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

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.

Ariadne's thread

Ariadne’s thread

And here in an isometric view:

Three views

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.

Ariadne’s thread for the template with slightly thicker lines:

Ariadne's thread

Ariadne’s thread

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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Further Links

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

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

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 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 square shape

in pentagonal shape

in pentagonal shape

in heptagonal shape

in heptagonal shape

in octagonal 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

3 circuits, 3 axes, triangular

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Further Links

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 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 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

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

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

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

Labyrinthine honeycomb pattern

To be continued …

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