One can create triangles with a compass that results in a pentagon, if you have the math right and the patience. That method seems more hit-and-miss than a compass and triangles. 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. If you have a friend with a machine shop and a CNC milling machine and some CAD/CAM skill, see what he thinks.Ī 12 sided die requires regular pentagons, removing the easy compass answer. ![]() Once you've completed one of these 20 faces, reposition the sphere, level the next three points and make sawdust from the ball. 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. 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. Adjust the compass, erase the previous points and begin again. The progression should result in some points being coincident to previously created points. If the math is correct and the precision of the compass is sufficient, you should be able to pepper the sphere with these points. Consider instead to create clear marks for each vertex. It would be challenging to draw straight lines on the curved surface. The difference between this triangle and one drawn on flat paper is that the lines connecting them will not be straight, but will be curves along a great circle of the sphere. Repeat until you have two arcs at each location. 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. Mark an arc in the direction of the next vertex. Set an ordinary drawing compass to that measurement and place an arbitrary starting point on the sphere. The calculator shows 2.628 cm for an edge. In your case, the strut length corresponds to the edge of the die faces. 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. You should be able to find the math for a single frequency geodesic dome and have the calculations available for this application. This is the foundation of a geodesic dome, but that's only slightly relevant. All vertices of the 20 faces lie on the surface of a sphere. You can use it as a foundation to consider one option.Ī 20 sided die is an icosahedron. I'm unable to process the mathematics involved, but that doesn't make it an impossible task. ![]() If you do not sand exactly parallel to the triangular faces, they will quickly be notably no longer equilateral. 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.Īfter 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. I would not recommend that anyone other than an experienced woodworker even attempt it.Įven the seemingly easy tetrahedron will undoubtedly have several failures before an acceptable die is cut. 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. 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. Please provide an example of the best way to do this using the 20 sided die as an example. However, as noted in comments, a wooden fair die is unlikely to stay fair very long. ![]() ![]() If you entertaining thoughts of creating a fair die, the angles must be accurate. The respective angles are: polygon polygon polyhderon dihedral 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.Įasier said than done, but certainly requiring some sort of fixtures or jigs to pull off. They can all be created without ever constructing any of the component polygons. There are five regular polyhedrons made of equilateral triangular faces, square faces or regular pentagonal faces. The issue, as you probably already know, is not one of drawing regular polygons, but one of shaping regular polyhedrons.
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