# 1: Perp vector to 3 curves. 2: Hexagonal sphere

**URL:** <https://discourse.mcneel.com/t/1-perp-vector-to-3-curves-2-hexagonal-sphere/200183>\
**Category:** Grasshopper\
**Tags:** windows\
**Created:** [February 24, 2025, 10:58am UTC](https://discourse.mcneel.com/t/1-perp-vector-to-3-curves-2-hexagonal-sphere/200183 "2025-02-24T10:58:12Z")\
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**Author:** ![DanielPiker](https://sea3.discourse-cdn.com/mcneel/user_avatar/discourse.mcneel.com/danielpiker/32/666337_2.png) [@DanielPiker](https://discourse.mcneel.com/u/DanielPiker)\
**Post date:** [February 24, 2025, 11:40am UTC](https://discourse.mcneel.com/t/1-perp-vector-to-3-curves-2-hexagonal-sphere/200183/3 "2025-02-24T11:40:44Z")

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The normal to a smooth surface is unambiguously defined, but when you have a faceted surface like this, which is not tangent continuous, there are multiple possible ways to assign a normal vector to the vertices. Which one is suitable here depends on what you want to do with it next.  
For example, you can take an unweighted average the normals of the surrounding faces, or you can weight these by area or angle. Also for this spherical geometry you could simply take the vector from the center of the sphere to each vertex, unitize it and use that as the normal.

As for creating a _full hexagonal sphere with even cells_, this is not possible. To make a closed sphere you will need some non-hexagonal faces. A popular choice is to use 12 pentagonal faces, with the rest being hexagonal. Also, even with these 12 pentagons, the hexagons cannot be all the same size and shape (except in a couple of special cases with few faces like [Chamfered dodecahedron - Wikipedia](https://en.wikipedia.org/wiki/Chamfered_dodecahedron)  
and [Truncated icosahedron - Wikipedia](https://en.wikipedia.org/wiki/Truncated_icosahedron))

> [@Dome with hexagons](https://discourse.mcneel.com/t/dome-with-hexagons/53663/3):
>
> 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](http://www.food4rhino.com/app/rhinopolyhedra) Rhinowaterman plugin i…

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