For every hexagram name I searched for words in which this character was a part of the character(-compound) or of a word (which is usually a combination of two characters). The meaning of the character itself can change in the course of centuries, but in compounds often the old meaning is retained. Looking at several of those gives a "theme", a basic or comprehensive meaning. In parenthesis are the meanings of the parts.
The characters at left: words or compounds with Taì
1 (taì + correct) calm; self-possessed
2 (taì + water) mother-in-law
3 (taì + mountain) sb./sth. of great weight/importance, another name for father-in-law. Mount Taishan: the most important of the 5 sacred mountains.
4 (taì + west) the West; the Occident.
5 (open + taì) go well/auspiciously
6 (taì + Dipper) eminent authority (TaiShan and the Great Dipper) short for:
7 (Taì Shan Northern Dipper) highly-revered person
'Grand' is the meaning which fits best in all compound characters. Lofty, great, like Mount Tai.
Hexagram 11 is the big mountain which connects the life of man with heaven, reaching up into the realms of the gods. The water of rain and snow comes down the slopes in brooklets, rivers and sources, fertilizing the valley at the foot. In the same way the blessings of the gods come down, and it depends on man if his soul is a fertile field, where these blessings can grow a rich harvest.
The blessings of heaven are a free and rich gift, but if one does not pick them up, one will often not even know they were ever there.
But if one does accept them, they make life beautiful and easy. "Small go, great come": small investment, large profit.
Blessings not only come down mountains, they can dwell in eyes or words, in gestures and attention. Even in strokes of luck, like finding on the sidewalk just what you need, or missing the bus that gets involved in an accident.
Pay attention though: many things which appear on your path are no blessings at all, even though they might look pretty. Be severe and say no to everything which can harm you: you need hexagram 12 as well.
About "The emperor marries off his younger sister" in hex.11 and 54
11.5 and 54.5. The emperor marries off his younger sister. It seems that this princess is the one who became the mother of King Wen. So she was destined to becomes the mother of a dynasty. He married her to a man of lower rank, the father of Wen.
By doing that, he connected the two families, and he even connected the ancestors of the two families. So later, when Wen (or rather his son Wu) had conquered the rulers of Shang, he still brought the sacrifices to their ancestors. Because they were also his ancestors. This marriage was a great blessing for both families and for the country.
For 11.5 the fanyao is about waiting with food and drink, so don't fuss about ranks or going far from home or having to adapt to another life. You are destined for something bigger. Or maybe you are the ruler Yi, and you have to put things together, to make them bigger than they are on their own. Whoever you are, your life deserves to be meaningful, so make it such.
For 54.5 there is another but related meaning. A warning not to demand the best place, or all the honor you deserve. Others might envy you, become enemies (fanyao 58.5). In a place which is not your own, it is better to be careful. Fighting for small things might make you lose the big things.
The characters at left: words or compounds with Pĭ
1 Mawangdui: (woman-broom) return. The 'broom' was probably originally an attribute of nobility, and only later got its meaning as broom.
2 (to-be + no) whether or not; is it so or not (Shi is right or sure as fact)
3 (no + settled) negate; deny
4 (no + rule) otherwise; if not; or else
5 (may + no) can or can't, affirmative or negative comment, whether it's possible or not
6 (able + no) is it possible...?; can or cannot?
7 (assist + no) whether or not
8 (skilful + no) pass judgment (on people)
Negation is the meaning which fits best in all compound characters. Negation: oppose, no, not.
Hexagram 12 is the hard side of law, the merciless answer of nature when one goes against it, the seemingly unjust death of people in disasters, the 'no' of someone who does not see your point. And even the frustration when one cannot accept the facts, and fights an impossible battle or loses one's happiness. "Great go, small come": large investment, small profit.
These laws are not easy or nice, but everyone needs them. As soon as they get lost, man becomes frightened, lost, disturbed. Without them life is a useless mess. But when one knows and accepts them, they have a great beauty.
And like the blessings of hex.11 can be in tiny things, the laws of hex.12 are also in everyday encounters. The ability to say no and also to accept no make daily life livable.
There is another side though to hexagram 12: it is the creativity of the earth (inner trigram Earth, manifesting through outer trigram Heaven): getting things done without doing. Letting life 'happen'. If you want something to happen, to be done, then don't press anything, "be" what is needed. The creativity of the Earth is the means to do something when the world tells you "no".