How to make a hexagonal roof

If for some reason you'd prefer a square based roof, click here.

The 3-D model of a hexagonal roof shown below can be dragged with your mouse so you can see all round it. Our problem is to know how to cut the 6 triangular panels, so we can make it

Each of the 6 triangular panels will look something like the 3-D model below (again, drag it with your mouse). Note the edges are bevelled.

Here is a photo of half a roof, kindly sent by Bob Sims in Australia. Bob reports that it's hard to cut the bevel angles accurately enough. Note here that the bottom edge is unbevelled - an aesthetic choice and a good one here I think.

I will give you the calculated measurements for the roof first, then if you are interested you can review how they are derived. Firstly we have to decide what size hexagon base to have.

We need to know the size of both w and v.
Either choose a size for w and calculate

or choose a size for v and calculate

Now decide the height h of the roof, and the thickness t of the wood you'll be using.

You'll need six triangular pieces of wood like this, where X is at the top of the roof:

We know what size w is from above.

The other sizes are:

So - one way of doing it:

• Choose sizes for h and t, and for w or v
• Calculate the other sizes using the formulae
• Cut out six triangular pieces of wood using straight cuts
• Turn the triangle over and mark out as shown by the purple outline
• Plane off the unwanted wood.

Or another way:

• Choose sizes for h and t, and for w or v
• Calculate the other sizes using the formulae
• Cut out six oversize pieces of wood using straight cuts
• Use scrap pieces of wood to set the angle for the bottom edge on a bench saw
• Cut the bottom edge of the triangles at that angle
• Reset the saw angle for the side edges of the triangles and cut them

Deriving the formulae

This is how I've worked out the formulae:

We have found the value of a, which defines a point on the underside of the triangular panel directly under the roof's apex. We know that when 2 planks meet at some angle the bevel will be the same right along the edge.

So, the purple line to mark on the underneath edge will be a constant distance (viewed from above) from the top edge X-Y - shown as c here. Knowing a we can derive c.

We can also calculate the angles of the bevels, in case there is an available bench saw which can reliably set the angles:

page date: 13Jun06.      I enjoy correspondence stimulated by this site. You can contact me here.