Design 3D Shapes: The icosahedron!
Check the diagram, read every step before joining any pieces, and be sure to understand how it works. Take your time if needed, this a bit harder to visualize than the cube… With this method, first you’ll build a “core” of the icosahedron, and then add the remaining faces. As in dodecahedron, it is pretty important to check that all edges of each pentagon are in the same plane.You can use pieces from other steps to help yourself check the geometry and join with the right angles.
Choose a size and make 1 Structure Pentagon-1, 1 Structure Pentagon-2, 1 Structure Pentagon-3 and 2 Structure Bottoms.
Attach Structure Pentagon-1 to one Structure Bottom, 101º angle, as the diagram shows, with a small bead. You can use Structure Pentagon-2 (step 4) to check the angle, or attach them at the same time.
Attach Structure Pentagon-2 symmetric to the last one, as the diagram shows, with a small bead.
Attach Structure Pentagon-3 as the diagram shows, with a small bead. Check that the three side faces are three regular, planar pentagons.
Finish the structure by attaching on top the second Structure Bottom triangle, as the diagram shows, with a small bead.
Make 6 Final Faces and 3 Final Edges in the same size as the other pieces.
Build the pyramids on each pentagon of the structure (3) by attaching 2 Final faces and 1 Final Edge on each one, as the diagram shows. The angle between faces and pentagon is 32º, you can attach two pieces at the same time to check that it is right.