Rings
Nearly every letter in the
Geomag logo is tangential to its adjacent ones, the tangency «point» consisting of two pentagonal prisms together with the intermediate cube. The only exception is the pair EO, whose subjacent circles intersect in two points:
Intersection of two 20agons
946 pieces: 231 balls, 494 rods, 36 pentagons, 185 squares (4.75 kg)

Each 20agon has two lower pentagonal prisms and two upper ones with a face perfectly horizontal, which makes using vertical supports very easy. The same structure of the previous picture could easily make a double arch:
Double arch
691 pieces: 172 balls, 340 rods, 32 pentagons, 147 squares (3.44 kg)

With these elements many different constructions can be done; the 20agons seem strong enough to withstand stacking. Three examples follow:
Rings 1
2056 pieces: 490 balls, 1077 rods, 78 pentagons, 411 squares (10.26 kg)

Rings 2
3008 pieces: 710 balls, 1531 rods, 122 pentagons, 645 squares (14.84 kg)

Rings 3
2752 pieces: 650 balls, 1409 rods, 110 pentagons, 583 squares (13.60 kg)
