Attached is a script to generate the slightly rounded deltoids, twisted and rotated about a circle.
Formula from wikipedia and a geomagic forum topic.
The avalue and bvalue do nothing at present, but could be added to the formula to generate different circle size,
and deltoid size respectively?
Might be able to modify the equation to create other hypotrochoids than the deltoid hypocycloid?
The deltoid is based upon 3 unit and 1 unit radii.
The torus circle radius is 7.

The challenge is to loft them into a solid. (In one piece)
(It is kind of a Moebius surface.)

I finally did a 1 gap loft, and trimmed it to 3 gaps and saved it.
Trimmed again to 5 gaps, and lofted just the 5 gap. Trimmed the 5 segments to 3 segments.
Imported saved 3 gap version, and did boolean union.
Copy, pasted to Geomagic and ran stitch. (Do not know if stitch did anything in Geomagic?)

- Brian

This one uses 20 deltoids, because 21-1 is divisible by 4. (Congruent to 0 modulus 4.)
Also each deltoid is made up of 33 points, because 34-1 is divisible by 3. (These are probably not important numbers.)
Larger values could be used

(Other attempts, using hypotrochoid script and twist and flow, did not seem to come out quite right, at these tighter radii ratios.)

Switched from deltoid based upon interpcurve to curve factory. Made units 3times larger.
Now Twist and Flow give an excellent surface.

Seems there is a glitch inside the UmbilicTorus when I ask a Closed Loft!




PS What was your regulates for the Unwrap method Circle--> Extrude / Hypotrochoid ? (so no need to strech)

120° of Twist ?

I have a little difference in making one pass!
Normally this must not arrive?

Response based upon memory only :-)

Was unable to do a one step loft. In order to get the solid, had to resort to Boolean union of separate parts.
Do not know why. Something like a torus of circles would only take one step.

Do not understand the "unwrap" question. Recall that 120 degrees was used for something.
The modular arithmetic may help make the 3 corners more equal in shape, since due to the rotation,
different corners meet up.

- Brian

< the unwrap question
Just
I draw a circle : UnwrapCurve : so I have the length of the extrusion of the volume for Twist it! :)
Then Flow along the circle
But the closed form is not perfect against your is marvelous!

Hi Pilou
Your are correct, the Flow does not result in a perfect connection.
Zooming in on the UTFlow one that I did, shows that the connection is NOT perfect. :-(

I see that using the stretch option did create a solid. Still imperfect though.

- Brian