(0,18,0,80,24)-deltahedron

(0,18,0,80,24)-deltahedron
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Type	Deltahedron

Rods	360 ×
Spheres	122 ×
Author	Amafirlian 15:42, 26 July 2007 (UTC)

Star-shaped (0,18,0,80,24)-deltahedron consisting of 8 convex spheres connected to 4 rods (forming a cube), and 12 concave spheres connected to 4 rods (forming an octahedron).

It is completely rigid, and highly reminiscent of Alain Lobel's frames.

Building Instructions[]

It is a tough one to build!

Start by building a cuboctahedron, and place it on the table before you for mental orientation: the square dimples in the main model are oriented like the squares in the cuboctahedron, and there is a convex bulge on the main model for each of the spheres in the cubocathedron.

For the main model, assemble four bulges with one dimple, reinforcing the dimple temporarily with a square panel, to limit the degrees of freedom whilst building. Don't be tempted to do the same for the square looking outward spikes, they turn out not to be exact squares.

It's really easy to get lost whilst assembling the model, so use symmetry to keep orientated: looking at the pictures build symmetrically from the foundation, taking care to count the valencies of the spheres - the four-valent points should be fairly obvious, and the seven-valent vertices mark awkward corners.

Another difficult feature of this model is that it is hard to close, because so many of the rods are arranged right at the edge of the steric limit. As soon as you can see the closure pattern, suspend the last square in the middle of the top of the model, like a swing.

Then, fill in the holes, not one by one, but simultaneously, always placing rods symmetrically. Done this way, when the last dozen rods approach, and you have to distort the whole frame to find the right fit, the local distortions will me minimized.

(0,18,0,80,24)-deltahedron

Building Instructions[]

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