Origami is the art/science (or practice) of paper folding. 

In Japanese, 折る (oru) means “to fold”, and the stem form of the verb is 折り (ori) 

折り

紙 or かみ (kami) means “paper”, but is usually written as がみ (gami) in rendaku form when joined with another word or character

紙

Combining the two words we get origami, written in Japanese as

折り紙

How can we describe the folding of flower petals?

Instead of combining a verb with a noun, here the emphasis is on the fact that organic materials in the form of flower petals are being substituted instead of paper. 

So taking the Japanese word for flower 花 or はな (hana) 

花

and using the same character for paper

紙

we can combine the two words to form hanakami, to mean using flower as paper, or flower paper

花紙

Maybe orihana would have been a better choice, but I am sure it is already used somewhere else, and hanagami might be more grammatically correct, except it also means tissue paper in Japanese (鼻紙).

Call it what you like, flower petals can be folded into delicate origami models, with intricate details that are revealed when you take a closer look (photography by Deb Yarrow).