A caveat before we start: horn shape, size, and orientation should not be taken overly seriously for ceratopsids, because all evidence indicates there was a lot of latitude for improvisation in life, and in death, well, you try fossilizing a big three-dimensional object like a ceratopsid skull and see how undistorted it stays. However, it is indeed the case that Regaliceratops and "Monoclonius" recurvicornis occupy a fairly uncommon chunk of space in the brow horn spectrum. Generally, we see either low knobs at most, as in many centrosaurines, or big ol' pointy things that would make any cowboy proud, as in many chasmosaurines. The middle space of "distinct but dainty" appears to have had few adherents; others include Ceratops montanus and some flavors of Chasmosaurus (apparently no two chasmosaurs shared the same kind of brow and nasal horns; it was a major faux pas). Figure 4 in the Regaliceratops description (Brown and Henderson 2015) shows this pretty well: there's a cluster of traditionalist chasmosaurines with long brow horns, a cluster of traditionalist centrosaurines with long nasal horns, and a diffuse cloud of specimens between the two clusters that serves to reinforce the point that chasmosaurs did whatever they pleased. "M." recurvicornis usually ends up in the centrosaurines when it is thought about at all. In fact, in the supplementary information to the Regaliceratops description (p. 35 of 61) it gets a brief nod in a data table where it is placed among the centrosaurines; it ends up beating all the other centrosaurines in brow horn length. Check out Table 4 again: it's the red triangle at the upper left corner of the centrosaurine polygon, although I suspect that it should be farther right because (spoiler) the nasal horn is incomplete. (It's also misspelled "recurvicornus", but then -cornus and -cornis are a bit of a pain; with dinosaurs, for example, we've got Ceratosaurus nasicornis and "Monoclonius" nasicornus.)
"Monoclonius" recurvicornis is known from a single specimen, American Museum of Natural History (AMNH) FR 3999, found in the Judith River Formation of Montana. Various illustrations in comprehensive popular dinosaur books may give the impression that it is known only from part of the facial section of the skull, but there are actually a couple more cranial bones known. The facial chunk is, to be blunt, kind of a weird-looking thing, especially after having been restored. This is where the oldest illustrations are helpful, showing that in particular much of the nasal horn is restored, and that what appears to be a single cranial section actually consists of parts that have been joined, with the brow horns making up at least one and the nasal fragment being its own chunk. Stripping away the plaster does not account for the horn configuration, though. You've got two straight conical brow horns, larger than the typical Centrosaurus/Styracosaurus/pachyrhinosaur brow horns but smaller than most chasmosaurine brow horns. You've got that turned-forward nasal horn ("recurved" in technical terms, which is the source of the species name). Finally, you've got a funny little node in front of the right brow horn. Unfortunately, the skull is missing the corresponding section of the other side, so it is not known if there was another one in front of the other brow horn (having just one makes a pathology look more likely). (One interesting note: most ceratopsid nasal horns were actually not right on the nose, but backed up a bit, sometimes behind the nasal opening itself. Triceratops is a bit of an exception in often having that third point over the sniffer.)
"Monoclonius" recurvicornis, or what will be named that, makes its first appearance in Cope (1877). It comes from the Judith River Beds of Montana, and is composed of a dozen skull fragments. Cope admits, in so many words, that he has no clue about the animal he's dealing with, but he does produce a fair amount of information for anyone wanting to reconstruct the fossils as he had them, and illustrations of some of the material are included. He doesn't actually name it until 1889, by which time good ceratopsid material is available for comparison. Aside from the name, we get some additional measurements, reidentification of some of the bones, and a few more illustrations, and we learn it was "colossal". He then goes on to name M. sphenocerus and M. fissus for good measure.*
*Dinosaur taxonomy was a different place before about 1920, in that the genus hadn't completely squashed the species. In fact, the farther you go back, the ratio tilts even farther. They loved coining species but were much more cautious about genera. The upshot of this is that there are a couple dozen species assigned to old-timey genera like Trachodon, Iguanodon, Ornithopsis, Omosaurus, Cetiosaurus, Laelaps, Megalosaurus, et cetera based on material which ranges from "mildly interesting" to "so useless it might as well have been reburied with the author", and without their own genera they are practically invisible today except when you have to do taxonomic heavy lifting. Then, of course, it turns out that some stupid tooth or jaw fragment or vertebra named by some beloved 19th century so-and-so because he was more so-and-so than we give him credit for, actually could represent the same animal as a long-established species that unfortunately was named two years later. The only sane thing to do, of course, is to assume that the fossil belonged to an individual of a similar but distinct species that was just passing through. There's certainly not enough material to disprove this hypothesis. The one downside for authors of dinosaur websites is that you can't just be lazy and say "synonym but ignoring the dates"; you must account for all of them and pretend that they inspire positive or at least neutral feelings, instead of a desire to travel back in time and throw the type material at the describer.
|"Monoclonius" recurvicornis in Cope (1877); per Cope (1889), the bones labeled "Figure 7" and "Figure 8" are our guy.|
|"Monoclonius" recurvicornis in Cope (1889), or at least the pointy bits.|
After Cope passed on, most of his species of Monoclonius went on to a quiet retirement in the collections of the American Museum of Natural History, although the genus itself had several more decades of fun. The grand Hatcher et al. monograph of 1907 provided some additional details, although the authors settled for reproducing his figures. In this work, the species gets shuffled off to Ceratops, which doesn't catch on despite being somewhat more congruent with what we know of Ceratops compared to Monoclonius or Centrosaurus; no doubt the main problem has been the perpetual lousiness of Ceratops and "M." recurvicornis. Hatcher et al. (1907) note it as fairly large, with an occipital condyle diameter of 76 mm and featuring no sutures. However, the two halves of the nasal horn are not fused, so we've got contradictory signals on traditional measures of ceratopsid age. In the years that followed, the species often was cited as "Centrosaurus" recurvicornis, for no particularly useful reason. When Monoclonius went on its slow fade, it left all its stuff to Centrosaurus except for the type species and Monoclonius lowei, which mostly exists to give ceratopsid hipsters something to talk about. If you know what Monoclonius lowei is, you're probably in the club. "M. recurvicornis" did manage to attract some more recent comment in the halls of the Dinosaur Mailing List, where it got its own thread over a decade age. The originator compared the nasal horn to that of Einiosaurus, a suggestion that has been made a couple of times over the Internet if you poke around. For example, here is a restoration that allows you to see what this might look like: the basic idea is you rotate the nasal fragment a bit. However, ceratopsid specialist Andrew Farke disagreed with an Einiosaurus-like reconstruction based on the lack of compression of the horn. The only solutions, of course, are to find another ceratopsid skull in Upper Campanian rocks of western North America with medium-sized brow horns and recurved nasal horn, or to spend some time picking plaster from AMNH FR 3999.
Brown, C. M., and D. M. Henderson. 2015. A new horned dinosaur reveals convergent evolution in cranial ornamentation in Ceratopsidae. Current Biology in press.
Cope, E. D. 1877. Fossils from the Judith River beds. Bulletin of the United States Geological and Geographical Survey of the Territories 3:588–597. (it's actually part of a longer work, but I'm all for getting right to the relevant part)
Cope, E. D. 1889. The horned dinosaurs of the Laramie. The American Naturalist 23:715–717.
Hatcher, J. B., O. C. Marsh, and R. S. Lull. 1907. The Ceratopsia. Monographs of the United States Geological Survey 49.