“P” is for Ptilodus.
P was a particularly difficult letter for which to select an appropriate genus. There are many very important “P” genera, including: Plesiadapis and Phenacodus. So I covered a bit about Plesiadapis here, and will cover a bit about Phenacodus when I get to Tetraclaenodon.
Ptilodus is an equally important genus in the Paleocene. It is a member of the multituberculates, a now-extinct group of mammals that most likely filled an ecological niche similar to that of modern rodents. In fact, it could be argued that the extinction of the multituberculates was caused by the advent of rodents, though they did manage to co-exist for several million years.

There are at least five different species of Ptilodus in The Breaks. They share in common a large, smoothly arched, blade-like lower fourth premolar (p4) with many distinct serrations along the edge. From each serration comes a long ridge going down each side of the tooth. Compare this with Fractinus for a different potential shape of a multituberculate lower fourth premolar.
The distinctions between species are made on the basis of tooth measurements, the curvature of the blade edge of the tooth, and the number of serrations. Ptilodus looks strikingly like Baiotomeus, which was described earlier.

Even though I describe these teeth as ‘large,’ I should hasten to qualify that statement. Ptilodus titanus (actually called Ptilodus sp. T in the literature because it hasn’t been formally published), the biggest member of the genus, has a total length of the p4 of about one centimeter. That’s less than half and inch. That’s huge for the Paleocene, but pretty tiny otherwise.
Here’s some SEM images of a smaller member of the genus, called Ptilodus gnomus.

The blade-like lower fourth premolar occludes against the upper fourth premolar, which is of an entirely different morphology.

In The Breaks, there were five certain species of Ptilodus, and a bunch of other specimens that were definitely Ptilodus, but I wasn’t sure which species. All together, of about 800 specimens total that were identified as distinct genera, at least 231 represent definitive species of Ptilodus and come from 24 different localities within The Breaks.
I spent a long time looking at teeth of Ptilodus.
Part of the Blogging from A to Z challenge
For 4-18-13