MHB Calculating angles for a physical regular icosahedron

[hephalumph]

This is actually for a wood shop project... but it certainly involves geometry! I am trying to build a real-world regular icosahedron. I know I need 20 equilateral triangles for the faces. But I do not know what the angles of the sides/thickness should be, to join those 20 triangles into a 3D shape. Nor do I know how to calculate it. I'll be perfectly honest - this is not some homework or test that I *have* to figure it out for myself and show proof of work, so if someone wants to just post the answer, I am fine with that. But if you want to make me work for it, giving me the formula as a starting point, (and probably working with me to verify I solved it correctly) is okay too.

Thanks in Advance!

 

[earboth]

This is actually for a wood shop project... but it certainly involves geometry! I am trying to build a real-world regular icosahedron. I know I need 20 equilateral triangles for the faces. But I do not know what the angles of the sides/thickness should be, to join those 20 triangles into a 3D shape. Nor do I know how to calculate it. I'll be perfectly honest - this is not some homework or test that I *have* to figure it out for myself and show proof of work, so if someone wants to just post the answer, I am fine with that. But if you want to make me work for it, giving me the formula as a starting point, (and probably working with me to verify I solved it correctly) is okay too.

Thanks in Advance!

Good afternoon,

have a look here: https://en.wikipedia.org/wiki/Regular_icosahedron

If I understand you correctly you are looking for the dihedral angle between two faces. You'll find the value of this angle in the table of properties of the icosahedron.

 

[johng1]

If you already know this, it's no help. But here's a way to construct an icosahedron: