In the history of writing we see a development from logographic writing (with thousands of different characters) via syllabic writing (with still fifty to several hundreds of signs) to alphabetic writing, for which only 20 to 40 different letters need to be learned. Apparently people never felt the need to simplify their writing system even further, maybe because learning 26 letters is already pretty simple, compared to learning to read and write. However, one more evolutionary step could have been made...

The letters of the Latin alphabet can be arranged more or less phonemically in the 26 visible cells of a 3*3 cube (cf Rubik's cube):

Front to Back:

Layer 1 (voiceless consonant): PTK-FSH-WLJ

Layer 2 (vowel&double consonant): IQU-Y*O-EXA

Layer 3 (voiced consonant): BDG-VZC-MNR

Left to Right:

Layer 1 (front&labial): PFW-IYE-BVM

Layer 2  (dental-alveolar): TSL-Q*X- DZN

Layer 3 (back&palatal-glottal): KHJ-UOA-GCR

Up to Down:

Layer 1 (close&plosive): PTK-IQU-BDG

Layer 2 (fricative): FSH-Y*O-VZC

Layer 3 (open&sonorant): WLJ-EXA-MNR

Obviously, some concessions had to be made: the C for instance, is not a fricative when it represents a K-sound, and is certainly not voiced. Moreover, letters are also used for other phonemes, especially in other languages than English. In Dutch for instance, the G is a voiced fricative and should be in the place of the C.

The arrangement results in a writing system with only 3 letters and 4 diacritics, as becomes clear when using the (lower case of the) font. On which axis to use letters and on which diacritics, is of course arbitrary. In the arrangement chosen here, a vowel is always an o.

We can make the claim that this is the smallest possible alphabet that remains readable. We could of course get rid of one of the 3 letters, but then some Latin letters would have to be represented by diacritics only.

In fact, what we're doing here is represent each Latin letter by a 3-digit ternary number: each digit is a variable that can have 3 different values, so there are 27 possibilities. The only way to make a smaller alphabet is by using binary; but if each variable could have only 2 values, more variables would be needed, so we would get letters with 3 or more diacritics.

A totally different way of representing the 26 letters of the Latin alphabet, following the same principle, is shown in the upper case. This writing system uses more space and is more abstract, but the ternary character is even clearer.

0=1-1  2=3-1  4=3+1  5=9-3-1  6=9-3  7=9-3+1  8=9-1