I'm going to come at this from another angle and see if it adds anything.

Triploidy is frequently encountered in orchid breeding. Most triploid orchids are pod fertile and pollen sterile. Pollinating a suspected triploid is no test of ploidy, since most triploid parents will readily carry a cpsule. It also isn't helpful, as the offspring are aneuploid and IMO, worthless for further breeding. But there are a few really oddball plants that will not bother trying to evenly divide 3 and just go with what they've got. Such a plant is Phal. Golden Sands 'Canary', the result of a cross between a yellow species (diploid) and a complex modern white (tetraploid) Many people tried to hybridize with it and no luck. It was deemed sterile, which was a huge disappointment at the time, since good yellow phals were so rare.

Eventually a cross was made that took, and everything changed. It was eventually discovered that 'Canary' made 3x ovules that, when paired with 1x (haploid) pollen, created tetraploid seedlings. 3x + 1x = "Houston, we are good to go."

Please be aware that triploid orchids that can do this are slightly less rare than frog fur coats. But back in the late sixties, it was a game changer. I wonder if the mechanism in daylilies is similar.

The information I have found about Phal. Golden Sands 'Canary' indicates that it is indeed a triploid.
R. J. Grlesbach wrote the following in the Journal of Heredity Volume 76:74-75. 1985 in an article titled "Polyploidy in
Phalaenopsis orchid improvement"

"For example, very few seedlings are obtained from crosses involving the triploid Phal. Golden Sands. In addition, most of the seedlings that are raised are aneuploid and produce deformed flowers. Through colchicine doubling a hexaploid form of Phal. Golden Sands was produced (Figure 2). Approximately 50 percent of the treated protocorms developed in polyploid plants. The hexaploid's flowers, besides being heavier and fuller, were much darker than the triploid's."

Figure 2 in the article is a photograph of the triploid form of Phal. Golden Sands 'Canary' (with 57 chromosomes) and the hexaploid form (with 114 chromosomes). The hexaploid form will be more fertile.

Dr. Griesbach also indicated in the article,
"The hexaploid form of Phal. Golden Sands was backcrossed to the tetraploid white parent. Approximately 5 percent of the
seedlings produced clear yellow/green flowers without spotting. The other 95 percent of the progeny had various degrees of
spotting. The form, size, and substance of all the offspring was much improved The best of this cross, which was registered as
Phal. Meadowlark (2n = 5x = ca 95), was then backcrossed to the highly colored diploid parent. The pentaploid Phal. Meadowlark, behaves as a tetraploid in that most of the viable seedlings when crossed with a diploid are triploid."

The hexaploid form of Phal. Golden Sands 'Canary' would be expected to be fertile with diploid Phalaenopsis and result in tetraploid seedlings (3x gametes from the hexaploid 'Canary' + 1x gametes from the diploid parent = 4x tetraploid seedlings.

Most triploid daylilies are more or less sterile with diploids although they may have some fertility with tetraploids. If a hexaploid daylily is crossed to a diploid it would be expected to produce tetraploid seedlings. If a triploid daylily is able to produce some 2n gametes (also called unreduced gametes) that is 3x gametes and is crossed to a diploid it would be expected to produce 4x (tetraploid) seedlings and aneuploid seedlings.

Edited:

I should add that once a hexaploid version had been created using colchicine there would be two versions of Phal. Golden Sands 'Canary'. The original triploid version with low fertility and the hexaploid version with better fertility and when crossed with diploids the ability to produce tetraploid seedlings. With the passage of time the original version might become scarce or disappear.

admmad said:In diploids each chromosome of the chromosome pairs has only one choice for pairing at meiosis. So they pair symmetrically at meiosis and there are 11 sets in daylilies. In tetraploids each chromosome has a number of possibilities when it comes to pairing/aligning. One set of four can align as a quadruplet or it can align as a triplet with one "unpaired" or it can align as two pairs. When the chromosomes separate, singles can be lost completely and quadruplets may separate as three and one rather than two and two. Each set of four does this independently of how the other sets align. The end result is that in diploids basically 100% of the gametes have a balanced chromosome set of one chromosome for each of the 11 sets - they have 11 chromosomes. In tetraploids the gametes do not necessarily have 22 chromosomes and even when the number is 22 it may not be two of each of the 11 sets. Unbalanced gametes are not necessarily viable and the seeds created by viable unbalanced gametes are not necessarily viable. The situation in triploids is much worse in terms of balanced chromosome sets in gametes. In hexaploids the alignments would be more variable and the viable gametes fewer.

That's the best explanation of limited fertility in tetraploids I've heard yet. I've found at least two tets that show a goodly amount of fertility, judging by the number of capsules carried to fruition.

Thank you for the information you have given us so far. It's better than chocolate. I love it.