Hi all,

After working with Orangery on this D32 (not numbered yet)

I decided to go on the idea of making dice from truncated spheres.

As you know, a round D6 can be defined as the intersection of a cube and a sphere:


Using the same method, I also designed a rounded D12 (intersection of a dodecahedron and a sphere).


As I originally wanted to make a D10, I put back two opposite portions of sphere to the D12 to get this round D10 with a 5-fold symmetry:

Then, instead of using the original portions of sphere, I replaced them by cones (tangent to the sphere) to get this pointed D10:


Another D10 with a 4-fold symmetry can be obtained by using a different underlying polygon with 10 faces (2 squares and 8 non-regular pentagons):

Note the strange way I had to numbered it: this is due to the fact that a face is not always opposed to another face but to an edge.

Finally, playing with truncated spheres and cones, I found this strange shape that is mid-way between a sphere and a cube.

Don't know exactly what to do with it (not a die anyway because it can stop on a "edge", even though it has no edge ).

Currently I am working on a 3rd D10 with a 3-fold symmetry (not finished yet) and also on a D9... So, more news will come soon!

[Updated on: Tue, 21 December 2010 22:23 UTC]

Hi all,

Here is my last family of truncated sphere D10. After 5-fold and 4-fold symmetry, these are the 3-fold D10s.
There are two models:
- the rounded D10 with 3-fold symmetry
- the pointed D10 with 3-fold symmetry

Both are base on a D14 non-regular cuboctahedron. This truncated sphere D14 numbered twice from 1 to 7 is also available.
To obtain the D10s, I add 4 portions of sphere (rounded version) or 4 tangent cones (pointed version) to the D14 to "cancel" 4 out of the 14 faces. So the symmetry of those D10s is the same as the symmetry of a tetrahedron (regular D4).

Check this picture to see them or click the links above.

Next steps will be having the D14 with twice the days of the week, and finishing numbering the D32.

• Attachment: D14_D10_3f.jpg
  (Size: 26.96KB, Downloaded 1984 time(s))

[Updated on: Thu, 06 January 2011 15:18 UTC]

Another member of the Truncated Sphere family (asked by Orangery ): the D4 Sphere.

Because the numbers are written exactly on the vertices, it is much easier to read the result than on traditional D4 (tetrahedron). And it should also roll better.

• Attachment: D4Sphere.jpg
  (Size: 9.61KB, Downloaded 1771 time(s))

[Updated on: Sun, 20 February 2011 08:02 UTC]

Hi Orangery,

You mean a set including the still missing D8 and D20?
Well, I am in the process of beginning the D8, but it will take some time. In the meantime, if you wish a special set of existing dice, just PM me.

The numbering of the D32 is a nightmare for me: each time I beging to look into it, I see new problem. I have to find the exact angles between the faces and, say, the horizontal plane if I want to do it proprerly (well, basically I need some courage ).
Numbering from 1 to 31 with an extra symbol (like a star) to represent either 0 or 32 or "replay" can be an idea.

I didn't try Uni Posca pens, but I heard about them in this forum. I have to see if they are available in France.
For now, I let Shapeways dye the dice and for inking the numbers, I use "Hybrid Gel Grip Mettalic", some gel ink rollers with 0.8mm balls from the Japaneese Pentel. The white in particular works very great. Then I finish them with some coats of acrylic varnish.

Good luck with your website!

[Updated on: Sun, 20 February 2011 11:18 UTC]

D8 Sphere added !

It was quite easy to do the first time, but there were not enough polygons in the rounded part. Adding more polygons made the process of "extruding" (should I say intruding?) the numbers fail quite often...
But finally, I did it!

• Attachment: D8Sphere.jpg
  (Size: 14.55KB, Downloaded 1749 time(s))

Carving numbers on dice, as any boolean operation (union, intersection, substration...) is a very... "random" operation. Sometimes it works, sometimes it fails...
It is (and has always been) a pain to do...

I will probably order the D4 and the D8 but not immediately: as an anti-addiction policy, I do not place a new order as long as the current one has not been delivered. And my latest order has not arrived yet and does not include dice, sorry...

PS: the downloads are just people reading the message, not peple ordering the die, unfortunately...

[Updated on: Wed, 23 February 2011 21:11 UTC]

Thanks Orangery: I am very happy that you like them (and I can only agree with you: any dice collector should have them ).
After dying or painting them, I recommend to ink the numbers with some gel ink pen. Gel is important so that the ink stay in the indentation instead of diffusing in the neighbourhood... And then some varnish...
Let us know the outcome.

I take advantage of this post to show you a die I did for Kevin Cook: this is a D33 to celebrate his 33333^th die.

• Attachment: D33Kevin.jpg
  (Size: 23.87KB, Downloaded 1551 time(s))

The long awaited Truncated Sphere D20 is now available!

This is the intersection of an icosahedron with a sphere. As you can see, due to the fact that a vertex is surrounded by 5 triangles, the rounded area is larger than in other Truncated Sphere dice. So the faces are smaller and the numbers too.
The distance from one face to the opposite one is 2 cm. This die is hollow, with a thickness of 1.5 mm (suitable for Alumide for instance).

• Attachment: D20.jpg
  (Size: 15.24KB, Downloaded 1448 time(s))

I also designed a D10 for percentage and a new version if the D6 (circle faces nearly in contact and wall thickness of 1.5 mm only).
As a consequence the Truncated Sphere Dice Set is now available !

