is-sator-square

Is Sator Square?

A Discovery

One fine day while ploughing the fields, Farmer Arepo found a stone tablet with symbols carved on it... he knew such artifacts may show a message in four directions, so he wisely kept it and resumed turning the soil. He found more tablets, but with crops to sow he had no time to decipher them.

Your Task

Please help Farmer Arepo by inspecting each tablet to discern whether or not it shows a Sator Square!

The Square

• is a two-dimensional palindrome (made from words of equal length)

• observes four symmetries: identity, 180-degree rotation, and two diagonal reflections

• can be read:

  • left-to-right (across)
  • top-to-bottom (down)
  • bottom-to-top (up)
  • right-to-left (reverse)

• can be rotated 180 degrees and all words still read in all directions

• is exemplified here in how to read a word ("TUBA") in the four ways:

                         down
                          v
           B A T S    B A T S    B A T S    B A T S
           A B U T    A B U T    A B U T    A B U T < reverse
  across > T U B A    T U B A    T U B A    T U B A
           S T A B    S T A B    S T A B    S T A B
                                   ^
                                   up

Some Details

• tablet (square) dimensions range from 2x2 to 33x33 inclusive
• characters range from ascii ordinals 33 to 126 inclusive
• tablets may contain characters that look similar yet are different
• you are not permitted to mutate the input

Input

public static Boolean isSatorSquare(char[][] tablet) {
  //  a two-dimentional array of characters (2 <= n <= 33)
}

Output

true or false  //  whether or not the tablet is a sator square