Wow, there are way more of these than I expected! There's one I think doesn't count, though, the Agrippa Neptune (depending on how picky we're being)... I think this one is unique to Claudius: Unique to Commodus (I assume): Unique to Septimius? Unique to Plautilla? This type with Serapis/Pluto and Cerberus seems to be unique to Caracalla (on imperial issues, at least): Elagabalus: Severus Alexander, restorer of the coinage RESTITVTOR MON: Standing VENERI FELICI seems unique to Julia Mamaea: DEO MARTI, Mars in temple, for Gallienus:
That's the real question. Perhaps the answer varies from person to person. Being someone who tends to focus on the interestingness of a coin's iconography/design, I am biased towards discounting differences in legends and minor devices when it comes to counting "types". It is understandable that collectors such as @maridvnvm and @David Atherton who are trying to further the understanding of various series are more focused on the other details.
Who else besides Elagabalus issued these? The question of this thread is reverses unique to a ruler. Some may have had variations of their unique type. Ops holding grain ears is Pertinax but Ops holding a scepter is Antoninus Pius. Are those each unique or do they share Ops? I have no Pius.
Maybe ... ... but, as @dougsmit notes, Is the same design with the legend in the dative case (Veneri Felici) a different reverse type from the same design with the legend in the nominative case (Venus Felix)? How about if one has Venus standing facing right, holding scepter and child and the other has Venus standing left, holding child and scepter?
The Judaea Capta series is chock a block full of unique reverse designs for Vespasian. However, it's this antiquarian pastoral scene that is one of my favourites. Vespasian AR Denarius, 3.19g Rome mint, 77-78 AD RIC 977 (R). BMC 220. RSC 220. Obv: CAESAR VESPASIANVS AVG; Head of Vespasian, laureate, r. Rev: IMP XIX in exergue; Goatherd std. l., milking goat l. Acquired from Ancient Delights, August 2012.
Here's a variation to one of the types illustrated. Trajan Decius Obv:– IMP C M Q TRAIANVS DECIVS AVG, Radiate, cuirassed bust right Rev:– PANNONIAE, The two Pannoniae facing each other, holding a standard between them Minted in Rome. A.D. 249 - 25 Reference(s) – RIC 26. RSC 81 3.41 gms, 21.54mm x 180mm
Uranius Antoninus, Defender of the East against Shapur, last of the Severans and Chief Priest of the Sun God of Elagabalus at Emesa, struck at least two types of Aurei in 253 aD in memory of the holy stone's voyage to Rome during his distant cousin's rule.
My criterion for the "unique" page was this: If you had the coin in hand (so you knew the size and fabric) and were looking at the reverse, could you identify the person on the other side before turning it over? I consider "type" to refer to the design and legend, not including mint control marks. Additional details (such as a letter in the field or mintmark in exergue) distinguish a "variety." There is a fine line between these concepts and knowledgeable experts can differ on where that line is. In his book Roman Bronze Coins: From Paganism to Christianity, 294-364 A.D. (images by @dougsmit ) Tory Failmezger listed all the types of the period. (I highly recommend that book.) We consulted about what was a different type and what was not. For example, the soldier-spearing-fallen-horseman begins large and shrinks to much smaller. Are the smaller ones a new type? If so, which size marks the transition? It has the horseman in distinguishable positions. Do those make "types" or "varieties"? Licinius issued a very common type with legend IOVI CONSERVATORI. The same design comes with legend IOVI CONSERVATORI AVGG and IOVI CONSERVATORI AVGG NN. Some are 24 mm and others smaller down to 18 mm. Some have radiate crowns and some are laureate. There are many lines that could be drawn to distinguish between them. But, if you start with a basic list and you draw fine lines pretty soon you have RIC's exhaustive listing, which was not his goal. Are two similar coins different types or not? It depends upon who is doing the collecting. If you are the British Museum, you want every variety of every detail. If you are on a limited budget, you probably think a different emperor makes for a different type, but perhaps a different mintmark does not. I repeat, my criterion for the "unique" page was this: If you had the coin in hand (so you knew the size and fabric) and were looking at the reverse, could you identify the person on the other side before turning it over? http://augustuscoins.com/ed/unique/unique.html
Maybe it's more like: if you knew the size and (basic) fabric & had a line drawing of the major devices and legend, could you identify the person on the other side? (Of course having it in hand gives many of us a lot of information not included in those factors.) Fair enough! The Agrippa definitely belongs there. I'm assembling what I'm calling a "reverse type set" of Sev Alex middle bronzes, but I don't count legend variants... just the major devices. E.g. many of them come in dated and undated forms, I don't intend to get both. Oops, of course!! I even have one of these! (With that mysterious object in her hand.) Since I wouldn't have included that, I'll add another to arbitrarily keep my total at 10. That's as good an excuse as any to post a coin... DIVO MAXIMIANO (Rome, struck under Constantine in 317-18)
Maybe I have a much more restrictive definition of "unique," but personally I find that about 80% of the coins illustrated in this thread aren't really what I'd call unique reverses. Here are just a few that illustrate my definition of unique: Here's an example of one that doesn't fit my definition of unique: Contrast the two coins immediately above, and ask yourself the following: if I were to glance (less than one second per coin) at these two coins, side-by-side, in a tray at a coin show or in a dealer's shop, which one would make me think "Wow -- there's an unusual reverse; I wonder if that's unique to the emperor?" Maybe my definition is too restrictive and non-quantifiable for this thread, but that's where I situate my idea of uniqueness relative to this thread.
I suppose I could have made a site of types that are remarkably unusual at first glance. Then your first three qualify and the Claudius, which has a standing figure (as do very many coin types), is not so unusual. Nevertheless, if I saw it in a dealer's tray I would know from the legend it was a type of Claudius because the type (which includes the legend) is unique to Claudius. I hope people have fun with the site. If you know a lot about Roman coin types you can get lots of positive feedback when you get coins right. If you don't know a lot you can learn about many reverse types from the site. I didn't think all of us could agree on what makes a coin's design special. I was going for reverse types that made the coin "identifiable," as opposed to "remarkably special."
It isn't one that comes up too often in trade. More scarce are Titus Caesar's denarii of the type! Titus Caesar AR Denarius, 3.53g Rome Mint, July 77 AD - December 78 AD (Vespasian) RIC 985 (R). BMC 230. RSC 103. Obv: T CAESAR VESPASIANVS; Head of Titus, laureate, bearded, r. Rev: IMP XIII in exergue; Goatherd std. l., milking goat l. Ex Harry N. Sneh Collection. If it wasn't for Harry Sneh, I wouldn't have one.