The last crossing labyrinths I want to show were all designed by Dom Nicolas de Rely. This clergyman from Benedictine abbey Corbie near Amiens has produced eight drawings with own labyrinth designs, all in pen and ink. Three of them are crossing labyrinths. I have ordered them by the number of axes and labelled them Rely 2, 3, and 4.

Rély 2 has 15 circuits. It is designed on a layout with 8 axes; however by shifting of one (real) single barrier, it can be reduced to 7 axes. The pathway crosses the main axis from the 7th to the 12th circuit. And it reaches the center from the innermost 15th circuit, which is a complete attached trivial circuit. Therefore it is an uninteresting labyrinth (fig. 1).

Because of its pseudo single barriers, Rely 3 has been already shown on this blog (see related posts, below). It has 9 axes and 5 circuits. The pathway crosses the main axis from the 4th to the 1st circuit and reaches the center after a full circle on an attached trivial 5th circuit. Thus, also this labyrinth has to be described as uninteresting (fig. 2).

The third crossing labyrinth, Rély 4, is designed on a layout with 14 axes and 15 circuits (fig. 3). This, however, can be reduced to 10 axes. The pathway crosses the main axis from the 6th to the 13th circuit. The entrance to the labyrinth is from the left side and (erroneously?) closed. The center is not reached at the main axis, but from the third side-axis on the innermost circuit. Therefore there remains a short piece of the pathway leading into a dead-end at the end of the last circuit.

I will have a closer look at the two labyrinths Rély 2 and Rély 4 in a later post.

In addition to the three labyrinths with one axis from my last post (see: related posts 1, below) there are also 7 historical labyrinths with multiple axes and with their pathway crossing the main axis. Of these, I want to present here four very different examples from Roman times until the 18^{th} century together with their patterns. I have already shwon on this blog how the pattern can be obtained in crossing labyrinths (related posts 2).

The oldest crossing labyrinth with multiple axes is the polychrome mosaic labyrinth in the Roman proconsul’s residence, House of Theseus, at Kato Paphos, Cyprus dating from 4 CE (fig. 1). Presented is the Ariadne’s Thread as a guilloche ribbon. The pathway starts from a dead-end on the first circuit. After completion of the full circuit, it crosses the main axis and describes a sector labyrinth with four axes on circuits 2 – 6. Then follows a full 7^{th} circuit that leads into a closed 8^{th}circuit.

Figure 2 shows the labyrinth of Bayeux Cathedral from the 13 CE. This has 4 axes and 10 circuits. The pathway crosses the main axis on the innermost circuit.

A strange labyrinth is depicted on a plaquette from Italy of the 16^{th} century. It has 6 axes that are distributed irregularly. There is a flaw between the third and fourth axis, where there is an encapsuled piece of a pathway that is not accessible. This piece circulates on the second and third circuit but has no connection with the pathway that leads from the entrance to the center of the labyrinth. Furthermore, the pathway crosses the main axis three times. This labyrinth can be easily reduced to three axes.

Also in this design for a hedge labyrinth from year 1704, the pathway crosses the main axis twice and then ends peripherally in a dead-end (fig. 4).

All these crossing labyrinths with multiple axes show particularities. Theseus has no entrance and no center, Bayeux is uninteresting, as it has simply a complete circuit added at the inside. The plaquette is drawn faulty and unnecessary complicated. And in Liger, no center can be spotted.

Most of all labyrinths we know are alternating labyrinths. In these, the pathway does not traverse the main axis. Every time it arrives at the end of a circuit it changes direction and skips to another circuit.

However, there exist some few labyrinths with the pathway crossing the main axis. This means, it does not change direction but only skips to an other circuit whilst following a piece along the axis. Up to now I simply have termed these „non-alternating“ labyrinths, since „alternating“ can be considered the rule. If we don’t want to term the property negatively („non-alternating“), we could also use terms such as „traversing“ or „crossing“. From now on, I will use the term „crossing labyrinths“ for such labyrinths.

Whether a labyrinth is alternating or crossing, this refers to its main axis only. That is the axis where the entrance to the labyrinth and also the access to the center are situated. In labyrinths with one axis, there is only the main axis. Labyrinths with multiple axes, have also side-axes in addition to the main axis. Note that the pathway always must traverse the side axes. Otherwise, no side axes could be designed.

Among the 87 types of labyrinths in my catalogue of historical labyrinths (see: further links, below), 10 are crossing, the others alternating. Here, I will show the three crossing labyrinths with one axis once more. All three have already been presented on this blog.

The most remarkable crossing labyrinth is the labyrinth of St. Gallen.

It has been repeatedly confused on this blog with the alternating labyrinth with 6 circuits and the same sequence of circuits, of which no historcal example is known (related posts 1 and 2).

Another very beautiful crossing labyrinth is the one by Al Qazwini (related posts 3).

The third crossing labyrinth with one axis is Folio 53r by Sigmund Gossembrot (related posts 4).

All three are interesting crossing labyrinths, in which the pathway does not enter on the first circuit nor reach the center from the last circuit. In St. Gallen and Qazwini it traverses on the full distance of the axis, in Gossembrot 53r only one part of the axis (from the 6^{th} to the 9^{th} circuit).

In my previously shown labyrinths the pathway takes its course through all pseudo single-barriers in the same direction. In the pattern this course is from top left to bottom right, as shown in fig. 1 from my last post. Correspondingly, in the labyrinth, the path runs in clockwise direction from an outside circuit to a circuit more inside the labyrinth.

This raises the question whether other arrangements of the pseudo single-barriers are possible, such that the path may also take courses from inside out or in anticlockwise direction. In fig. 2, I show such a labyrinth. This is self-dual and has 4 axes, 9 circuits and 2 pseudo single-barriers in each side-axis.

Here, we have the following courses (fig. 3):

from top left to bottom right at the first axis upper barrier and at the third axis lower barrier

from bottom left to top right at the first axis lower barrier and at the third axis upper barrier

from bottom right to top left at the second axis.

However, a course from top right to bottom left is missing.