Same size hexagons on curved surface like hemisphere

[user2918]

Hello
I want to cover a hemisphere with hexagons, but hexagons are not the same size and get smaller and bigger. How can I make them one size?

[tay.othman (tay.0)]

To get them close to each other you need to equalize them using kangaroo. It won’t be 100% exact but close enough.

Also you need to run it on a triangulated mesh.

Hexagonal Pattern Pavilion | Grasshopper + Kangaroo Catenary

[tay.othman (tay.0)]

I found a project that I designed few years ago, you can use the script to generate Hexagons & Pentagons, the script is a bit old and messy, but you can see how it may help you understand the principles.

Honeycomb Sphere.gh (30.9 KB)

also If you want to expand your knowledge furthermore, I highly recommend this Class:
https://thinkparametric.com/courses/panel-clustering-using-machine-learning-soumaya-museum

[DanielPiker]

See also some previous posts on this

Problems with Hexagon tessellation on half sphere

[image] moebiushexplanar.gh (9.4 KB)

Introducing TriRemesh - high quality triangular and hexagonal remeshing and shrink wrapping

Piping the boundaries of the dual can be a way to easily convert any object into a 3d printable lattice: [image]

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.
If you include some pentagons or heptagons you can get less variation in size. For general freeform surfaces you can get this sort of pent/hex/hept mesh with TriRemesh. For spheres specifically, you could use a geodesic dome, based on a dodecahedron.

Dome with hexagons

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…

Same size Hexagon on spheroid

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…