Assemble the pieces to make a 'lantern'. Each row of the cylinder is a hexagonal antiprism made of twelve equilateral triangles.
From the outside, each piece is a hexiamond - a shape made of six equilateral triangles.
The pieces will be quite slippy, so print two copies of the base to hold the thing together - one on top and one on the bottom.
Inspired by mathpuzzle.com's page on iamonds