# How can I make the opposite of Reuleaux triangle?

What I'm trying to make, is the opposite of that, meaning the lines bend inward to looks something like:

I achieved that by making three circles, but it's a pain to align the third circle properly.

I'm sure that there's an easier way to make a shape like this. (geometrically)

It's pretty easy to make this with a 4 sided (diamond) Just lay out four circles in a box (smart guides make it take a second) and cut out the center.

• There is 3rd obvious shouce since you knew how to draw the Reuleaux triangle you could have mirrored the aechs along the triangle. Commented Apr 10, 2018 at 7:51

Here are 2 ways:

• Make a circle
• Duplicate the circle so it touches the other
• Rotate the newly created circle around the first one by 60 degrees (alt to click to trigger numeric input and copy).

Image 1: Animation of first method

• Draw a same sided triangle
• Draw a circle with radius of half the length of triangle edge (or diameter of edge).
• Copy a circle at each triangle vertex.

Then use shape builder to remove the excess.

## For the super pedantic

Now somebody brought up that this wont be perfect. And they are right. Bézier splines can not make a perfect circle so even though it would be mathematically super accurate there's no way I can use a 3 segment Bézier to be super pedantically accurate. However, I can construct a more accurate approximate circle with for example jooGraphFunction that is made out of 12 segments (instead of 4) then it will be perfect within limits of floating point precision. This also makes cloning trivial since you have a control point at each intersections so just drag the point to point and be done with it.

A quicker way to align the circles...

Use a Transform effect (Effect → Distort & Transform → Transform...). Set the movement equal to the diameter (i.e. width) of the circle, 2 copies and a rotation of 120 degrees...

Then expand and use Shape Builder or whatever else to delete the unneeded pieces.

...

You can also create something like the Reuleaux triangle by adjusting the movement on the Transform effect...

• Transform effects :facepalm:
– Welz
Commented Apr 9, 2018 at 18:49
• You can do anything and everything with transform effects
– Cai
Commented Apr 9, 2018 at 18:54
• Your second "something" has a name! "Borromean rings" Commented Apr 9, 2018 at 19:29
• @WELZ What's wrong with transform effects? Commented Apr 9, 2018 at 23:17
• @MCMastery Nothing, they're awesome.
– Welz
Commented Apr 9, 2018 at 23:18

You can construct this with compass and straight edge.

Draw a circle with a compass. "Walk" the compass round the circumference of the circle locating 6 points on the circumference. Draw an equilateral triangle by joining every second point. The other 3 points can be used to locate the mid points of each side of your equilateral triangle by joining each one to the opposite vertex of your triangle. They will cut at the mid point of each side.

Set your compass at half a side length and draw 3 arcs, each centred on a different vertex of your original equilateral triangle and each within the original equilateral triangle. It used to be a school exercise many years ago and probably in some Greek "schools" B.C.