A totally symmetric Latin square is one that is equal to all 6 of its conjugates (also known as parastrophes). That means that the set of (row,column,symbol) triples can be thought of as unordered triples!

Here we give catalogues of totally symmetric Latin squares up to isomorphism.

- order 2
- order 3
- order 4
- order 5
- order 6
- order 7
- order 8
- order 9
- order 10
- order 11
- order 12 (gzipped file)
- order 13 (gzipped file)

If you want to know what format these files are in, it is my usual latin squares format.