Tricots are not normal with most plants. As far as being able to propagate it, I am not sure. The internet seems all over the board on whether or not they are sterile, stronger or weaker growing, or can be bred. My take is that it would be a hard trait to breed for but can occur as a mutation. The effects are interesting.
I've seen it occur with coleus. (the branch will remain that way until the tip gets broken off. When it branches off, it does so in 3's. The offshoots returned to normal.) I've also seen it occur on a common Milkweed. I've also seen it occur with dandelion blooms. (even more so if they got "fertilized" with weed killer.)
But an African violet?! Nope. This is Laughing Anna. I'm not sure if this is typical for the variety or if mine is a spontaneous mutation. I have a hunch it is a mutation. It isn't the first one I've had for that variety. (A year or two ago, I had a Laughing Anna produce a single huge flower and one small leaf from the center instead of two normal leaves.)
Anyways this is how the plant is affected. From the top:
Unusual symmetry. Leaves grow out at an equilateral triangle. Looks like it has a 180 degree rotation with the tip of the triangle pointing up or down every other leaf set.
Siamese twinning. On. every. Stalk.
Fewer flowers. Stalks twice as long and twice as thick. (To be fair, I didn't typically see lots of flowers per stalk before.)
Everything grows in sets of threes from the crown. Three leaves. Three bloom stalks.
It's still keeping to it's 3 leaf at a time growth pattern. As a result it is filling in quite quickly.