The altar shall be foursquare. That this signifies thus what is just, is evident from the signification of foursquare, as what is just — of which in what follows; and from the signification of the altar, as a representative of the Lord and of the worship of Him. Wherefore by the altar being foursquare is signified what is just in the Lord, and therefore in worship. Worship is said to be just, when the good and truth which are in it are from the Lord, and not from man; for what is just is from the Lord alone... That foursquare means what is just originates in the representatives in the other life. In these representatives goods are presented as round, and the goods of the external man, which are called just, are presented as foursquare; truths however and things that are right are presented there as linear and triangular. On this ground then it is that by foursquare is signified what is just, as also by the altar of incense being foursquare (Exod. xxx. 2), and by the breastplate of judgment being a doubled square (Exod. xxviii. 16), and likewise by the new Jerusalem being foursquare (Apoc. xxi. 16). The new Jerusalem here means the new church of the Lord which is to succeed our present church; the external good of it, which is what is just, is signified by its being foursquare. (Heavenly Arcana, n. 9717).A square is often used to create a square foundation. Thus to be square represents good in the external form. A circle, whose ratio from its length to its circumference is pi, an infinite irrational number - is good in the internal spiritual form. The desire or intention to do good in one's mind is thus represented by a circle, and the actual work or deed based on that intention is good in the external form. Any form of measurement must take place by ruler or by triangulation: thus a line or triangle represents truth.
So the meaning of the line, triangle, square and circle are now known. Now compare what Swedenborg said to the below video. I do not agree with everything it says - the presenter seems to know that the Bible is symbolic of something, but does not know what that something is. For that, the inner spiritual meaning of the Bible was revealed to Swedenborg which he explained in his massive work Heavenly Arcana, otherwise known as Arcana Coelestia, meaning "Heavenly Secrets." But one thing he says which is correct: that geometric shapes with straight edges tend to represent the "male", while round forms such as the circle represent the "female." This is correct. Because male and female are also symbolic: the male represents truth, and the female represents love. The male is intellectual, the female is volitional. The union of good and truth is represented by marriage. This symbolic correspondence is used over and over again in the spiritual meaning of the Bible. This spiritual correspondence, which flows into all living things, is the origin of the desire for sex in the natural form. As each good has its corresponding truth, and each truth its corresponding good, thus the spiritual representation of that is the marriage of one man with one woman. This is why perversions of this order: such as adultery, fornication, polygamy and homosexuality - are not permitted within the Christian Church. As many cultures of this world practiced polygamy, they are not allowed to know the Christian revelation. And that is the reason why we have Islam: Islam is for cultures which allow polygamy, for those who are in external good, but they are not allowed to know the internal spiritual revelation of Christianity. Thus many Muslims are taught from their youth the Bible is "corrupt", even though ironically that disagrees with the Quran (Koran). The end result is many do not even bother to open scripture, and ignore the textual evidence that it was not corrupted.
I am digressing a bit...we are discussing the spiritual symbolism of geometry. But to understand the spiritual symbolism of geometry, one must first understand the the basic spiritual symbolism of the male and female. The below video also introduces the concept of the Vesica Piscis and the Seed of Life. For the symbolism of those shapes, see my previous blog entry, Sacred Christian Geometry - the Seed of Life.
Here is part 2, which also discusses an eight sphere pattern known as the "egg of life", which pattern shows up in the embryo of all living forms. It also discusses the five Platonic solids: