Icosahedron joints for straw

This is a corner joint to build up an icosahedron (20 faced solid) from 5mm straw diameter.
Work in progress.
Process: a tube were tilted 57° from vertical and was made an array of 5 tubes by 72° each other.

Tilt must be çorrected since the angle isn't 57 degrees. The right one is 58.25 degrees.