Math Question

paul_bartlett

I am trying to create a sphere using 60 triangles each extruded 1 inch and the bottom surface is beveled at 8.95 deg and the 2 side surface are beveled at 13.22 degrees. when I assemble 5 of them which gives me a pentagon shape the last one over laps the first on by a small amount meaning I do not have the 13.22 angle quite right. Would anyone know how to figure out the correct angle? 12 of these pentagons would create the sphere I am trying to get.
https://cad.onshape.com/documents/2a58d84a32fa24a92fe052f7/w/915d6437d094bcab63b4b12f/e/5a10fa294451dfc5847b9ec6

paul_bartlett

Similar to this only mine would be 1" thick wood triangles. Notice that 5 triangles assembled make a pentagon shape as I have done in my Onshape file. the angle slightly off as you can see when I assembled the last triangle. 
https://cad.onshape.com/documents/2a58d84a32fa24a92fe052f7/w/915d6437d094bcab63b4b12f/e/5a10fa294451dfc5847b9ec6

john_mcclary

I wouldn't go off of definite angles, rather use the geometry itself and build off of that. Angles will accumulate error the more you link together. It's better to let the parasolid engine slice it up.

Check out this guy's walk through for an Icosahedron
https://www.youtube.com/watch?v=AZJMIVVUHiI

paul_bartlett

Thanks for the help but this is only 20 triangles and all 3 sides of the triangle are the same length. With a 60 triangle the base is a different length than the 2 sides and the  chamfer angle is one angle and the 2 sides are another angle. I would love to see how someone would build this. I started it here using the angles but they are a little off. 
https://cad.onshape.com/documents/2a58d84a32fa24a92fe052f7/w/915d6437d094bcab63b4b12f/e/5a10fa294451dfc5847b9ec6

john_mcclary

I understand that was not the same shape, I was merely giving an example of how it should be modeled to try and avoid rounding errors from math equations. (which is likely why your example is slightly off)

CAD can be picky and cause mate errors, or faces being out of alignment if it is even slightly off. In these cases where irrational or high decimal precision numbers are used, it is usually better to build off geometry and take advantage of boolean operations to cut the faces and angles in 3D space.

But it sounds like you may be describing a "pentakis-dodecahedron" according to This Site
I'm not a mathematician so I don't know for sure

But it looks like there is enough information to describe your shape with math on that site.

jon_sorrells

Like John said, it's generally better to avoid calculating the angles and typing them in, let Onshape do the calculations for you.

Here's a document I made with a similar shape: https://cad.onshape.com/documents/88a894fd013dabb95e52dd3e/w/fd346d43a1da771a7dd6c767/e/40d586d3c86c7c106fb0250b (I used equilateral triangles, so the final shape is not quite what you're looking for, but hopefully this is helpful).

I started with making the pentagon shape out of 5 triangles.  I made one sketch with a pentagon, then another sketch with a triangle, where one point was constrained to be coincident to the vertex of the pentagon, and the hypotenuse was set to be the same length (so that it would be an equilateral triangle).  Then I lofted the first sketch to the point of the second sketch to get the desired shape.

Next, we need 3 of these pentagons to come together at a vertex, so I made a pentagon with vertices connected to two midpoints of a triangle.  I used the same method as before to make a triangle in another sketch to find the height of the center vertex, and then transformed the part from before into place.

The center of the polyhedron will be the same distance from these two vertices, and on the same plane as the triangle sketch from the previous step, so two lines constrained to the same length as each other give us the center point.  Then loft from the first part to the centerpoint to get one section of the final polyhedron.

From there, I patterned the section a few times to get the finished shape.

paul_bartlett

This is exactly what I am trying to create in Onshape The 60 triangles are not equilateral the base is a different length than the 2 sides. Still no clue as how to create this because of the  non-equilateral triangles. I can definitely do it if the triangle sides are all the same. Sorry to keep hounding on this. I just cant seem to let it go. But maybe I'll have to.

NeilCooke

This looks about right:


https://cad.onshape.com/documents/3a40059de1a0758ff8e1527e/w/fbec920598b1f8a352f30418/e/eb9b7e0dabb852fa03571647

john_mcclary

Very elegant solution @NeilCooke

paul_bartlett

I like it but to make one of these out of wood with each of the 60 triangles being 3/4" thick I need to know the Dihedral angle  (bevel/miter on each edge).  Can this be found from this model somehow. I do know the base bevel/miter angle is different than the the 2 side angles. I know it impossible to cut the miters perfect and the accumulation of error will have to be dealt with. If I can draw it in OnShape then I would be able to adapt that method to other similar projects.
https://cad.onshape.com/documents/3a40059de1a0758ff8e1527e/w/fbec920598b1f8a352f30418/e/eb9b7e0dabb852fa03571647

NeilCooke

Yep - just loft a face to the center - https://cad.onshape.com/documents/3a40059de1a0758ff8e1527e/w/fbec920598b1f8a352f30418/e/d62f17a2f036530e7e47f9f2

paul_bartlett

I do not seem to be able to do that. Could you give me an example or do 2 triangles in the model.

NeilCooke

Click the link above 

paul_bartlett

Thank you, Mission accomplished. I have learned a lot thanks to Neil and everybody here.