# Communication via a Rubik's cube

So, I watched The Promised Neverland recently and after exploring a little, I found out that Norman used a 5x5x5 Rubik's cube (aka a professor's cube) to communicate when he was held at the $$\Lambda\text{-}7214$$ research facility. The image below describes the same. So, I began wondering how one could possibly use a cube for communication. One idea struck me which involved using one row to encode one alphabet. Here's the method I devised : The image above shows a row of a 5x5x5 cube as seen from the front.
Here are the numbers associated with the six colours that constitute the cube :

• White : 1
• Blue : 2
• Orange : 3
• Green : 4
• Red : 5
• Yellow : 6

It's hard for me to explain how I came up with this or why it is what it is but I think stating some examples will help you understand it just fine.

So, let's say that the alphabet that we need to encode is at the $$x^{\mathrm{th}}$$ position in the alphabets. Here's what we need to do to encode it in a row.

First, we need to see if $$x\leq24$$. If yes, we follow algorithm $$A$$. If not, we follow algorithm $$B$$.

Algorithm $$A$$ :

• Find $$\left\lceil\dfrac x6\right\rceil \overset{\mathrm{def}}{=} y$$ where $$\lceil k\rceil$$ gives the smallest integer greater than or equal to $$k$$.
• Find $$x-\left\lfloor\dfrac x6\right\rfloor\overset{\mathrm{def}}{=} z$$ where $$\lfloor k\rfloor$$ gives the greatest integer smaller than or equal to $$k$$. If $$z=0$$, make it $$6$$.
• Fill the $$y^{\mathrm{th}}$$ square from the beginning with the color corresponding to $$z$$ and fill the last square with the colour corresponding to $$y$$

So, we have devised a way to represent the first $$24$$ alphabets in this way. The remaining two will be covered via Algorithm $$B$$.

Algorithm $$B$$ :

• Paint the last square with the colour corresponding to $$4+(x-24)=x-20$$. So, if $$x=25$$, paint the last square with the color red, if it's $$26$$, paint it with the color green.

Examples :

So, if we need to encode $$S$$, we first find the value of $$x$$ which comes out to be $$19$$. Also, $$y=4$$ and $$z=1$$. So, $$S$$ is denoted by : (Black : not relevant)

Similarly, the word TEST will be denoted by : To decrypt a row, let $$x$$ be the number corresponding to the color of the rightmost square and for $$x\leq4$$, let $$y$$ be the number corresponding to the $$y^{\mathrm{th}}$$ square from the left. If $$x>4$$, then for $$x=5$$, the alphabet is $$Y$$ and for $$x=6$$, the alphabet is $$Z$$.

For $$x\leq4$$, the alphabet is the one at the position $$6(x-1)+y$$

So, what I want to know about is the potential drawbacks of this method. One is, obviously that three out of the five "squares" in each row are wasted. Another drawback is that it's hard to show more than 5 words on the whole cube but that doesn't seem to be a problem with the method.

Also, what are some alternatives to this? What are some other ways that you have heard of to accomplish this and how do they compare with this method?

• Each face can encode $6^25$ possibilities, which is equivalent to 13 English characters. Dec 23, 2020 at 2:04