I did some further checking under the article
https://en.wikipedia.org/wiki/List_of_A ... uth_Africa
which lists 5 species:
Rhombophyllum albanense (L.Bolus) H.E.K.Hartmann synonym Hereroa albanensis L.Bolus, endemic
Rhombophyllum dolabriforme (L.) Schwantes, endemic
Rhombophyllum dyeri (L.Bolus) H.E.K.Hartmann synonym Hereroa dyeri L.Bolus, endemic
Rhombophyllum nelii Schwantes, endemic
Rhombophyllum rhomboideum (Salm-Dyck) Schwantes, endemic
[Martin Heinrich] Gustav Schwantes [standard author abbreviation Schwantes] is the original author of the Genus Rhombophyllum. He wrote articles and books on botany, horticulture and archaeology until his death in 1960. I can't find the original paper or book in which he proposes this Genus but I suspect it was around 1928 when he named the Genus Carpobrotus (Hottentot Fig).
In <
https://en.wikipedia.org/wiki/Rhombophyllum>, there is a color drawing of Rhombophyllum dolabriforme. This drawing looks nothing like the plant known (and pictured here) as Elk's Horns. It has differently shaped leaves and a visible long internode. The only reference listed for this wikipedia article is [Z. Sukkulentenk. 3: 16, 23. 1927.] which may be the paper where the Genus Rhombophyllum is first named. I found confirmation of this article at:
http://colplanta.org/taxon/urn:lsid:ipn ... es:16330-1
This site seems to have links to photocopies of herbarium sheets but only some of them are coming up with my slow phone connection.
I therefore conclude that this photo is Rhombophyllum dyeri and that this is the correct scientific name for the plant known as Elk's Horns in the photographs above.
Doing an image search for Rhombophyllum nelii brought up lots of photos which appear to be Elk's Horns but these two match the name Shriner's Plant and I believe that these are correctly identified.
https://www.etsy.com/listing/693687133/ ... la=1&gao=1&
http://llifle.info/Encyclopedia/Plant/F ... llum_nelii
Some plants appear to be hybrids between the two species, having laterally flattened, crescent shaped leaves but with a forked tip. One other is completely different and may be Rhombophyllum dolabriforme or one of the other species.