Ahh, the topic of word squares! Let me start by saying this: If you find this sort of thing even remotely interesting, you owe it to yourself to immediately order Making The Alphabet Dance (https://www.amazon.com/Making-Alphabet-Dance-Recreational-Wo...) one of the best references on recreational wordplay (another good source to consult is the journal Word Ways, https://digitalcommons.butler.edu/wordways/). Ross Eckler has a whole chapter on this topic alone, the following tidbits are taken from there:
Eckler states that the modern history of word squares (following in the footsteps of the SATOR square) started with the following one, published in 1859:
CIRCLE
ICARUS
RAREST
CREATE
LUSTRE
ESTEEM
This is called a single word square, same words appearing in both horizontal and vertical directions. When these are different it's called a double word square, which are much are harder to construct.
Here's a six-square:
RACISM
EVINCE
PERSON
ASCENT
STUCCO
TASTER
Here's a nine-square, with all words from the OED, published in 1993:
Constructing a 10-square using all words from a single language's dictionary has not been successful so far (who knows, with the new word additions to the OED...) Wikipedia calls this " the Holy Grail of logology" (https://en.wikipedia.org/wiki/Word_square#Order_10_squares)
And then he goes on to discuss word cubes! An n-cube contains n words repeated three times each and n(n-1)/2 words used six times each, it has a total of 3n^2 words. And yes, people have extended the idea to hypercubes.
I don't intuitively see why a double word square would be harder to construct than a single word square. After all, if you allow the words to be different, surely there are more options / more degrees of freedom to complete the square?
Interesting. I feel like Sator is cooler though because it actually has a meaning (other than "Arepo") and is grammatically valid. It also seems to have some deeper philosophical connections with early ideas of time cycles.
They're a lot harder to find (especially for English) though.
Each word needs to be valid both forwards and backwards in a Sator, right? There's a number of 5x5 Sators, but no 6x6, 7x7s, or higher because the number of words which satisfy are much smaller.
Eckler states that the modern history of word squares (following in the footsteps of the SATOR square) started with the following one, published in 1859:
This is called a single word square, same words appearing in both horizontal and vertical directions. When these are different it's called a double word square, which are much are harder to construct.Here's a six-square:
Here's a nine-square, with all words from the OED, published in 1993: Constructing a 10-square using all words from a single language's dictionary has not been successful so far (who knows, with the new word additions to the OED...) Wikipedia calls this " the Holy Grail of logology" (https://en.wikipedia.org/wiki/Word_square#Order_10_squares)And then he goes on to discuss word cubes! An n-cube contains n words repeated three times each and n(n-1)/2 words used six times each, it has a total of 3n^2 words. And yes, people have extended the idea to hypercubes.