# The 3 Circuit Labyrinth on Rubik’s Cube

In the context of the theme Labyrinth and Flower of Life, the similarity to a cube has been mentioned more often. The hexagonal shape of the labyrinth was just too reminiscent of a cube. And that got me looking for the labyrinth on the cube.

I have a magic cube and as a small brain training I solve it once a day. This is now memorized and routinely.

In Further Link below you can find out what a magic cube is.

First, I tried to put Ariadne’s thread on the small squares. This is relatively easy.

For better representation, the 6 sides of a cube are “flattened”:

The layout

You can draw in there Ariadne’s thread for a 3 circuit labyrinth type Knossos. Generally known, this has the path sequence: 3-2-1-4.
The beginning is on the frontside below at left. Then we go to the third line, to the second and the first line and finally to the center in 4 up in the middle square.

And here in an isometric view:

Three views

I hope you can imagine that on the drawings?
We see the lines on 5 sides of the cube, the bottom remains empty. The middle is slightly larger, but we do not touch all the small squares.

If you want, you can download, print or copy the template as a PDF file.

Such a cube would certainly be quite easy to solve as a magic cube. Especially if you have a template of it in mind.

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# A 3-Circuit 5-Axle Labyrinth

The preceding contributions ask for a continuation.

However, the focus should not lie any more on the flower of life, but on the shape of the labyrinth. The square form pleased me. And, besides, particularly the depth effect through the accentuation of the middle in the diagonals, and the irritating appearance of the spatial visualization.

A 3-circuit 3-axle square labyrinth

Could one not increase this by underlining all diagonals, and thus make from a 3-axle labyrinth a 5-axle labyrinth? The 3 circuits could remain. I have applied only one more time the same “barrier technology” that I used to get 3 sections in a 3-circuit labyrinth. And because the first “redirection” is immediately on the beginning of the way, I have shifted the middle vertical lines a little bit to the right.

A 3-circuit 5-axle square labyrinth

This layout is not necessarily designed for a labyrinth to walk. It should only show that with only three circuits quite a lot of movement and irritation can be generated. It will fit better as a tile pattern. But, at least, it is unambiguously a labyrinth with all requested characteristics.

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# A 3-Circuit 3-Axle Labyrinth

In an older post about the 3-circuit labyrinth I had announced a continuation. Here it is:

There the labyrinth had a hexagonal form; but the round shape is also possible and than it looks like this:

The 3-circuit, 3-axle labyrinth in round shape

The origin was a 3-circuit labyrinth type Knossos to which, however, at two places “obstacles” were inserted. This is only possible at these both places: first between the 3rd and 2nd circuit, and then between the 2nd and the 1st circuit. The axes must not be applied under an angle of 120°. It is only important which circuit is split through the barriers. One can find out that by trial and error.

Now the question: When and from whom was “invented” this type of  labyrinth?

In Hermann Kern’s book “Labyrinths” triple labyrinths and those with three sectors are mentioned, but no historical labyrinth has exactly the alignment shown here.

It belongs to the multi-axle labyrinths, and these were first the Roman labyrinths. However, they mostly had 4 sectors.

The medieval labyrinths had more circuits and also more “barriers”. Such a simple labyrinth did not appear amongst them.

So it is a contemporary labyrinth. Presumably it has been developed by different people and to different times independently of each other.

Jeff Saward has informed me that he has drawn those and similar outlines together with Jim Kimmis about 30 years ago without publishing them largely.

Andreas Frei considers this labyrinth to be the simplest form of a type which he describes as “serpentines in layers”. From him I have also got the tip to a labyrinth in Aarau from 1987.

In the USA John Ridder has sketched a 7-circuit and a 3-circuit labyrinth divided into three parts about 10 years ago. Together with Warren Lynn he has developed under the name “3 circuit Triune” a canvas labyrinth with the title “The story Path labyrinth” especially for children.

Here are still more labyrinths of this type, each in an other shape:

in square shape

in pentagonal shape

in heptagonal shape

in octagonal shape

Even other forms are imaginable. Also one could arrange the axes at an other place. Or make the middle bigger or smaller. Or make the boundary lines and the paths in different width. (Almost) no limits are set to your imagination.

Here finally the triangular one:

3 circuits, 3 axes, triangular

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# The Hexagonal Classical 3 Circuit Labyrinth

We still had the whole labyrinth inside the Flower of Life on this blog (see related posts below). However, the middle was as small (one path width) as we know that from the classical 7 circuit labyrinth.

How does it look now if one makes the middle bigger and maintains, besides, the hexagon?

The 3 circuit labyrinth in hexagonal shape

The paths are still defined by the well-known path sequence 3-2-1-4.
Also the classical 7 circuit labyrinth can be brought into hexagonal form and will preserve its typical path sequence 3-2-1-4-7-6-5-8.

The 7 circuit labyrinth in hexagonal shape

The different labyrinth types do not depend from the external form.
Another type ordinarily is got through a changed path sequence.

Thus can be inserted, for example, within our 3 circuit labyrinth at two places “barriers” which cause another alignment. Thereby the firstly one axis labyrinth will change to a 3 axis labyrinth.

