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.)