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Geometric Drawing of the Tower Octagon

The tower octagon can also be drawn in place using a geometric construction, folio 108:01.

The following is one such construction procedure. The octagonal ring is a more useful reference for this purpose.

The construction start by drawing a circle that fits inside the ring space and is centered on the base octagon diagonal inside the tower ring space, folio 108:02. The radius of this circle is half the ring width, t.

Two of the corners of the tower octagon are the intersections of the circle with the base octagon diagonal, folio 108:03.

The octagon minor diagonals serve to identify other tower octagon corners.

The octagon minor diagonals are those joining every third corner of the octagon. The lines joining every fourth corner are the octagon diagonals that are also referred to as major diagonals, to differentiate them from the minor diagonals. The last set of diagonals, those formed by joining every second corner of the octagon are the side of the square inscribed in the octagon.

The base octagon minor diagonals intersect the tower circle and define two more corners of the tower octagon, folio108:04.

The extensions of the minor diagonals of the octagon inscribed in the base square also intersect the tower circle and define two more corners of the tower octagon, folio 108:05.

A line perpendicular to the base octagon major diagonal and drawn trough the center of the tower circle intersects the tower circle to define the last two corners of the tower octagon, see folio 108:06

The tower octagon is constructed by joining the eight intersection points on the tower circle with straight line segments, folio 108:07.

This geometric procedure is repeated in each of the eight corners of the base octagon for each of the eight tower octagons.