell, D6 Shell, D8 Shell.

D3 Sphere

Available Truncated Sphere Dice: D1, D3, D4, D5, D6, D7, D8, D9, D10, D%, D11, D12, D13, D14, D15, D16, D17, D18, D19, D20, D24, D32, D33
Alternative shapes: alt D6 (3-fold), alt D7 (2-fold), alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed), Optimal D11, alt D24 (snub)
Coming soon: D21, D22, D23, D50
Related dice: Concave D4, Concave D6, D3 Shell, D4 Shell, D6 Shell, D8 Shell.

Truncated Sphere D33 Frosted Edition

This is the Frosted Edition of the 33-sided die specially designed to be the 33333rd entry of Kevin Cook's dice collection.
This die has a diameter of 20 mm and a wall thickness of 1 mm only.
It should contain the white wax used as support material.

The numbering has been carefully studied.
All numbers are by groups of 3 that sum to 51:
 - the 3 numbers at the North and South pole
 - the 9 numbers at the equator and at the 2 tropic taken 3 by 3 (any 3 numbers at 120°)
All numbers sum to 34 by group of 2 (except obviously 17, since only 17 itself can sum to 17 to give 34):
 - all the numbers of the poles and of the tropics with their symmetric number relatively to the equator
 - all the numbers of the equator (except 17) with their symmetic number relatively at number 17
 

Concave D6

A sphere on which 6 faces have been carved as concave portions of spheres of the same radius.

D20 Sphere

The Truncated Sphere D20 is obtained by intersecting a sphere with a icosahedron.

This is one of the seven dice from the .

D10 Sphere for Percentages

Truncated Sphere D10, numbered from 00 to 90. Used with a regular D10, it allows you to get random numbers from 00 to 99 (percentages). 

This die is also part of the Truncated Sphere Dice Set.

D10 with a 4-fold symmetry.

I did this one before knowing about the repulsion force polyhedra, although the shape is the one of the typical result you can obtain through this technique with 10 points : the dual polyhedron has 2 squares and 8 irregular pentagons. I calculated the positions of those points to have a maximal radius for the circles resulting from the intersection of this dual polyhedron with a sphere. The result is a truncated sphere with 10 circular faces of same radius.
It is numbered from 0 to 9. Only 2 faces are opposite one to the other and can hold numbers. The others have edges as opposite, thus the numbers on 8 edges.

This die has an approximate diameter of 24mm and is made of a shell of 1.5mm that contains support material to make it heavier. The engraved numbers have a 0.7 mm depth.

More informations in this post.

The current version has deeper numbers compared to the ones in the pictures (0.7 instead of 0.5 mm).

Truncated Sphere D10 with a 3-fold symmetry.
Rounded version. A pointed version is also available.
Based on a D14 (non-regular cuboctahedron).
Numbered from 0 to 9.

More informations in this post.

Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.

Truncated Sphere D4

I was ask to make this die because it is easier to read the result than on traditional D4. It also rolls far better.

This is one of the seven dice from the Truncated Sphere Dice Set.

See this thread for more informations.

Available Truncated Sphere Dice: D1, D3, D4, D5, D6, D7, D8, D9, D10, D%, D11, D12, D13, D14, D15, D16, D17, D18, D19, D20, D24, D32, D33
Alternative shapes: alt D6 (3-fold), alt D7 (2-fold), alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed), Optimal D11, alt D24 (snub)
Coming soon: D21, D22, D23, D50
Related dice: Concave D4, Concave D6, D3 Shell, D4 Shell, D6 Shell, D8 Shell.

Truncated Sphere D17 with a 5-fold symmetry

This die is inspired by the repulsion force polyhedra. In fact, the underlying polyhedron (not rounded) is very similar to the shape that can be obtained through this technique with 17 points repulsing each others.

Actually, I calculated the positions of 17 points to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere with the following constraints:
- 1 point per pole (upper and lower face - parallel to the horizontal plane)
- 5 points around each pole
- 5 remaining points corresponding to 5 faces perpendicular to the horizontal plane

The result is a truncated sphere with 17 circular faces of same radius.

For the numbering, as usual:
 - the sum of the 5 numbers of the two tropics and of the equator is constant (and equals to 51)
 - the sum of the 2 poles, of two numbers of the tropics that are symmetric relatively to the equator, of two numbers of the equator that are symmetric relatively to number 9 is constant (and equals to 18)

See this thread for more informations.

Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.

Pointed Truncated Sphere D10, with a 5-fold symmetry.
A rounded version is also available.
Numbered from 0 to 9.

More informations in this post.

Truncated Sphere D12.

Numbered from 1 to 12.
This is one of the seven dice from the Truncated Sphere Dice Set.

More informations in this post.

This is a new version with 6 and 9 followed by a dot instead of being underlined. The orientation of the die has also been changed to allow a better printing.

Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.