Why would a non-Flash solution make them happier?

I think I addressed this earlier in the thread. They, like many companies, want this function available when someone is browsing via an iPad or iPhone, which does not support Flash.

Ah, well it's worth noting that the iPad/iPhone browser doesn't support any plugins at all (from what I've read... I don't have one) or Java, so the only solution is WebGL. But IE doesn't support WebGL, so it requires a plugin or Java (and Java requires the user to have installed Java). Poking around, it appears a lot more internet users have Flash than Java (95% compared to 75%, thinks StatOwl).

There's no universal solution for your client, so you'll need two. WebGL/HTML5 for iPad and iPhone and some sort of plugin for IE users -- Flash seems to make the most sense.

EDIT: I don't actually know if iPad/iPhone support WebGL, but they apparently support HTML5 pretty well, and the conversation thus far seems to imply WebGL is the iPad/iPhone solution.
EDIT2: Looking back at earlier posts, maybe that won't even work for iPad/iPhone, in which case there's no solution.
EDIT3: But maybe sometime soon it will.

Well, with that need you won´t find a solution, although WebGL might be supported in the future, as it is already supported for iAds on iOS. While WebGL (and also native client, but that is chrome only) has to be supported by the browser all other solutions I can think of basicly run additional software which then renders into an area of your browser, which means that you´ve got no chance for something like that to run on iOS. So what I would do as it has already been suggested is to use WebGL where supported and flash everywhere else, nothing will work on iOS except some HTML5 canvas 2D stuff, which would probably be very slow, like this one: http://gyu.que.jp/jscloth/ (which I just tested on iOS and runs with something like 0.5fps on my iPhone 4s)

Good info, everyone. Thanks!

(And, thank you, Apple, for making this so frickin' hard on everyone ... and MS, too, damned IE)

I would create an app for phone that downloads the model from the internet and then displays it in opengl, and flash for the pc browser.

what would you use this for? for showcasing models you want to sell?

that wouldn't be a good idea since everyone will be able to grab your model. i would use movies in this case.

@ventilator: I think this is briefly referenced in this thread. There is a company that makes high-end sunglasses. They want 3D models of their glasses that the end-user can rotate and view from any angle on their website (integrated into their website). They want their site, with the 3D models, to work on all platforms, including the iPad and iPhone (so, no Flash).

Like it was already said a few times, there is no solution that works on all platforms. So you HAVE to use at least two solutions, or drop support for some platforms.
Its this simple, and I don't understand whats so hard to understand about this or why you don't want this solution.