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I have a glass pyramid, about 4 inches high, blue in color, and it's six-sided. I want to build a box to hold the glass pyramid and install a small light in the box so the pyramid will look like a beacon or lighthouse. The finished overall height will only need to be about 2 feet tall. Can anyone help me with the math to figure out how to build the wooden sides so that I end up with a six-sided box that is fat at the bottom and smaller at the top to hold this glass pyramid? I only took shop in 7th grade with Thomas Edison as my classmate ;), and what I know now about woodworking could fill a page (a very small page).

Many thanks from a new member.
 

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Hi, Welcome.
360º ÷ 6 sides = 60º ÷ 2 = 30º each side of the joint.
Your 6 sided box will have 60º degree corners. Each side of the joint will be cut to 30º which will give you a 60º corner. How wide is the base of the glass pyramid? You want the top of the box to match the bottom of your glass pyramid so it looks like one continuous line? If so the box will be 20" tall when finished + the 4" glass to you a 24" finished height.

You can draw it out on a piece of scrap wood or large paper. Without knowing the width of the base of the glass you have you can draw two parallel lines 24" apart. Draw another parallel line down 4" from the top line. This is the height of your glass pyramid. Use a framing square & draw a centerline that connects the top line & the bottom line. On the centerline that is 4" down center the width of the bottom of the glass pyramid. Draw a line from these two points to the center mark on the top line. This should be the size of the glass pyramid.

Now take a straight edge & line one end up with the top centerline mark & move it across the bottom line until it lines up with the line for your 4" glass pyramid. Then draw a continuous line to the bottom. Do this on the other side & you should have a full size drawing of the sides.

Now your top & bottom of each side would have to be mitered to sit flat (parallel with each other) if it matters to you but without knowing any other measurements for the taper (base width to zero center point top)?
 

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Bob that works for a round cylinder on square stock but you have to cut the tapered pieces first before using the bit. He wants to match his glass pyramid on top. Either way you still need to know the finished diameter to know how wide your 6 parts need to be.
 

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Hi Mike
did you make calculator? If so there are also two outside diameter's used in stave construction depending on desired need. One is outside center of each stave & the other is point to point. Could these be added?
Hi James,

Yes, I made the calculator for a friend who was making an assortment of boxes. One of them was a 17 sider. (I don't know why 17, and didn't think to ask.) :"^)

He was only concerned with the inside diameter measurement and I didn't have the experience to know there were other measurements that needed to be considered.

Adding the other conditions should not be a problem and I'd like to have a more complete calculator. It would be a more useful tool to use and share.

Since the ID is always a circle, having an odd number of sides isn't an issue. I'm not sure how to easily measure the OD or outside point to point on the odd number sided polygons. Is there some logical method to use? And how do I address the thickness of the stock, or isn't that a consideration?

Thanks,
Mike
 

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Hi James,

Yes, I made the calculator for a friend who was making an assortment of boxes. One of them was a 17 sider. (I don't know why 17, and didn't think to ask.) :"^)

He was only concerned with the inside diameter measurement and I didn't have the experience to know there were other measurements that needed to be considered.

Adding the other conditions should not be a problem and I'd like to have a more complete calculator. It would be a more useful tool to use and share.

Since the ID is always a circle, having an odd number of sides isn't an issue. I'm not sure how to easily measure the OD or outside point to point on the odd number sided polygons. Is there some logical method to use? And how do I address the thickness of the stock, or isn't that a consideration?

Thanks,
Mike
I've only had to deal with outside dimensions not insides. Depending on the need or want the outside measurements I was given for diameter was from the center of the flat on the stave or point to point. If you draw circles around your example you would come up with different diameters for these points. I guess you could use the inside dimension & just remember that it is an outside number. Your shortside number would reverse & be a longside so you don't cut your pieces too short.

I don't think thickness would matter. Unless you are turning a bowl. Then you would want to know the minimum you need to end with the desired thickness.

Number of sides do not matter since it is all calculated from 360º & ÷ by the desired number of sides. It is a simple but useful calculator.
 

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Hi

====
 

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I've only had to deal with outside dimensions not insides. Depending on the need or want the outside measurements I was given for diameter was from the center of the flat on the stave or point to point. If you draw circles around your example you would come up with different diameters for these points. I guess you could use the inside dimension & just remember that it is an outside number. Your shortside number would reverse & be a longside so you don't cut your pieces too short.

I don't think thickness would matter. Unless you are turning a bowl. Then you would want to know the minimum you need to end with the desired thickness.

Number of sides do not matter since it is all calculated from 360º & ÷ by the desired number of sides. It is a simple but useful calculator.
Just thinking... the outside diameter on the flats would be the inside diameter plus twice the thickness of the material. So a 10" ID using 3/4" stock would be an 11.5" OD regardless of the number of sides.

Coming up with the points diameter, ID or OD, won't be as simple... some geometry formulas needed that I don't recall right now.

I can see where calculations for either ID or OD could be needed depending upon the intended use of the polygon.

I think I'll play around with it some more.

Mike
 

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I've found an error in my stave calculation formula.

Mike
 

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Looking in my Practical Math Dictionary I believe the radius that measures from the center of each flat is called the "radius of inscribed circle". The radius that measure from point to point is called the "radius of circumscribed circle"
 

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G'day N/A

Welcome to the router forum.

Thank you for joining us
 

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Discussion Starter #16
I'm amazed at the wealth of information I've received from one simple post. I truly appreciate all the help I've gotten from the good people of this forum. As soon as I get a chance to cut these pieces, I'll see if I can post some pics so those who've helped can see the fruits of their assistance! Thank you all so very much.
 

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To make my tapered lighthouse sides, I first built a jig to cut them.
It is as tall as the sides will be, and has 2 steps in the bottom edge which are (c) 1/2 the distance of the bottom edge (b) minus the top edge (a).
I cut the sheet stock on the table saw with the sheet on the first stop, turn that piece over, place on the second stop, and make the next cut.
Very simple to do. After making the first cut, just turn the stock over and continue cutting the remaining pieces.


I then use the router table with a chamfer bit to form the correct angle.
In my case with an 8 sided LH, I use a 22.5º bit. In your case, a 30º bit.
 

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