2: The Tower

Quaternity is a term Jung used first in reference to trinity. In his first approaches he insisted heavily on the idea that each revealed trinity should be completed by a concealed element to form a quaternity.
He found too the number four was essential in the mandala:

I knew that in finding the mandala as an expression of the self I had attained what was for me the ultimate.

(MDR, Confrontation with the Unconscious)

He identified four in the 3-4 pattern with four in mandalas, although a mandala offers most often a perfect symmetry. Some mandalas Jung painted in the Red Book show a little dissimetry, like the one above, but most of them are pure "circumambulations of the center", as this Window on Eternity below which he painted in 1927.

Jung was in conflict about that with his friend Wolfgang Pauli, for whom the ultimate symbol of the psyche had to be symmetrical. Remo Roth explores this here.
Maybe Jung finally changed a bit his mind as, in Memories, Dreams, Reflections which was achieved just before his death, he uses the word 'quaternity' (Quaternität) only one time, alluding to the mandala, without any link to the trinity. In this book doesn't appear the "axiom of Maria Prophetissa" which runs like a leitmotiv in his previous works, as a proof of the 3+1 pattern.
I can be straight on that as I have e-texts of MDR in English and German, allowing word searches.
Jung uses the word quaternity in a comment of a dream he had after his illness in 1944. He dreamt he arrived to a chapel, and he went in:

To my surprise there was no image of the Virgin on the altar, and no crucifix either, but only a wonderful flower arrangement. But then I saw that on the floor in front of the altar, facing me, sat a yogi in lotus posture, in deep meditation. When I looked at him more closely, I realized that he had my face. I started in profound fright, and awoke with the thought: "Aha, so he is the one who is meditating me. He has a dream, and I am it." I knew that when he awakened, I would no longer be.

Maybe it's useful to recall that Jung saw Virgin Mary as the 4th element to complete Christian Trinity.
Jung goes on with deep insights about this dream, and here comes 'quaternity':

As a rule, we see this causal relationship in reverse: in the products of the unconscious we discover mandala symbols, that is, circular and quaternity figures which express wholeness, and whenever we wish to express wholeness, we employ just such figures.
(MDR, On Life after Death)

I put in bold "quaternity" as the English translaters Richard and Clara Winston put there the word 'quaternary', but Jung used Quaternitätsfiguren.
In reverse, there is only one time 'quaternity' in English MDR, and it's in a passage where Jung used the word Vierheit, but it needs a deep study as there might be the most striking example of quaternity-quintessence in Jung's life.

A whole chapter (among 13) of MDR is devoted to The Tower, the house Jung built himself in Bollingen, by the lake of Zurich, where he bought some land in 1922. He first wanted to build there a kind of primitive hut,

But I altered the plan even during the first stages of building, for I felt it was too primitive. I realized it would have to be a regular two-story house, not a mere hut crouched on the ground. So in 1923 the first round house was built, and when it was finished I saw that it had become a suitable dwelling tower.
(MDR, The Tower)

It represented for him the maternal hearth. He became increasingly aware that something was still lacking. And so, four years later, in 1927, the central structure was added, with a tower-like annex.

That was just a second step:

After some time had passed - again the interval was four years - I once more had a feeling of incompleteness. The building still seemed too primitive to me, and so in 1931 the towerlike annex was extended. I wanted a room in this tower where I could exist for myself alone. (...)
In my retiring room I am by myself. I keep the key with me all the time; no one else is allowed in there except with my permission. In the course of the years I have done paintings on the walls, and so have expressed all those things which have carried me out of time into seclusion, out of the present into timelessness. Thus the second tower became for me a place of spiritual concentration.

There is no picture for this 3rd step, and then came the 4th one, 4 years later:

In 1935 the desire arose in me for a piece of fenced-in land. I needed a larger space that would stand open to the sky and to nature. And so - once again after an interval of four years - I added a courtyard and a loggia by the lake, which formed a fourth element that was separated from the unitary threeness of the house. Thus a quaternity had arisen, four different parts of the building, and, moreover, in the course of twelve years.

I put in bold "quaternity" as it is not Jung's word, who used Vierheit, while the "unitary threeness" was dreiheitlichen Hauptkomplex. Probably the translaters were good Jungian disciples who felt the keyword 'quaternity' matched perfectly this 3+1 pattern.
A striking thing is the insistance upon the four-year period, as if a superior time-dependant force had led Jung in its architectural adventure. In 1923 he was 48, 12 times 4, and in 1935 he was 60, 15 times 4. Another way to put it is that he was 4 times 12 when he started a 12-year building activity, a perfect 4-1 pattern.

But a fifth step came in 1956:

After my wife's death in 1955, I felt an inner obligation to become what I myself am. To put it in the language of the Bollingen house, I suddenly realized that the small central section which crouched so low, so hidden, was myself! I could no longer hide myself behind the "maternal" and the "spiritual" towers. So, in that same year, I added an upper story to this section, which represents myself, or my ego-personality.(...)
It might also be said that I built it in a kind of dream. Only afterward did I see how all the parts fitted together and that a meaningful form had resulted: a symbol of psychic wholeness. It did develop, like an old seed which would have germinated.

I put in bold the last sentence, which is not present in English MDR, but I checked it was in the original German: Es hatte sich entwickelt, wie wenn ein alter Same aufgegangen wäre.
I won't try to guess how could have been forgotten this sentence, which looked very meaningful to me when I read the French translation. From the Quaternity (or rather Vierheit) arose a fifth part, like from 68-year old tired Jung in 1944 arose another himself, who would produce his essential works, within another 17 years.

Jung built his tower in a dream. These two nouns look a bit alike in German:
der TURM
der TRAUM (same 4 letters plus an 'A' in the middle)

Before the last step in 1956 came another important event, on Jung's 75th birthday:

In 1950 I made a kind of monument out of stone to express what the Tower means to me.

It's quite striking this came 15 years after the first ending of the Tower in 1935, when Jung was 60, 4 times 15.
MDR is so rich everything should be quoted, how the stone arrived by chance in Bollingen, how Jung noticed in its natural structure a small circle, a sort of eye, which looked at him. He chiseled it, and in the center made a tiny homunculus, namely Telesphoros, the Greek child-god of convalescence, thinking of his recovery in 1944.
This face of the stone is a perfect mandala, with four quarters around Telesphoros, with a Greek inscription:

Time is a child - playing like a child - playing a board game _ the kingdom of the child. This is Telesphoros, who roams through the dark regions of this cosmos and glows like a star out of the depths. He points the way to the gates of the sun and to the land of dreams.