Tower Corner Notch and the Irregular Tower Octagon
The anchoring of the outside face of the façade wall to the footing corners BB" and HH" creates notches at the inside corners where the towers meet the facade wall, folio 118:01.
The facade wall meets the tower not at the corners B" and H", but a distance away from these corners along the hidden sides of the tower, fully exposing the tower corners and a bit of the hidden tower sides, folio 118:01
The result is a notch at the place where the tower meets the facade wall, a corner notch, folio 118:02.
There are 16 corner notches in the plant design as each of the eight tower has two meeting corners with the facade wall.
This small, triangular notch is a problem if left as an open space in the final design. It is a likely eyesore looking at the castle from outside. More significantly, however, it breaks up the masonry continuity along the path of the lateral thrusts, passing from façade wall to tower. It needs to be solid masonry as the horizontal forces will not flow through an air gap at the corner notch.
The corner notch is filled in by masonry (page 116) in the modified design, folio 118:02.
The corner notch is the spandrel area discovered by H. Götze (Castel del Monte, Geometric Marvel of the Middle Ages, chapter IV.6, The Spandrel Formation, p. 175).
The corner notch is an equilateral right-angle triangle with sides m. The measure m is the distance of the tower corners B" and H" from the façade wall. The measure m for the corner notch is related to the measure f, folio 118:03.
This corner notch is clearly visible in the masonry work on the roof, folio 118:04.
The filling of the corner notch with masonry causes the length of the tower octagon sides abutting the façade wall to be longer by the measure m, folio 118:05.
With the other two sides merged into the façade wall masonry, the result of the final design gives the first-hand impression that the tower shape is an irregular octagon, folio 118:05.
The tower octagon irregularity is a matter of interest and ample discussion by H. Götze’s in his book on Castel del Monte. While he perceived the presence of a regular tower octagon, he could not rationalize the provenance of the spandrel.
Even without an actual scrutiny of the two hidden sides of the tower octagon and without the rationalization presented here, the regularity of the tower octagon can be inferred from the footing octagon where the visible octagon sides are all of the same measure, folio 118:06.
The façade wall is anchored to the footing octagon corners BB" and HH", producing six footing octagon sides that are visible and all of the measure ss", folio 118:05
The visible tower octagon sides have the measure s" except for the two sides that abut into the façade wall that are longer by the measure m, folios 118:05 and 118:06.