Cross Vaults Lateral Trusts
Square cross vaults generate lateral trusts that are focused at the four corners of the square and are directed outward along the directions of the square diagonals, folio117:01.
Without proper lateral support to contain the lateral thrusts, the vault collapses. Piers at the four corners of the square serve to contain these lateral forces, folio 117:01.
Positioning cross vaults side by side provides some natural balancing in the direction of the cross vault line up. Four cross volts located in a square pattern eliminate completely the lateral thrusts on the center support, folio 117:02.
In the example of folio 117:02, there are nine load points. The center one has no lateral thrusts, but the eight load points at the perimeter of the structure need piers.
The plant octagon with its minor diagonals provides a unique solution to lateral thrusts. Only eight piers are sufficient to contain the lateral thrusts for eight cross vaults lined up in a circle and a total of 32 lateral thrusts flowing in different directions.
When the cross vaults diagonals are lined up with the base octagon minor diagonals, the lateral thrusts are consolidated and channeled to the eight corners of the base octagon; see the next page.
The essence of Castel del Monte is a masonry proof that the octagon provides a natural and simple solution to the lateral trusts from a circle of eight cross vaults. The pentagon, the hexagon, the heptagon, the nonagon, etc., do not provide any similarly elegant solutions.
The octagon, so much celebrated at Castel del Monte, is a mystical figure in the religiosity of the Middle Ages. Castel del Monte shows that this divine figure provides also a solution to an earthly problem.