This set is composed of 7 regular Truncated Sphere Dice:
- D4
- D6
- D8
- D10
- D%
- D12
- D20
Ideal for dice collectors and RPG players!

I will probably create later another set for unusual Truncated Sphere dice (D9, D11, D17 etc.)

• Attachment: SphereDiceSet.jpg
  (Size: 18.96KB, Downloaded 1452 time(s))

I have seen outstanding results in metal after sanding and polishing, but my post-production skills stop at inking and varnishing plastic...

The Rhombic Dodecahedron is definitvely different from the regular Dodecahdron and will come with the Rhombic Triacontahdron (D30).
By the way, the Rhombic Dodecahedron is from the same family as the D9 and the future D15 (because 9=3+3+3, 12=4+4+4 and 15=5+5+5)

I plan also to make a different D8.

Concerning the D10s, you are speaking of the D10 with 4-fold symmetry (polyhedron with squares and pentagons) and the D10 with 5-fold symmetry (derived from a regular dodecahedron), right?
Is there a problem with the 3rd one (D10 with 3-fold symmetry, derived from the D14) or is is just that you did not test it?

[Updated on: Mon, 11 April 2011 21:19 UTC]

@Orangery No, unfortunately, n cannot be 1 or 2. Or more precisely when it is 2 the polyhedron is degenerated.

For instance, 1+3+3+3+1 implies that the face of the poles are triangles (because n=3). If you put n=2 then the poles degenerate into simple edges (a polygon with two vertices is a "double-edge") and what you actually get is 2+2+2 which is a simple cube (D6)...

Same thing for 1+n+n+1 (n=4 gives your favorite D10 )
For n=3 you get the regular octahedron (D8) and for n=2 you can consider that the poles degenerate into perpendicular edges and you obtain the regular tetrahedron (D4).

The new D8 will actually be a 4+4, like the regular octahedron, but with a twist of 45° on the four lower faces.

I also have some ideas for a D3...

@Henryseg Yes, I had a look at them and at the repulsion force polyhedra of Martin Trump, but basically I found it difficult to take advantage of this information (maximum angle for the cones or coordinates of the center of the points). So, sometime I use them to fin a good approximate position for the face but then I try to solve equations to maximize the radius of the circles.

[Updated on: Wed, 13 April 2011 10:36 UTC]

As announced in the previous message, I am glad to present the Alternative D8 Sphere.
It is not based on the regular octahedron but on an trapezohedron ("antidiamant" in French) that are dual of the antiprisms.


It is a co-creator, so you can choose your numbering.
With numbers on edges, the number will be on top of the die, when it lies on a horizontal plane. With the numbers on the bottom faces, you will have to look under the die to find out the result. Choose no numbers if you prefer contemplating the shape or if you would like to take care of the numbering by yourself!

• Attachment: D8Alt_poly.jpg
  (Size: 12.11KB, Downloaded 1348 time(s))

I am glad to introduce the D15 Sphere:

3 rows of 5 faces (5 at each tropic, 5 at the equator).
The numbering follow the usual rule (as for the D9 for instance): the sum of each row is constant (it's 40 in this case), the sum of two numbers of the tropic symmetic to the equator plan, and the sum of two numbers of the equator circle symmetric to the "middle number" (8 here) is constant (it's16 in this case). Note that there must be an exception (all the numbers cannot go by pair since there is an odd number of face ) and that is 8: 8 cannot have a symmetric since the sum of two symmetric numbers is 16 (and only 8+8 = 16).

• Attachment: D15.jpg
  (Size: 13.44KB, Downloaded 1248 time(s))

This a a die I designed a long time ago and that I forgot numbering.
So, after a long time on the drawing table, here is the D18 Sphere:

As the number of faces is even, each number is exactly on a face (sometimes, these dice look very usual ).
Instead, the numbering is very interesting in this case.
Opposite faces numbers sum to 19, obviously. As a consequence any group of 8 numbers of a large diameter sum to 76. A more unexpected consequence is that any group of 5 numbers follows this strange rule: if you sum the double of the central number to the 4 other surrounding numbers, you obtain 57.
Example in the rendering image:
...4..
9 18 5
...3..
2x18 + 4 + 9 + 5 + 3 = 57
But the most interesting property in this particular numbering is that the sum of the six numbers surrounding a spherical zone is always 57.
Example here: 18 + 5 + 7 + 11 +13 + 3 = 57
I had to use a computer to find the good combination (there are a lot of them, by the way).

I could number this die from 1 to 9 twice (I found a way of doing it where the 8 numbers of the large diameters always sum to 40) or from 1 to 6 three time or even from 1 to 3 six times. Let me know if you want some particular numbering.

• Attachment: D18.jpg
  (Size: 14.78KB, Downloaded 1260 time(s))

[Updated on: Sun, 01 May 2011 08:49 UTC]

I have sent along a couple of pictures of the D10's that I bought from you (3 sorts). The black and white one turned out pretty good but I hope to redo the other two (I didn't have a fine enough pen for the brown die).

• Attachment: Dice 10.JPG
  (Size: 130.94KB, Downloaded 1140 time(s))

As for the D32 football dice, well I must admit I got in a bit of a muddle with the numbering. Some are not even finished. I tried using rubber number stamps for one of them but the white ink did not cover very well and it was difficult positioning numbers .

I used 'Uni Posca' pens for the base colours and the numbering (obviously hand written!).

• Attachment: Dice 32.JPG
  (Size: 70.14KB, Downloaded 1114 time(s))