Need help patterning a hexagonal prism around a sphere

matthew_goehring

It's hard to put down the shovel, but here I am... deep inside a hole of my own creation. I am mostly a self taught Onshape user, and have little functional knowledge of geometry to understand why what I'm doing isn't working. I'm attempting to use a set of sketches and the circular pattern tool to arrange what's basically a hexagonal prism around the outside of a sphere. I'm also using a series of sketches on planes to connect points across the outside profile of the sphere. These planes contain the entities I'm patterning the prism with. The main problem I'm facing is that when I arrange the prisms along these guide sketches, the pattern gradually loses alignment and the hexagons overlap in a non-uniform fashion. I feel like this problem must have an easier solution than the insanity I've been working with in my document here: https://cad.onshape.com/documents/39155957293aac7c62b9dd4f/w/8ba88bb64ec93e8bff535215/e/79fec97a399560f93274c74e?renderMode=0&uiState=6667c2a29459c7761a44df48

Please tell me in excruciating detail all of the ridiculous things I'm doing improperly, I need to hear it so I can get better.

NeilCooke

This may help:
https://cad.onshape.com/documents/261d380bbcc214b3e7ec933d/w/e36c79629104111d9f232c9d/e/66c88bd0ec654ad3da5e6530

It's similar but not the same, but in any case, create a small section that can be patterned at the end.

_anton

I should remark that it isn't actually possible to tessellate the surface of a sphere with just hexes; some of them have to be pentagons (think a football/soccer ball).

https://www.wikiwand.com/en/Geodesic_polyhedron
https://en.wikipedia.org/wiki/Goldberg_polyhedron

Perhaps this would help? https://cad.onshape.com/documents/2c40f522f1b5a02f6ce9ce01/w/32e0799ad10a8f40ac24abb5/e/dd23a5b64fbc7cefbf67ffbd

jelte_steur814

I think the most efficient way computatively would be to create a triangular pattern on the face and then a point pattern for the hex parts combining it into a composite part. However that triangular pattern may be difficult. Fill pattern FS only works on flat faces... 

below is an attempt with circular patterns. you could play around with the instances and angles. It's very slow though.

https://cad.onshape.com/documents/55de7c59fc9251c7b016e7db/w/c0220edda631dd231e4b3606/e/ef97d8b91de351a347ea8775?renderMode=0&uiState=666854022928f64a3afd66fd 

matthew_goehring

@NeilCooke @_anton @jelte_steur814 Thank you all so much for all this useful info and examples, I see so many new tools here I've never used and some very relevant examples. The articles about these geodesic polyhedrons were especially enlightening.