Calculating angles for a physical regular icosahedron

In summary: Start with a square piece of paper. Draw 20 equilateral triangles on the paper, with the points of the triangles aligned so that the bases of the triangles are the same distance from the center of the square. The angles at the vertices of the triangles should be 120 degrees.Next, cut the triangles out of the paper. You'll need 20 of them. The triangles should be the same size and shape.Now, join the triangles together by overlapping the edges of the two triangles. Make sure that the triangles are all the same size and shape.Finally, draw a circle on the paper around the shape that you've created. The center of the circle should be at the center of the square.
  • #1
hephalumph
1
0
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!
 
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  • #2
hephalumph said:
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.
 
  • #3
If you already know this, it's no help. But here's a way to construct an icosahedron:

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FAQ: Calculating angles for a physical regular icosahedron

How do I calculate the angles for a physical regular icosahedron?

To calculate the angles for a physical regular icosahedron, you can use the formula 360/20 = 18 degrees. This means that each angle in the icosahedron will measure 18 degrees.

What is the formula for finding the angles of a regular icosahedron?

The formula for finding the angles of a regular icosahedron is 360/20 = 18 degrees. This formula applies to all regular icosahedrons, regardless of their size or dimensions.

How many angles are in a physical regular icosahedron?

There are a total of 20 angles in a physical regular icosahedron. Each of the 20 faces of the icosahedron has three angles, resulting in a total of 60 angles. However, since each angle is shared by multiple faces, there are only 20 unique angles in the icosahedron.

What is the sum of the angles in a physical regular icosahedron?

The sum of the angles in a physical regular icosahedron is 1800 degrees. This can be calculated by multiplying the number of angles (20) by the measure of each angle (18 degrees).

Are the angles in a physical regular icosahedron all equal?

Yes, all of the angles in a physical regular icosahedron are equal. Each angle measures 18 degrees, making it a regular polyhedron. This means that all of its faces are congruent and all of its angles are equal.

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