Just took a look with my 345 and a few sheaths....
I do not have a 112 ecolite sheath so can't say on that one.
It does not fit a 112 leather sheath (it fits in, but flap is not long enough to snap)
It does not fit a 500 leather sheath (it fits in, but flap is not long enough to snap)
It does fit a leather 110 sheath
It does fit a nylon 276 sheath
It does fit a leather 279 sheath