I hadn't read Allen Steele before picking up Hex on a run to the bookstore and if Hex is representative of his work, I probably won't bother doing so again.
I tend to favor hard SF that tries to get its science right but have no problem with a bit of good soft science space opera or even fantasy if it's done well. This book seems to be trying for some amount of hard science chops but flubs it badly and in ways that should have been incredibly easy to avoid. Almost as bad, it seem to depend on the characters acting like idiots in order to create any sort of tension or drama. As far as specifics, let us count the ways:
1) The background for most of the story is a Dyson sphere, a huge artificial structure enclosing its entire star. Probably moderately familiar to most SF readers. In this case, the sphere is spun for gravity. Steele mentions this and then promptly ignores this fact for the entire rest of the story, with his spacecraft (which appear to use some sort of nuclear fission or fusion rocket or even chemical thrusters) just flying right up to it. Problem is, that an object this size, spinning fast enough to produce the 2 gravities of centrifugal force at its equator that is mentioned, would be moving at hundreds of miles per second (Larry Niven describes this in detail in his excellent book Ringworld, with a 1 gravity spin for the ringworld requiring it to move at 770 miles per second. The spin also plays a role in various parts of the story and later books). As mentioned, in Hex this spin gets about 1 sentence and is then ignored.
2) It is mentioned several times in the book that the sphere is made up of about a trillion open hexagonal structures. Less than 15 minutes of research on google to locate the appropriate calculators plus maybe a minute or two more of number crunching reveals that the sphere would actually consist of a bit more than 43 billion hexagons. Still a very large and impressive number but nothing in the same league as a trillion plus.
3) At one point the sphere is said to have a volume of 1.086e17 miles (that's 1,086, +14 zeros). Normally you would say cubic miles, but Steele leaves this out. Possibly because this number isn't the volume of a sphere this size but the surface area. The actual volume 3.37e24 cubic miles (that's 3,370,+21 zeros roughly).
Ok, so maybe it's not critical to the whole story, but given that Steele actually goes out of his way to produce some nice little drawings of details of the sphere structure at the beginning, includes another graphic elsewhere in the book (mine was a hexagon in the paperback copy, they must have fixed it since the other reviews were written), and has a page on which he presents several of the dimensions of the sphere, in one case exactly and out to three decimal places, it would appear that some sort of calculations were done. They just appear to have been incomplete and sloppy.
4) At several points in the book it appears that the main exploration ship is effectively hanging in space near where the action is going on. This would be impossible even if the sphere weren't rotating. Apparently Steele has no real comprehension of the concept of an orbit.
Moving on to the interpersonal issues that try to drive the story:
A longstanding trope in SF is the idea of "Crashlanding on and Exploring the Big Alien Object". The most famous is Niven's Ringworld, possibly followed by Bob Shaw's Orbitsville, and Terry Pratchett played with a similar concept on a much smaller scale in his book Strata. In all the examples mentioned, the actual cause of the crash is something the characters didn't see coming or couldn't anticipate or the like. In Hex, the characters crash on the Big Alien Object (and spend the rest of the book trying to leave) because they do something (or possibly several things) stupid that they should have known better than to do in the first place. Let us count the ways (warning: Possible spoilers):
a) A running source of (mild) tension through the book is the strained relationship between the captain of the exploration starship and her son, who is a member of the "Explorer Corps" team picked to go check out the new world. At one point, when the captains asks him to reposition the camera he is using to record the exterior of the sphere so that the main ship can get a better view of something (a perfectly reasonable request one would think) his reply is described as filled with sarcasm (picture the response of a teenager being asked to take out the garbage).
b) Another member of the Explorer Corps team makes a sarcastic comment about a high ranking official who is coming aboard and is dressed down by her commanding officer. Whereupon she promptly does it again *to the officials face* and *in front of her commanding officer* and other ranking members of the ships crew. It is left to the official (one of the few characters in the story who seems to have half a brain) to explain his qualifications to her which has the effect of embarrassing her. Beyond that no one in her own or the ships chain of command does anything in response to her insubordination.
c) The commanding officer of the Explorer Corps team is generally painted as a twit, doing things (like grabbing the controls away from the pilot of the landing craft in a fit of panic) that make you wonder how he ever managed to get to his rank, and apparently existing for no other reason than Steele needs him to do stupid things to keep the story moving, at least until he ends up getting killed off by doing something stupid.
Overall the Explorer Corps seems to have a level of training and discipline that would make a Cub Scout troop look like Special Forces military in comparison.
d) The captain of the ship also contributes to the whole 'the only way we can make the story happen is if we act like idiots' theme of the book. Starting with entering an alien solar system, discovering the first ever known Dyson Sphere(!) and then following up with lines like "We didn't come here just to take pictures! We're going in!" when the aliens who invited them to the place (without actually mentioning what it was) aren't immediately responsive to hails.
e) Although it is mentioned that humans have been trading with multiple alien races for some years, the aliens who built the sphere are known and invited the humans, and the builders of a Dyson Sphere seem likely to outgun and individual human just a little bit, the preferred default position for the human's behavior in at least two different parts of the book is to strap on weapons and go out to confront the aliens. Any advice to the contrary is summarily belittled and dismissed. Of course then it turns out that this was a stupid (or at least pointless) think to do.
And so on and so forth. The above doesn't represent all the issues with the book, but gives a broad cross section. The only reason I'm giving it two stars is that the actual writing isn't bad. But the story and characters could have been done so much better.