Approximate Spheres with Polyhedrons

The most standard way to build sphere has been using Lowell’s sphere. But when building a large sphere, a SNOT sphere is too part consuming and too heavy. Since we can approximate circles with polygons, surely we can approximate spheres with polyhedrons. We are going to focus on Archimedean solids, and mainly talk about truncated icosahedron (Wikipedia is really my friend, saved me all of the explaining).

A truncated icosahedron (I’ll call it Buckyball from now on) has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices, and 90 edges. To build a Buckyball, you need 2 things, a way to build regular hexagon or pentagon and a way to build arbitrary angles. Since its hexagon to hexagon dihedral angle is 138.189685°, you won’t be able to build it with any fixed angular parts.

Hinge Plate Version

The first way that we are going to look at is probably the most popular way. Parts needed are also the most readily available. Hexagon is built with hinge plates, and intersection angle is built with clip & bar plates. You can adjust the length of the hexagon sides to change the size of the sphere. If you leave it at that, then the result would be a skeletal sphere. If you want to add something to the hexagonal faces, you’ll need 3-Branch Cross Axle W/Cross H. Once you have a concentric technic axle, you can add dish or other things to cover up the hexagon.

sphere

 The end result of the skeletal version looks like this.

sphere1

Technic Version

The second version uses this technic Toggel Joint for hexagons and technic axles and beams for angles. Because the friction pin is not enough to hold the whole hexagon together in place, you also need the 3 Branch Crosshole W. Hole to secure the hexagon. You can attach dishes and the like on to the hole in the center.

sphere2

The end result looks like this.

sphere5

CCBS Version

Lego Character and Creature Building System (CCBS) is the revamped Bionicle & Hero Factory building system. I personally love it. CCBS parts can make the sturdiest spheres. First make hexagon using any limb parts. Then connect the hexagons together with double-cup parts like 3M Double Ball Cup- Hf 2012 or Beam C 5M Cup/Cup Ø10.2.

sphere4

The complete sphere looks a bit like this. You can connect things onto the unconnected balls.

Picture1

Examples

Here are some of the examples MOCs that I’ve done with these sphere. Again with all of these spheres, you can adjust the length of the hexagon sides to change the size of the sphere.

Alien Cottage

globe

Demonic lamp

As always, download the LDD file below.

Spheres (187.4 KiB)

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