5 Sided Dice Template
Mazie Wingeier
I've just bought a d8, and noticed that the number arrangement is different from my other one. My new die has only even numbers on one half, and only odd on the other half. My old die has 1,8,5,4 on one half and 2,3,6,7 on the other.
For 6-sided dice it is normal to have sides paired 1,6 / 2,5 / 3,4, each pair adds to 7. There are two different ways of having this arrangement. If you take a large number of 6 sided dice from different sources it is very likely you will find you can group them into two sets that both follow this arrangement, but which vary in how you can rotate them to match.
For why this arrangement is common, many sources claim that it helps to keep averages correct for imperfectly-shaped dice. If your 'cube' is shorter on one edge, it would favour two opposite sides - if those sides don't give you an overall advantage, this is seen as fairer. Although it may also have been driven by numerology, and the design kept by tradition.
Rotate the die so that you are looking down onto a point with the 1 at "12 o'clock" and withthe 2 at either "3 o'clock" or "6 o'clock" (one of these positions will be possible, if not thenyou have already got 1 and 2 on opposite sides, which of course makes the total 3). Read the numbers, startingfrom the 1, in clockwise order.
If you see one of the above variations, it does not prove that the opposite sides sum to 9. If you are not sure, then you need to check that also. And worth repeating: It is not a problem if you find a d8 that does not have one of the above patterns or does not have opposite sides sum to 9.
I tried to find some extra information related to why this is happening because this is the only die size that has this happen. All the other dice have standard distributions: D6 sums to 7, D10 (starting with 0) sums to 9 (as well as the percentile dice that sum to 90), D12 sums to 13 and D20 sums to 21. This is on any brand or manufacturer.
The current common choice is one of the configurations which implement the opposite-faces convention: values on opposite faces sum to one more than the number of faces. In the case of the d8, the sum is nine.
There are 8!=40320 ways to map numbers 1...8 on the regular octahedral die (d8), but many of these configurations are rotationally indistinct. The size of the symmetry group G=24. There are 8!/G=40320/24=1680 rotationally distinct configurations. This count includes mirror images. If we conflate the mirror images, then the count reduces by half to 840 symmetrically distinct configurations. Rolling a fair d8 in a perfect world means that dice makers may choose any of the configurations. But, the world is not perfect. In our imperfect world, dice makers have chosen a few configurations, and the chosen few have appeared on the market and later in dice collections.
Even so, dice implementing configurations other than the opposite-faces convention are available. Earlier this year, I bought a 1-8-5-4 d8 from GameStop. A visual inspection of the faces on the six square pyramids reveals that this die does not implement the even/odd split; each pyramid has two even and two odd numbers on its faces. Nor does it implement the high/low cluster.
I've haven't seen an 8 sided die before that wasn't the "1,8,5,4 // 2,3,6,7" combination before as life total die are normally higher using d10s and d20s. When you have a die that doesn't have the smallest paired up with the highest values, there is the chance to increase the odds of a better than average roll depending on how you throw it. That said, if you're not trying to cheat with it and throwing it intentially so it rolls to one side over the other it shouldn't matter.
Make your own dice in this fun and easy do-it-yourself (DIY) art craft project for both kids and grownups. There are many printable paper dice templates to choose from: 6-sided, 10-sided, and 12-sided dice in black & white, ivory, red, blue and green. The 10 & 12 sided dice are particularly great for role playing board games.
Thank you! I was hunting 10 and 12 sided dice to make a math game for our home school. Your website was very easy to access and templates were easy to download and print, even on my dinosaur computer. I appreciate that. Many thanks.
They can all be created without ever constructing any of the component polygons. The trick is in knowing the angle between the faces (known as dihedral angles) and then setting your saw blade to the appropriate angle and your miter gauge to the appropriate plane angle (or its complement) associated with each poylgon.
This particular request is absolutely the most difficult of the 5 because at some time you will be cutting with your workpiece resting on a relatively small triangular base which is inherently unstable. You will need to devise a fixture that holds the workpiece in such a way that your hands are nowhere close to the saw blade and the workpiece is stable. I would not recommend that anyone other than an experienced woodworker even attempt it.
Even the seemingly easy tetrahedron will undoubtedly have several failures before an acceptable die is cut. I recommend that you master each of the smaller four (even cubes can prove to be a challenge) before entertaining the construction of an icosahedron.
After you cut the dice, you will want to smooth their faces, but as soon as you begin to sand the size of faces will be changed due to the removal of material. If you do not sand exactly parallel to the triangular faces, they will quickly be notably no longer equilateral.
