# Truncated Spheres

Discussion in 'My Work In Progress' started by Magic, Dec 21, 2010.

1. Magic Well-Known Member
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!

Last edited: Dec 21, 2010
2. clsn Well-Known Member
Nice. I had made a d9 using the same technique. I was going to un-"hide" it, but looking at it I realize that I just numbered the faces even though it doesn't land with a face up. Woops. Well, something else to fix. I'd like to make a bunch of other odd-sided dice ("odd" both in the sense of an unusual number for sides of a die and also some that are odd and not even), and do some randomness tests on them, see if they're close to fair.

It looks like your method of intersecting spheres with dual polyhedra yields the same results as the one that I tried, with slicing identical circles off a sphere at the appropriate points (but yours is probably simpler).

3. Magic Well-Known Member
Yes, I suspect that the 2 methods leads to the same result and our D9 are more or less the same (yours is actually "rounder" that mine, I think).
Feel free to show it in this thread if you wish, once it is finished.

For the numbering, I thought doing it as the D10 4-fold (with numbers in the edges) but another method would be to put the numbers near the bottom, on the adjacent faces, as in a standard D4.

4. Magic Well-Known Member
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.

5. clsn Well-Known Member
6. Orangery Member
Magic, the dice look great. I didn't think the D10 with four fold symmetry would work. It looks fair too! I have not seen anything like it before.

Look forward to seeing the D9.

Unfortunately I have still yet to decorate the D32's that you made for me as I have been bogged down with other things.

Last edited: Jan 6, 2011
7. Magic Well-Known Member
Thanks Orangery. On my side, I have still to number the D32 and the D9.
I ordered all the other truncated sphere dice today. I will test their fairness as soon as possible.

8. Orangery Member
Personally I think the number on a die should be read face up whether on a face or an edge. I don't particularly like the 'normal' D4 where you have to read along the bottom.

I like all your D10's except the ones with cones (I'm funny like that :laughing. My favourite is the one that is made up from 2 squares and 8 non-regular pentagons as it has the optimal surface area to land on and as far as I know, is unique.

I think It would be nice (as you have come this far) to finish off the set with a D4, D8 and D20 as an alternative to the usual D&D dice and give them a posh name.

The D9, D14 and D32 could be available as add-ons. I hope to buy most of these dice this year once some spare cash comes available.

9. Magic Well-Known Member
Yes you are right, I can do a D4 (numbered on the round part), a D8 and a D20 to complete the set.
And perhaps also a D12 based on a rhombic dodecahedron.

So many things to design, so little time...

10. Magic Well-Known Member
11. Magic Well-Known Member
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.

Last edited: Feb 20, 2011
12. Orangery Member
This looks a fun die... nice work. Do you think you will get round to making up a 'set'?

By the way have you tried 'Uni Posca' pens. They are great for colouring the dice. I tried them out on the D32's you made (pictures to follow). I painted the numbers in by hand (still have three to do). The colours look good (they still need to be varnished) but I want to try and improve on the numbering as I like things to look consistent (may try rubber stamp blocks).

Numbering of a normal D32 from 0-31 might be used for days of the month. If the die lands on a zero the player could choose any day of his/her choice (or throw again). Just a thought.

I started on my web site... http://the-orangery.weebly.com/

13. Magic Well-Known Member
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.

Last edited: Feb 20, 2011
14. Magic Well-Known Member

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!

15. Orangery Member
I wasn't sure what you meant about the numbers failing as I don't think you have mentioned having trouble with any of the other die. I'm okay with 2D stuff, not 3D,

16. Magic Well-Known Member
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...

Last edited: Feb 23, 2011
17. Orangery Member
I have just received the three different versions of the D10's. They are brilliant! Every dice collector should have these. Now I just need to paint them without messing up.

18. Magic Well-Known Member
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[sup]th[/sup] die.

19. Youknowwho4eva Well-Known Member
wouldn't that be 33333rd? Keep up the good work. These are definitely different.

20. Magic Well-Known Member
I should have pronounced it mentally to avoid my mistake...
Thank you for the kind words, Mike.
The D9 and D11 are already available. Other will probably come later.