See also some previous posts on this
Piping the boundaries of the dual can be a way to easily convert any object into a 3d printable lattice:
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You can’t cover a full sphere with just hexagons. You can cover a half sphere, but the hexagons will have to vary a lot in size.
With the exception of dodecahedron, it is impossible to cover the entire surface of a sphere with pentagons only, but you can do it with a mixture of hexagons and pentagons, and with many other shapes. These domes are called geodesic grids. You can make these domes easily with the help of free Rhino plugins called Rhinopolyhedra (Polyhedron command) and Rhinowaterman (WatermanPolyhedron command).
Rhinopolyhedra plugin is here: http://www.food4rhino.com/app/rhinopolyhedra
Rhinowaterman plugin i…
Here’s a go at this.
It relaxes a triangular mesh to get as close to regular as it can, then takes the incircular dual, then fits a perfectly regular (and flat) hexagon to each cell of this.
The base mesh before subdivision I used here is a hexagonal antiprism, which I believe gives a better fit for this shape than simply an icosahedron. It still has only 12 pentagons, but in a different arrangement. I think any other coarse mesh with more irregular faces is likely to result in worse gaps.
Re…