Updated April 10, 2015. This error was corrected in the reptile tree long ago, but the post was not updated until today.
The recent paper on Arganaceras (Jalil and Janvier 2005), the horn-snouted pareiasaur, got me thinking about pareiasaur phlogeny, a dodgy issue involving turtles and lanthanosuchids, not to mention diadectids, which aren’t even supposed to be reptiles~!
Arganaceras
A recent paper by Jalil and Janvier (2005) described a new Late Permian pareiasaur with twin nasal horns, Arganaceras vacanti. They nested it as a “much derived form ” close to Elginia, a pareiasaur with atypical bull-like horns developing from enlarged and pointed supratemporals (Fig. 1). For comparison, Deltavjatia (Fig. 2) was a more typical basal pareiasaur.
Revised Reconstruction
Two reconstructions of Arganaceras are shown (Fig. 1), the original and an alternate with modifications. From examination of the printed materials and comparisons to sisters, it appears that the lacrimal should be a small bone and the frontal should broadly contact the orbit. No other pareiasaur has such a large lateral naris, so by reversing the nasal bone a more typical morphology reappears.
Arganaceras was not tested yet against a large number of pareiasaurs, but at present it nests as a basal one. Elginia was indeed a sister, but it also branched off near the base along with Arganaceras.
A Pareiasaur Skull Table
Below are several diadectid/pareiasaur/turtle skulls in dorsal view and in phylogenetic order. In some the orbits are not visible in dorsal view. In others they are barely visible in lateral view. In some the quadratojugal expands laterally to form cheek extensions, but not in others. In some horns develop from the supratemporals. Others develop horns elsewhere. Turtles developed a shell. Others were more lightly armored. Lanthanosuchus was the first in the lizard lineage to develop a lateral temporal fenestra. So, beyond traditional views that consider them odd offshoots, pareiasaurs were instead key taxa, vital to our understanding of reptile evolution during the Permian.

Figure 3. Click to Enlarge. Basal diadectomorphs featuring Pareiasaurs, Procolophonids, Lanthanosuchids and Turtles. New data shows that Milleretta was basal to both diadectomorphs and the pareiasaur/turtle clade.
Procolophonids?
Taxa with over-sized orbits, such as Hypsognathus, have been traditionally considered procolophonids. Such overextended orbits are thought to have also contained jaw muscles. Here only Hypsognathus nests with Procolophon. Be that as it may, the present tree indicates that some phylogenetic distance separated Nyctiphruretus and Macroleter from Procolophon. The putative procolophonids, Owenetta and Barasaurus were further removed, derived from Macroleter and kin.
Turtles in Convergence
Turtles nest as sisters to pareiasaurs, but from above Odontochelys appears to share more traits with Orobates and Proganochelys appears closer to Diadectes. These convergences only emphasize the problems paleontologists have had trying to nest turtles with other reptiles. And thank goodness for PAUP*!
As More Taxa Are Added This Tree May Change
These millerettid descendants have never been tested together, which is the reason why this tree varies from the one posted on Wiki. Don’t take this as the final word either. (Updated April 10, 2015, thank you, L.A. for noticing the problem.) See the large reptile tree for the latest nestings. When this post was first created in 2011, there were far fewer taxa and some of the data was poor.
References
Jalil N-E and Janvier P 2005. Les pareiasaures (Amniota, Parareptilia) du Permien supérieur du Bassin d’Argana, Maroc. Geodiversitas 27(1):35-132.