# How to calculate rotation for three square interlocking angled legs?

I was inspired to try to create this style of legs for a small side-table that I am building:

However I have been running into some trouble trying to work out how to construct it.

I've been attempting to model it in SketchUp so that I can get all the measurements / angles worked out before I get to work, but I can't seem to figure out how to get the rotation of the legs right, so that the sides of each of the wooden strips on all three legs all lay flat against each other at the joints.

The first thing I attempted was to simplify things a bit and just model 3 straight square legs, intersecting right in the middle of each other... each leg is angled at 45° inwards. I had assumed that a matching rotation of 45° of each leg about it's lengthwise axis would get everything lined up, but it's ever so slightly off:

So the question is, how do I calculate the proper angle for the rotation of the legs, ideally for any given inward angle (ie: the legs will intersect closer to the top than the bottom, so are angled inwards at only 28°)?

• For most things like this the longitudinal axis of each of the three lengths is at 90° to the others. Don't know what's up with the model but if those legs are rotated correctly the overlapping area should be perfect, so it's likely a simple error or something wrong in SketchUp. Anyway, if you alter the intersecting angle it hugely complicates things since you're then into compound-mitre cuts which most find so difficult they avoid doing them a second time after they've done them once LOL Commented Jan 6, 2018 at 8:07
• If it is just SketchUp that's to blame that would be both a relief and a big annoyance! (I did spend a few hours reconstructing the model multiple times to make sure it wasn't user error, as that was my first assumption haha). As for the more complicated angle... I do tend to make things very difficult for myself - but the result is usually more interesting! Sometimes it's worth the struggle, I'm hoping that will be the case here Commented Jan 6, 2018 at 23:58
• Well if someone doesn't come along with an Answer that helps here on how to do this at a shallower angle than a three-way 90° intersection (unfortunately highly likely now given the doldrums) I think your best bet would be to Google to see if you can find out how someone else has already done it. Always best to not reinvent the wheel if possible. I was going to suggest starting from how the joint is done at 90 and extrapolating from there but I suspect that won't work and instead a purpose-suited three-way joint would have to be executed. Commented Jan 7, 2018 at 9:57
• I can duplicate the problem, but I cannot figure out what I (or sketchup) is doing wrong. I think it is resolving the intersection incorrectly.
– Ashlar
Commented Jan 8, 2018 at 2:56
• Im going to add to this even though it was so long ago. This page has a great calculator rechneronline.de/pi/corner.php If you lookup cuboid it will help. In terms of the bevel, it is 35.24 degrees and a 45 degree mitre. Commented Jun 10, 2020 at 16:13