Newbie -Reciprocal frame calculations

[Andrew G]

Greetings. Just stumbled across this group as I've been playing around with some reciprocal frames.  Also a new sketchup user - and racking my brain to figure out how to work that program.  However, I have found some unbelievable models in the warehouse to give me some guidance if not new ideas.   I came across a couple models: icosahedron, truncated icosahedron, and pentakis dodecahedron ... all using square wooden struts.

I was thinking of trying to duplicate them myself. That's looking at 120 or 90 identical struts each with several cuts to accept the other struts. 

Was curious if there was a basic/known formula to calculate the angles that someone could share or point me to a particular source. 

Thanks.

[TaffGoch]

Hang in there, Andrew. I've been pretty busy the last couple of weeks, but will have time to help, after tomorrow evening.

Here's a depiction of the basic "skeletal" geometry of the three puzzles:

-Taff

[TaffGoch]

Andrew,

You start the process with the basic "fan" geometry.

If you add dowels (nexors) that just touch each other, you get nexorades.

Switching to fatter square-cross-section sticks, you get the orientations of the three wood reciprocal-frame puzzles.

Note that each puzzle employs repetitions of TWO distinct stick lengths (color-coded above.) The sticks in each puzzle are NOT identical, as you initially assumed.

Once the geometric orientations are thus established, SketchUp can "intersect" the sticks, to define the notches, as the LAST step.

_________________________

As it turns out, I SketchUp-modeled one of the puzzles, years ago, using "fat" dowels:

https://taffgoch.deviantart.com/art/Geodesic-Puzzle-201922604

-Taff

[TaffGoch]

Andrew,

"Cutting" the notches is done with SketchUp's "intersect" feature. Here you can see my results, for the first puzzle:

Note that the left puzzle (red/yellow) has lines that define notches, while in the second puzzle (green/cyan,) the sticks cross each other, but no notch lines are present, since the "intersect" step has yet to be done.

Here is where I processed the intersections to produce the notches. Each notch-depth is "halved," so that the intersection overlap is equally shared by the two involved sticks.

Note that the stick lengths differ, and the notch depths and angles differ, as well:

Since I made the puzzle sticks as SketchUp components, notching one modifies all similarly-named component sticks. So, if a modify one of the yellow sticks, the other 59 yellow sticks in the puzzle change, as well. The same concept applies to editing the 30 red stick components - by editing just one of them.

Final desired results:

-Taff

[Andrew G]

Amazing. You have no idea how impressed that I am. Did you have this already done or did you just create it?  

My issue in SketchUp (one of many ) is getting all of the pieces intersecting equally.  And I was assuming that they would all be identical - or close to it.  (Likely because I have a dodecahedron where all the sticks are identical.)   

So where you halve all the sticks so that each piece shares the intersection equally, I'm assuming that you just as easily could keep the ends of each stick intact and its just the center two cuts that carry the entire intersection?   And once the cutting is done - is there a way to "automatically" show the angles and dimensions or is that measured independently?

Thanks.

-Andrew