The Cosmology Gallery in the picture is basically a 3V, 5/9 icosahedron dome, only using the "B" struts, the middle length struts. See:

simplydifferently.org/Geodesi...me_Notes

The green struts in the 3v, 5/9 dome (roughly mid-page) are the "B" struts. They are the same as the ridges/joints on the Cosmology Gallery.

If you were using sheets of plywood you would cut six pentagons, 10 hexagons, and 5 1/2-hexagons. You'd then bevel the hex-hex edges to about 69 (69 degrees, 5 minutes, and 30 seconds exactly) degrees and the hex-pent edges to about 71 degrees (71 degrees, 18 minutes, 30 seconds exactly). See:

www.coolmath.com/reference...edron.html

You'll need between 9 & 18 sheets of plywood/osb/insulated panels for this, depending on the size you want. You'll also have to cut strips of wood to join the panels, side screwing plywood at these angles would be near impossible.

If you built a classic 3V, 5/9 dome using 3/4 EMT as a Bucky Ball, you would need 59, or so-depending on the door, struts vs. 165 for a standard dome. You'd also only have 21 vs. 105 faces of a standard dome.