Vitruvius Principles

Vitruvius invented all the styles that are currently considered to be "Greek", such as the Norman Arch and the Big Temple.

One of his principle of architecture is to makes use of pleasing proportions.

"For the human body is so designed by nature that the face, from chin to the top of the forehead and lowest roots of the hair, is a tenth part of the whole height; the open hand from the wrist to the tip of the middle finger is just the same; the head from the chin to the crown is an eighth, and with the neck and shoulder from the top of the breast to the lowest roots of the hair is a sixth; from the middle of the breast to the summit of the crown is a fourth. If we take the height of the face itself, the distance from the bottom of the chin to the under side of the nostrils is one third of it; the nose from the underside of the nostrils to a line between the eyebrows is the same; from there to the lowest roots of the hair is also a third, comprising the forehead. The length of the foot is one sixth of the height of the body; of the forearm, one fourth; and the breath of the breast is also one fourth. The other members, too, have their own symmetrical proportions, and it was by employing them that famous painters and sculptors of antiquity attained to great and endless renown.
Similarly, in the members of a temple there ought to be the greatest harmony in the symmetrical relations of the different parts to the general magnitude of the whole..."

Symmetry is not the proportion but just how an object looks when cut by planes or rotated about a point

for example draw an equal sided triangle. it could be rotated 1/3 turn and look the same

also you could cut from point to bottom line and have two halves that look the same

a "rough potato shape" does not have that property"

Vitruvius cared about human proportions in relation to geometry and how we can apply that to architecture