There have been other rare Imperial coins displaying full facing obverse portraits before (Denari of Augustus, a Bronze Medallion of Commodus) and after (a Carausius Antoninianus and various designs by Maxentius, Constantinus I, and the Licinii), before they became standard designs from Constantius II onwards, but I believe these two Aurei of Postumus (the second one depicting the Emperor radiate, so it might actually be a Binio) and the gold Quinarius of Tetricus are unmatched in style and amongst the unobtainable prizes in Roman numismatics (all three are of course unique and in Museums). Sigh... I´ve got nothing to offer myself but maybe some of you have a facing bust type to show
Yes, they are in museums and, yes, fakes exist. There are rare but obtainable facing heads of Licinius I and II. Common ones come later. Arcadius AE4 Antioch mint Concordia Avgg Honorius ditto Theodosius II solidus (ex jewelry) - This is the most common Roman gold coin and demonstrates well why facing portraits really are not a good idea for circulating currency. Sorry about that, nose.
I have a Honorius face-on coin bronze coin as well as an Arcadius. I find them pretty interesting. They came in a hoard of LRB (200 coins) that I bought about a year ago. Sure would love to have one of those gold pieces. As I read in a Roman coin picture book, "Postumus commanded the services of a fine die-cutter" to say the least.
You must mean these Aurei of Licinius I and II - they may be obtainable, but not really for me . Same goes for the facing Maxentius Aureus (I believe there are two known to exist). There seem to be three or four different types in gold for Constantinus I (each just known from a single example and all in Museums also), but I only have a quality picture of the one below...
CNG shows three Licinius facers in recent years so all that keeps us from having one is the $60k+ or whatever. Not obtainable are the things with two known and both in the public museums or hands of a collectors who intends to pass it on in his will (quite likely to a museum). There are coins with no demand and only one known that might sell for a relatively low price if they were to sell but first the owner has to decide to sell it. If you are 20, you have a better chance of seeing that happen.
The level of skill and craftsmanship to create such lifelike busts as on the OP aureii is mind-boggling to me. It looks downright impossible.
What a shame that the prototype for the 3/4 facing portrait, this bronze Medallion of Commodus in the British Museum, has fallen victim to a radical case of Damnation Memoriae: But Carausius in Britain seems to have used the Gallic Aurei as an Inspiration for this rare Antoninianus...