3DPrinting
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Took a quick crack at doing it by hand, subdiving an icosphere in that specific way and copying it around.
Definitely a bit time consuming but not too bad for that many faces. I imagine scaling it up would make finding an automated solution more important though. That was maybe 10 minutes of work? not bad
scaling it and solidifying yields this
Step by step:
Basic icosphere
Subdivided the edges and connected to opposing corners to find the middle of the triangle
Cut the last edge in and dissolved unnecessary edges
Repeated for each level, then duplicated and rotated 5 times to make the sphere out of these divided faces (mirrored on the z axis to save half the work)
Selecting all those midpoints with a side on xray view
From there just scaling them out to make the pyramids