My 40 watt CO2 laser is offended at being called a “stencil cutter” 
.
I miss that comic.
That said, there are definitely lasers out there that put mine distinctly in the toy category. A laser suitable for small children, maybe. So I’m possibly inviting a kind of you call that a laser? response.
Thanks for helping me with this. I finally got it made. No calculations - just Solidworks features.
This is how I made it:
Parts 1-5
The following on all planes(Front plane, Top, Right)
Circle diameter 50 units
Circle diameter 49 units
Boss 1 unit (mid plane)
After choosing material Custom plastic (Appearance Black, Red, Blue, Green & Orange) save using their color in filenames like bl3x, re3x…
Part 6
Circle of diameter 49 units boss 1 unit
Circular pattern 5 times around 360 degrees
Save as finSphere
Part 7 (optional)
Sphere of 49 units (Custom white plastic)
Next mating (Assembly)
Load finSphere and place it’s origin in Assembly’s Origin (OK sign does it) aligning the axis.
One by one insert the five parts (bl3x, re3x…) mating them with the assembly’s origin (but not aligning axis) and parallel to the fins. You should use the same order as seen in the image above
(black, blue, red, green, orange).
Half way through - now you can insert the white plastic sphere to hide the other side. Look at the image again. This pentagon in upper left corner is your map of mating the rest. Black circle is intersected by orange and blue. You may have noticed that they have small knobs of their color on them. It means that they are crossed with their orthogonal circles. Other crossings have white knobs. Every pentagon has a knob of each color and a white one in between. So before mating the intersections of this pentagon, look at the other pentagons and intersecting circles to match the size. It will be easy if you placed the optional white sphere.
Here is my 3D-printed (bad quality) disdyakis triacontahedron. If I explained the fin-part of the design poorly, maybe this image clarifies things…
Interesting.
What kind of 3D printer is that? The surface quality is variable, but some of the surfaces are quite smooth. It does not look like either a filament or resin printer. Or maybe you used some postprocessing step, like acetone vapor treatment?
I see some interesting tools in the background. A nice machinist’s vise, some ER collets, a good size face mill… and a spoon 
. Is that your personal space or do you have access to a nice shop?
Well, it isn’t my living room. Those collets and other equipment are for Hyundai cnc milling machine I work with. 3d printer Makerbot Replicator +. I know the person who owns the spoon, but I haven’t seen him in two to three years…
Nice! Any kind of Hyundai CNC is a serious piece of equipment. I might be able to justify a Tormach someday… for now I do have a spoon (and laser cutter).
Looking at that first example it looks like the vertices lie on circles in 3 sets of 5 planes that are rotated around 3 axes. I’d create a set of 15 planes and draw a circle on each plane with a constant diameter. I’d use the intersections as vertices and then fill in each triangle with a surface. I’d take those surfaces and knit them into 1 surface and then convert that surface to a solid.