Frank, it really looks nice. Basically the same technique as Antonius, but without the center trajectory. The advantage of your method is that Creo will gladly split it with a plane down the middle. The full circle method didn't allow this.
I'm still amazed that Creo makes the surface with the arc length going to zero.
Played with this problem some time ago.
Creo 2.0 model attached
Frank, there seems to be something unstable to this sweep. I went back to build a UDF for future use, and as soon as I change sizes either the sweep or the solidify fails. I then went back to your model and changed the cube to 2" and immediately your sweep failed as well. I tried changing accuracy but that didn't make any difference. Any ideas?
Curious why you chose a conic arc for the sketches. Is the RHO value of .410 significant?
So do any of you know how this technique could be adapted to work if you DO want a radius on each edge? I imagine the edge radii could either already exist or possibly be created as part of these features. There is also a possibility that each edge radius could have a different value.
Rho value of sqrt(2) - 1 (truncates as .414-ish) gives a true circle, anything above or below that gives an ellipse, a parabola, or a hyperbola..
You could piece together an n-sided mesh to do what Antonius showed, basically like this:

agreed solidworks does good job in this case.
the "Fill Surface" tool in solidworks does it nicely.
I'll look at it. I played with the rho value and it worked fine....except for a value of .6, for some reason. Didn't have time to really monkey with it. Try replacing the conics with simple arcs. I changed them to conics because conics are more truly tangent, and work better for surfacing.
Yes, you can drive a surface TO zero, but not FROM zero. Also, you cannot have an arc radius go to infinity (become a line segment).
I didn't bother making a relation in the cube itself, so when you tried to change a value to 2, it failed because one leg of the cube was 1", the other was 2", and I set up the curves to be 1/2 the length of the leg. Easy fix with a relation. Or you could assign a hard number for the distance, which is what I'd do if making a UDF. I played with it, and it seems pretty stable with regards to changing rho values, except when you get to .1, then it gets a little funny in the one corner when zoomed WAY in where the VSS section goes to zero. And occasionally it doesn't like a rho value of .6, but that seems intermittant. You can sneak up on it.
Two step solution,
Use a variable round and use the add radius option and place these points between the corners, now give them a tiny value. Next, you can use the corner sphere transition and that's it.
The model was created in Creo Parametric 2.0 Student Version, sorry for that.
Look this dice.





