In the last post I have introduced the three crossing labyrinths by Dom Nicolas de Rély (see: related posts 1, below). Here, I want to have a closer look at the labyrinth Rély 2. At first glance it looks like a labyrinth with 8 axes and 15 circuits. The main axis points to the right.

For a further analysis, I have rotated the labyrinth such that the main axis is oriented downwards (fig. 2). By shifting two turns of the pathway in the upper right quadrant and one turn of the pathway in the lower right quadrant the number of axes can be reduced from 8 to 6. For this, I assume that if turns of the pathway can be aligned to each other, they will be aligned. Thus, the labyrinth can be drawn with the minimal number of axes needed.

The pathway of Rély 2 crosses the main axis from the 7^{th} to the 12^{th} circuit, as is indicated with the piece of the Ariadne’s Thread drawn in red.

In addition, the labyrinth contains one complete innermost 15^{th} circuit (similarly drawn in red). From this circuit the pathway is the directed to the center.

The labyrinth even shows one more particularity, that I have overlooked so far. On entering the labyrinth, the pathway turns to the fifth cirucit. However, it also continues straightforward into a dead-end on the 6^{th} circuit, highlighted with a red cross.

In figure 3 I show the pattern of the labyrinth adjusted to 6 axes. (Re. patterns of crossing labyrinths see also: related posts 3).

Rély 2, thus, is an uninteresting labyrinth. The innermost circuit can be omitted without loss. But even if this circuit is dropped, we still obtain a labyrinth of little interest. The pathway would then again be directed from the innermost (14^{th}) circuit to the center.

The entire labyrinth looks not really well constructed. This becomes clear especially in the original version with 8 axes, in which the turns of the pathway are distributed quite arbitrarily.

Rély 2 is not the only labyrinth showing an unnecessary high number of axes. I have already introduced one specially prominent example on this blog, the „complicated labyrinth“ by Sigmund Gossembrot (related posts 2). Whereas the intention of Gossembrot probably was to cause confusion and uncertainty and to transform the Chartres type labyrinth into a maze, it seems to me that the intention of Rély was to bring about especially complex labyrinths with multiple axes.

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.