Hi David,
There are several ways to do that, but not a single click solution is available to my knowledge.
Just use the Extrude Inner function and then the Weld Tool, to merge the three points. Since that needs to be done for each “face”, it might not be the one.
Similar to that is the Extrude Inner, while pushing it very close to get the new points to come close together, then use the Optimize Function with a larger threshold.
This is also doable with the Bevel Function in combination with the Optimize.
I think you can see the process here, it is always a two step process, produce new points and merge them.
To do that precisely, I would just type in what you have given in data already with the object. Have a look here; One minute clip:
https://www.amazon.com/clouddrive/share/uIypZEn9Uv2HdxavORwOQIGpGUEbh2LTRx0y22gupO5
The idea is based on a equal sided triangle here. This means that we can half it, to gain a triangle with a 90º corner in it, and we have one part of a tangence, which leads to a simple “half the length” and half the angle fo this triangle (which is 60º, so 30º). In short half of the side times the tan of 30º. Now the optimize can work with default settings.
Enjoy