Where does one begin and the other end? I ask this because I was looking at some seashells that are called volutes, and I thought that they seemed more to be helixes because they crossed many planes in rising (or falling) spirals. I think of a volute as a spiral along one broad plain, as a volute in a fiddlehead (i.e., violin).

But perhaps volute and helix are pretty much interchangeable as words. I don't know.

Would someone care to comment on these shapes?

volutes vs helices

Interestingly enough both words come from the same PIE root *wel- 'to turn', whence English to well. Volute is from Latin and helix from Greek. It's common for a PIE /w/ to be dropped, but sometimes it changes to a rough breathing /h/ in word-initial position and sometimes not. (cf. oinos ~ vinum 'wine', ergos ~ work 'work'.)

http://www.bartleby.com/61/roots/IE565.html

Ah! How interesting. I just read that the two shapes do overlap in how they're used. In AHD, there is one definition of helix that is rather comical if you're thinking about any possible differences between the two similar shapes. That definition is that the helix is the volute of a Corinthian column. I found that amusing and hope you will, too.

One definition of the helix indicates that the angle to the plane of the cyclinder or cone in a helix is constant. I immediately imagined a group of angles that were quite inconstant--a mental image of stairs that rose in a herky-jerky fashion at all kinds of jerry-rigged angles.

Since those stairs rising upward wouldn't be considered to be a helix due to the abrupt change in angles, I wonder what the rising shape would be called. An anti-helix?

Edit: OK. One more thing and I'm out of here. It's my birthday, so please indulge me today in a bit of going overboard on the board. I checked out the adjective forms, helical and voluted--helical has a very nice sound when you use the soft 'e' rather than the alternate long one. Here's a soft phrase:

A pelted pelican fell helically.