The disphenocingulum
The disphenocingulum is Johnson solid number 90:
Disphenocingulum
58 pieces: 16 balls, 38 rods, 4 squares (323.48 g)
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A ring can be made from 17 disphenocingulums and 17 square pyramids:
Ring of 17 disphenocingulums
1020 pieces: 255 balls, 680 rods, 85 squares (5.54 kg)
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The ring is not exact but it is nearly so (although not as nearly as the ring of 16 sphenocoronae).