A 20 sided die is an icosahedron. All vertices of the 20 faces lie on the surface of a sphere. This is the foundation of a geodesic dome, but that's only slightly relevant. You should be able to find the math for a single frequency geodesic dome and have the calculations available for this application.
What that means is if you can find a wooden sphere of 5 cm, the above-noted calculations would give you the chord lengths for each "strut" of the geodesic sphere. In your case, the strut length corresponds to the edge of the die faces. The calculator shows 2.628 cm for an edge.
Set an ordinary drawing compass to that measurement and place an arbitrary starting point on the sphere. Mark an arc in the direction of the next vertex. Place the compass center on that arc and create another arc crossing the original starting point and another in the approximate location of the third point. Repeat until you have two arcs at each location.
If the math is correct and the precision of the compass is sufficient, you should be able to pepper the sphere with these points. The progression should result in some points being coincident to previously created points. If not, there's an error. Adjust the compass, erase the previous points and begin again.
If hand tools are your only resource, you'll want to clamp the sphere in such a way as to place three of the points level to the earth. A hand plane, a file/rasp and sanding blocks applied in a careful manner will allow you to remove the wood that is above the first selected triangle.
A 12 sided die requires regular pentagons, removing the easy compass answer. I would consider to build a pentagon shape in thin plastic to match the math and trace faces on the sphere with that as a template. That method seems more hit-and-miss than a compass and triangles. One can create triangles with a compass that results in a pentagon, if you have the math right and the patience. I found a slideshow presentation for creating pentagons with a compass, but it's for flat areas and would be useful only for creating a template.
I have a laser cutter and would create masks/templates, but create a half-dozen with 1 mm variation and see how well they fit when traced on the ball. It would probably be useful to sand away previous marks for those tests that don't fit until you get to a working template.
I have a mini-mill for flattening the shapes, but the clamping aspect would be insane. It would require a special jig to hold the sphere as the job progressed, removing portions of the ball each time. I suppose that once you get a pair of parallel faces, things would get a bit easier, or maybe not.
Hi,
I'm not on this site as much as I used to be, but I have received quite a few "you've got a new PM on cake central" and its pretty much always asking how I did my 20 sided die. A recent one got me thinking I should just make a post so people don't have to email. Though please feel free to PM if you have any questions. CC will let me know you rang.
So first off, a 20 sided die seems really complicated. But we really took a look at it, and found a way to break it down easier.
We found the wiki article for "icosahedron" to be a big help. There is an orange & yellow flat template that may be of use, as well as some formulas if that's your thing. But the big breakthrough was the interactive rotating model. From that we broke the cake down like this.
We chose to balance the cake on one point for ease of carving & layout. This makes basic shape a pentagon. You'll need two of the same size pentagon boards. These pentagons DO NOT line up - each point will meet the middle of one of the sides. 10 equal triangles form the middle of the die - 5 point up & 5 point down. I wish I could give you a size or template, but its all dependent on your size cake - but DO make a template of your triangle face! (or two!) Each of the bases of these triangles form the pentagons. 5 more triangles share the other side of that pentagon, with their points coming together to make the top & bottom points. (Think of a crown shape, then push in the tops to meet.)
So you'll need to figure out what to make your base out of. . . we used styrofoam. I know, I know...use whatever makes you happy. Doing this again, we would either make a special base of wood or make a pentagon "table" and use RKT under it for the point. But the main point is the cake isn't actually resting on this point, of course. We had a support running through the middle of the cake that screwed into the base. 3 more dowels kept the base on point, and those were hidden by the smaller die. Again, I would do it different now, but that's what we did then. You can see one of the side support dowels in the pic.
On top of this base, you'll use round cakes, larger than you need. The edges of these triangles point OUT - the top or bottom-most points will be the highest, the triangles will go lower into the base at the pentagon. It really helps to have a die to look at. Put the second pentagon on top of the cake & use your triangle templates to help know where to carve. Use a very very dense cake & keep your edges as sharp as possible. Then repeat the bottom for the top point.
We coated the entire cake in a thick layer of buttercream and a large sheet of fondant and from there I used my fingers to mold & sharpen the edges of the die. (Like Bronwen Weber molds her fondant on her cakes -- see her face in the pumpkin cake for the food network challenge.) You have to work quickly, just pinch the edges up gently. Once the fondant starts setting they'll stay.
The numbers in a 20 sided die don't all go the same way. Use a real one for reference. We just painted our numbers on, but cutting them out of fondant would look much better.
So good luck & hope this helps!
The cake: