# hexagon mitres



## Entwyze (Jun 14, 2007)

I want to build hexagonal garden beds from 2x6 PT,what angle should i cut? each side will be 24"


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## Template Tom (Apr 23, 2007)

*Cutting Mitres*



Entwyze said:


> I want to build hexagonal garden beds from 2x6 PT,what angle should i cut? each side will be 24"


60degrees
Tom


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## skymaster (Oct 30, 2006)

Tom: 60 is the included angle the MITER is 30:yes::smile:. My brain went foggy on this in the first post on this :laughing:
JackM


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## Template Tom (Apr 23, 2007)

skymaster said:


> Tom: 60 is the included angle the MITER is 30:yes::smile:. My brain went foggy on this in the first post on this :laughing:
> JackM


Jack 
The internal angle is 120 therefore the angle to cut is 60
Tom


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## TheRealMacGyver (Jun 15, 2007)

Template Tom said:


> Jack
> The internal angle is 120 therefore the angle to cut is 60
> Tom


Tom's right here guys, but before I explain why...how many times did this op post this question and have they been back to respnd???

Here's why:

The least number of sides on a polygon is 3 (triangle). In any triangle, the sum of all angles must equal 180 degrees. Now, every time another side is added, you must add another 180 degrees. So for a rectangle it's 180 + 180 = 360, and since it's 4 sided, 360/4=90 and half of 90 = 45 degrees for the miter.

Now, a hexagon is a 6 sided polygon, so that's 180 + 540 (180 * 3) = 720. So, the sum of all angles in a hexagon must equal 720 degrees. 720/6=120 and half of 120 = 60 degrees for the miter.

If you think about it it makes sense, look at how the angles get larger with the addition of sides:

Equalateral triangle: each angle = 60 degrees
Rectangle/Square: each angle = 90 degrees
Pentagon: each angle = 108 degrees
Hexagon: each angle = 120 degrees


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## skymaster (Oct 30, 2006)

Tom: :smile: The angle is 60 however you must set your miterbox to 30 to cut the miter that will equal 60. All miterboxes referance from the fact that they are already at 90, therefore to get 60 subtract from 90 and the answer is 30:yes:.

Real: In any polygon there are only 360 degrees. any multiple sided polygon is figured out: 360 divided by the amount of sides:

6 sides = 60 degrees
8 sides = 45
10 sides = 36 
etc etc:icon_smile::smile:
JackM


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## TheRealMacGyver (Jun 15, 2007)

skymaster said:


> Real: In any polygon there are only 360 degrees. any multiple sided polygon is figured out: 360 divided by the amount of sides:
> 
> 6 sides = 60 degrees
> 8 sides = 45
> ...


That's what I was thinking too Jack, but that isn't how it works. I forgot about it until Tom brought it back up again and I started thinking about it. Your calculations above are incorrect. The total degrees of polygons work out like this:

Triangle=180 degrees
rectangle=360 degrees
pentagon=540 degrees
hexagon=720 degrees

Think about it, everytime you add another side, each angle has to "open-up" or get larger.


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## TheRealMacGyver (Jun 15, 2007)

Just did a search and found this site http://www.coolmath.com/interior.htm if you don't think you get it, check this out and it will help. But the miter on the hexagon is 60 degrees, I wanted to clear this up, because I too had it mixed up before.


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## skymaster (Oct 30, 2006)

Real: Ok I read it; re-read it :blink::huh: bookmarked it will re-re-re-read it. However thanks always willing to learn . :yes:. Brain needs adjustment :laughing::yes:
Jack


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## TheRealMacGyver (Jun 15, 2007)

Dang-it Jack  I think I messed that up! I'm sort of right, but as far as the miter goes, I'm wrong! What I said is correct for the interior angles, but I have something off somewhere....I'm working on it now, I'll be back.


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## TheRealMacGyver (Jun 15, 2007)

Okay, I got it (maybe I should start a new thread with this?)

Calculating each interior angle of any polygon is shown in my post above (and is correct).

The problem is that we need to use that angle and subtract it from 180 degrees. This new angle is what we use (divide by 2) to cut a perfect miter.

So, in this case going back to our original hexagon question (where is that op anyhow?) we have 6 sides, which means we have a total of 720 degrees. Divide 720 by number of sides 6 and you get 120. Now you take 180 (which is a straight line) and subtract the 120 from it. We now have 60 left. Divide the 60 by 2 and we have the miter for each joint=30 degrees 

Now, just to lay this thing to rest, I made paper patterns and put 30 degree angles on them using my speed square, and voila, perfect hexagon!


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## edp (May 25, 2007)

*?????Angles/Angels????*

Why make it hard on yourself? On any arrangement of planes where the lengthy of each plane is the same, Divide 360 by the number of planes (sides) and the result is the included angle of each joint. Divide by 2 and that will be your miter setting.

Ed


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## TheRealMacGyver (Jun 15, 2007)

I know Edp, the problem is that I've taken too many math courses! What you said works perfect, I was trying to use geometry and trigonometry, when all you need is reallifeology to figure this out! For what it's worth, it works because all miters in any polygon will always line up with the center point of the polygon (provided all sides are equal length). If you look at all the "imaginary" lines coming from the center point that align with each miter, they must all add up to 360 degrees. SO yes, the easy way (which I originally thought until I took a tangent) is to divide 360 by the number of sides, then split that number in half for each miter.

WHOO, sorry for the confusion, just trying to make sure the angle of the dangle is perpendicular to the mass of the _ss :laughing:


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## skymaster (Oct 30, 2006)

OMG!!!!!!!!! Ya mean I was right all along??????? :laughing::yes::smile::thumbsup: THANKS. Just could not figure out how after more than 20 years cutting 30 degree miters for a hex it didnt work? LOL LOL 
JackM


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## skymaster (Oct 30, 2006)

skymaster said:


> Tom: :smile: The angle is 60 however you must set your miterbox to 30 to cut the miter that will equal 60. All miterboxes referance from the fact that they are already at 90, therefore to get 60 subtract from 90 and the answer is 30:yes:.
> 
> Real: In any polygon there are only 360 degrees. any multiple sided polygon is figured out: 360 divided by the amount of sides:
> 
> ...



EDP kinda like this right? :laughing::yes: Then divide by 2 for miter angle


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## Trubakoff (Jul 2, 2007)

Just think of it Like a huge hexagon Pizza with slices that are cut right where the miter takes place and run to the exact middle, Figure out the angle of the slice and CUT.

(360/#of sides)/2


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## pykler (May 3, 2017)

You set the miter gauge on the table saw at 30 which creates a 60 degree cut, because normal cutting is a 90 degree cut, by setting the miter to 30 you are removing that from the 90.


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