someone in the Name that Plant forum actually identified my mutated plant part photo as a 'pantaloon'. I was surprised to find that these things and several others mutant combos have names.
I found another occassion to post this elsewhere, and I thought of this post.
Since posting this I have learnt that such an oddity is known as a "homeotic mutation". There is an interesting discussion going on in the daylily forum about a daylily with petaloid leaves.
They are found fairly commonly among cultivars of some plant groups, for example azaleas. Sometimes described as "hose-in-hose" (which may go back to the time when hose meant sock or stocking).