The empty triangle is bad
The black group to the left is an empty triangle as there is no stone at a. The white group is not an empty triangle (it is a full triangle), as there's a single black stone next to it.
Why is an empty triangle so bad?
First of all, the empty triangle doesn't maximize its liberties. It has 7 liberties in isolation, wheras the straight three have 8 liberties. Both make a strong connection. The loss of a liberty without any kind of gain is unacceptable. There are many, frequently occurring positions in real games, where this one liberty is vital.
Secondly, two stones in a diagonal are connected, in the sense that they cannot be separated in one move, but they can be sacrificed if desired. Now the empty triangle is connected too, strongly, has a little bit more influence but must be sacrificed as a whole if needed. The one extra stone adds close to no value. It is a wasted stone.
Also, if Black wants to develop to the right, then play the marked stone instead. White cannot cut this formation without help from surrounding stones. Black's stones are securely connected. Closer to the side, farther extensions are virtually connected. This development is much more efficient than the empty triangle.
In contrast, the full triangle is very strong and efficient. In the upper position, Black can be cut. So, below fulfills a very important function: it connects two stones. By doing so, the white stone becomes very weak. The investment is 3-1, whereas in the empty triangle it is 3-0. Black's moves all have purpose.
However, he puts himself in a bad position. Black's straight three are strong, while White's zigzag three are weak. Black threatens to cut at , and White has to connect.
Now he has connected, but forms two empty triangles and serves no purpose whatsoever, while Black's peep is on the outside and provides support to the attacking stone .
Instead of exchanging - White should just jump out to . If black later plays then is needed. But right away is way too slow. The one point jump is hard to cut anyway. See don't try to cut the one point jump.
is the only way to save the all important cutting stones. According to An Younggil in his commentary on gogameguru, pros don't care as much about good shape these days. However, a few moves earlier he also commented that was an overplay .
Probably White had it all planned out until Black came up with this , which was a brilliant move according to the commentary, so that indeed White willingly anticipated the empty triangle in the previous diagram. Nevertheless, the shortage of liberties of the empty triangle created this opportunity for Black.
This comparison does not mean that this shape is good. In fact, you will not find this shape, with no opposing stone on any of these neighboring empty points, in a professional game. So any shape discussion is most relevant with actual game positions.
BramGo: Well, there are exceptions: Choi Cheolhan, 9p vs Meng Tailing, 5p, (2011-06-25) , move 106.