A hexagonal 3-circuit 3-axle labyrinth

The alignment is a little more complicated and the path sequence is: 3-2-1-2-3-2-1-4. Three sectors are walked one after the other like in a Roman labyrinth. First I turn to the middle, then outwardly, then again to the middle, again outwardly and from very outside, finally, I reach the center.

I can also turn the labyrinth and take a horizontal edge as a base. Then it looks as follows, drawn inside the Flower of Life:

The switched hexagonal labyrinth inside the Flower of Life

This does not arise compelling from the geometry of the Flower of Life, hence, is a further development or a playful modification.

I could imagine this quite well as a labyrinth from paving tiles. Who builds one?

Nice honeycomb patterns can be generated from the hexagon. The bees make this; why could we not have a labyrinthine honeycomb pattern?
The hexagon can be mirrored and switched (six times) and combined in different patterns.

Labyrinthine honeycombs

If one makes now a wallpaper, or wall tiles, or flagstones from it, the entrances will get “enframed”. But, nevertheless, within each single honeycomb the unequivocal way of the labyrinth (Ariadne’s thread) can be seen.
Otherwise, even irritating visual perceptions are possible. Since the hexagon contains also the edges of a cube.

Labyrinthine honeycomb pattern

To be continued …

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# The whole Labyrinth inside the Flower of Life

There are two important lines in a labyrinth:

• The one is the so-called Thread of Ariadne, the path or way from the entrance into the middle and back again. This is always an uninterrupted line, without branches or overlaps.
• These are the boundary lines (the walls, the sidelines) which delimitate the way, and between those the way runs. They may cross already once and overlap.

Only one of both lines is mostly shown in a labyrinth. Frequently this are the boundary lines. For a labyrinth that can be walked this is so almost always. Then the way is the free space between these lines.
However, in drawings or images even only the thread or even both can be shown.
This can be sometimes confusing if one has to distinguish a labyrinth from a maze.

The whole labyrinth inside the flower of life

In my first article (see Related Post below) I had only marked the way (Ariadne’s thread) that is contained within the flower of  life. It is the path of a 3 circuit labyrinth from the type Knossos with the path sequence 3-2-1-4.
The corresponding boundary lines arise if one constructs other lines parallel to the path. These also run between all petals, only the extreme line runs outside, however, touches the outside circle of the flower of life at six spots and thereby forms a hexagon, a honeycomb.
In this labyrinth even the walls form only one single line. They run from one turning point to the other one without crossing each other.
The cube enclosed in the flower of life is even very good to recognize.

The labyrinth unites square and circle. And here still the hexagon as a basic element of life for growth and development.

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# How to Make a Temporary 3 Circuit Classical Labyrinth

I had to take over this task recently. There was a birthday party and there was short of space.
On this occasion a 3 circuit labyrinth fits best. Nevertheless, it is good to have enough width for the path to walk. And a bigger middle. Thus I adopted a circular labyrinth with the path sequence 0-3-2-1-4.

A 3 circuit Knidos labyrinth

I had a space of about 4 m. As path width I chose 50 cm, the middle had a diameter of 1 m, and the overall diameter was 4 m. Thus arose a length of about 39 m for the walls which can be marked, e.g., very well with a rope. I have done this with two ropes of 20 m length.

The 3 circuit labyrinth

The 3 circuit labyrinth

But I was not really pleased with it. Since the middle seemed to me a little bit too small. I still hold the 4-fold path width as a good measure for the center.
Hence, I have developed a sort of prototype which I would like to introduce here:

A 3 circuit Knidos labyrinth with a dimension between axes of 1 m

The dimension between axes is 1 m, the center has 4 m and the overall diameter is 10 m. The walls have a length of 86.83 m, the way into the center amounts to 66.34 m. The other dimensions and the radii can be taken from the drawing.

One can split the whole distance of the walls: So I get 38.56 m from A to C, and 48.27 m from B to C (total length 86.83 m). This can be laid, e.g., with two ropes of 50 m and 40 m length.

The walls do not overlap and are made from one line, differently to the 7 circuit classical labyrinth.

Here you may see, copy or print the design drawing as a PDF file.

The whole is scaleable. That means that if you wish other widths or diameters, the radii, lengths (short all dimensions) will change accordingly. If, e.g., only a 4 m overall diameter is possible, the dimension between axes would become 40 cm and the internal radius 0.80 m (the center therefore 1.60 m). I must multiply all dimensions by the factor 0.4. The path length would be 26.54 m and the (splitted) walls 15.42 m and 19.31 m.

Here the dimensions of the prototype are multiplied by the factor 0.5. Everything becomes half as big: The dimension between axes 50 cm, the center 2 m and the overall diameter 5 m. The path length decreases to 33.17 m and the /splitted) walls are 19.28 m and 24.13 m (43.42 m added together).

A 3 circuit Knidos labyrinth with a dimension between axes of 50 cm

Here too, you may see, copy or print the design drawing as a PDF file.

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# The Labyrinth Inside the Flower of Life

The Flower of Life contains a lot of things. However, is a labyrinth also hidden in it?

I explored the flower, examined the connections contained in it and would like to present the result: