A header at the very least is required or the door and the entire unit will be very wobbly, the company I work for will not even sell nor install a Neo-Angle enclosure without a header (even if the customer is willing to sign off accepting full responsibility) due to this fact as we fell it is dangerous.

Thanks for the link, pbx2. The showers that I see without a header seem to at least have a half wall that the bottom hinge is mounted to.
millworkman, I heard about some sort of L bracket that could be used on the fixed panels to attach to the wall that could make it stable enough to put the door in the center without a header. Has anyone done this or know of another way? It is a tiny bathroom and I really want to minimize the amount of metal, so that your eye just goes right through the shower. I am continuing the tile wainscoting and chair rail through the shower for this reason, too. A header would just spoil the effect, I think. I am not tiling the ceiling over the shower, either.
One of the pictures on houzz had no glass at all. Would a 42" neo angle be big enough to be open? The whole bathroom is only 6 1/2' x 7'. I appreciate any ideas you all might have. Thanks!
Any other ideas? Thank you!

should have said, unless you want to make the whole thing a wet room.

I was afraid of that, even though there will be tile wainscoting on the walls and this shower gets used VERY infrequently. I don't want someone having to wipe water off the toilet seat after showering. So, any pros out there have other ideas on neo angle shower glass without a header?

You can use something along the lines of this. But at the minimum these support bracket. Also you can mini-clips as opposed to channel. The company I work for will not install a Neo-angle without some sort of support.

I talked to one shower glass company that I think was talking about this option, but I couldn't picture it -- thanks for the drawings. I have to say that I like this option even less than the header. Would it help any if the door could be mounted into a half wall at least on the bottom hinge and then to the glass panel on the top hinge?

Could I avoid the header and support bracket by using thicker glass, like 1/2"?

no, will only wobble more as the glass is heavier.

Make the whole thing a wetroom. Not only will your guests have more room than a cramped neo-angle (I HATE using a neo angle) provides, but you won't have to worry about glass at all. The additional waterproofing needed will actually be cheaper than the glass you're considering.

Have you seen sochi's amazingly gorgeous bath? Maybe that will give some ideas for how to incorporate an open shower in a small bath:

Here is a link that might be useful: sochi's master bath

What if I only put glass on the sides of the neo angle and left the door off -- would that be weird? Do you think water would splash out of the shower area on the infrequent occasions when the shower is used? This is the bathroom that is really our powder room, so I want it to be pretty and special looking. I never imagined how difficult this little room would be.

I think water would splash out on frequent occasions, as in all the time. In a neo angle shape you just can't get the shower head far enough away from the door. My point in posting sochi's bath was to show an alternative to an angle shower.

If you want a neo angle shower you need a complete enclosure and that needs to be supported, even if it's not beautiful to do it.

writersblock is correct on all points except water will definitely splash out!

Isn't that what I said? :)

Since this bathroom is virtually square, I really have no option other than the neo angle unless I remove the shower altogether, which I don't want to do, because it does come in handy when we have a full house of visitors and I have been told by realtors that removing it would reduce the appraisal value of the house.
Millworkman, what is the shortest that support bracket in the corner can be and do you think it would be less obtrusive than the header? I have never seen the support bracket done. Thank you.

If you want to see more pics of support brackets in action, Vigo uses them for several of their enclosures. If you click to see the large photos from this page you can see it in action. Personally, I prefer the frame to that. There are lots more photos if you look at their other frameless enclosures.

Here is a link that might be useful: frameless neo round shower enclosure.

I just had a 36x36 neo angle shower enclosed with glass.

Same issue - we have a header. One advantage aside from structural of a header is you can use pivot hinges - i.e. the hinge mounts to the door and a pin pivots in the shower base and header. No hardware on the side glass panel and the hinges are much less 'in your face'.

We also went with a simple knob for the door handle - no big D handle.

It's sturdy and looks good IMHO. I don't have pics but am happy to snap a couple.

Don't over think it. The header isn't that big a deal. Like others have said, if you want to be truly minimalist and even likely save some money, make it a wetroom. Not nearly as common in North America as it is overseas, but worth thinking about. No glass at all, and also the shower could be curbless for ease of access if that ever becomes an issue.

Thanks, writersblock, for the link to the pictures -- not really liking the look of the support bracket.
Toronto Tim, does water leak out of your neo-angle? The glass guy was here this morning, and said that water will leak out but they have some (ugly) plastic strips for between the glass panels to help with that -- sounds like I might get a wet room, whether I want one or not!

Plastic strips must be used as a water seal or yes it will leak out without a doubt. As writersblock mentioned (I was being a bit of a smartass((not unusual for me)) as you said you think it would splash out) it would splash out for certain idf the shower head is on the wall opposite the door. If the head is pointed at the side panel maybe not so much.

If you would consider taking the glass all the way up to a small soffit near the ceiing, you could use pivot hinges at the top and bottom without a header. The door swings in or out which is helpful in a small room. We wanted to minimize hardware so we did this in our masterbath. We have a good vent fan in the shower and keep the door open (in) when the shower is not in use.

Thanks for all the suggestions.
I have another question: What kind of support is needed inside the walls for the headrail option vs the support brackets? I would want to use clips at the floor and preferably just silicone on the walls without a channel. Thanks.