I'm looking for some help in constructing a hexagonal pyramid- something like the engine shrouds from the 2001 Discovery-
http://www.palantir.net/2001/tma1/pics/mission02.jpg
or a WWII German flakpanzer-
http://www.achtungpanzer.com/flak4.htm
The tricky part (for me) is calculating the angles and lengths of the individual side pieces. Any guidance would be much appreciated!
Thanks,
Andrew
Looking for geometry help-building a hexagonal pyramid?
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Andrew Gorman
- Posts: 2703
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Well.... This is a handy ref for this. The easy way is to draw out the parts in a drafting or illustration app and work out the angles. But even that's not easy to give instructions for without pictures.
Abolish Alliteration
Hi Andrew,
Say you want to build a hexagonal pyramid where:
H is the height when viewed from the side.
B is the length of each of the six base segments that form the hexagon.
R is the distance from the center of the hexagon to the point of the hexagon.
S is the length from a point of the hexagon to the top of the pyramid.
You want six triangles with two sides of length S and one side of length B.
Fortunately since this is a hexagon B = R.
S= sqrt(B^2 + H^2)
Now you can lay out your triangles with a ruler and compass.
The angle you need to sand the sides of the triangles is more difficult to determine.
HTH
Mike
Say you want to build a hexagonal pyramid where:
H is the height when viewed from the side.
B is the length of each of the six base segments that form the hexagon.
R is the distance from the center of the hexagon to the point of the hexagon.
S is the length from a point of the hexagon to the top of the pyramid.
You want six triangles with two sides of length S and one side of length B.
Fortunately since this is a hexagon B = R.
S= sqrt(B^2 + H^2)
Now you can lay out your triangles with a ruler and compass.
The angle you need to sand the sides of the triangles is more difficult to determine.
HTH
Mike
Thanks Ti Raven,
Fortunately, it's a hexagon. A 17-sided pyramid or the general formula for an N-sided pyramid would have required some real trigonometry or a reference book.
I wonder if Andrew has enough information. You might need some math to calculate the angle to bevel the edges of the sides for a flush fit. I expected someone to post the equation.
Although, you know a flat hexagon made from six isosceles triangles needs 90 degree edges and an hexagonal prism (a pyramid where H = infinity) has 30 degree edges. There should be a way to come up a solution or an estimate that's close enough.
Mike
Fortunately, it's a hexagon. A 17-sided pyramid or the general formula for an N-sided pyramid would have required some real trigonometry or a reference book.
I wonder if Andrew has enough information. You might need some math to calculate the angle to bevel the edges of the sides for a flush fit. I expected someone to post the equation.
Although, you know a flat hexagon made from six isosceles triangles needs 90 degree edges and an hexagonal prism (a pyramid where H = infinity) has 30 degree edges. There should be a way to come up a solution or an estimate that's close enough.
Mike