4 way switch with only two switches
As Speedy said, your wiring is indeed characteristic of a four-way switch.  Four-way dimmers are not a COTS item; however, you can put a dimmer there with the help of a 3-position, 2-pole (DPDT) wall switch such as this Hubbell-Bryant 4825I, mounted in a dual gang box and wired as in the following diagram (travelers are black and red, grounds are green, neutrals are gray, and in-box jumpers are blue, but you can use any color for those save for white, gray, or green:



Do be forewarned though that the results of this aren't quite the same as a regular four-way switch: in particular, if you flip the switch fully at this location, you won't be able to turn it on at one end without flipping the switch at the other end as well.  (I might come up with a better answer -- but it'll take me a while to fiddle with things, and 4PDT wall switches aren't a thing, either -- can you use a suitably rated electronics-type toggle switch in mains wiring?)