Interfacial tensions between a polymer crystal and its melt play a central role in nucleation theory. While the tension on the end face (lamellar surface) can be obtained from melting-point suppression, tensions on the sides of a crystal nucleus have not been measured. We use our recently developed "plunger" simulation method to obtain melt-crystal interfacial tensions for polyethylene (PE) and isotactic polypropylene (iPP) ordered phases against their melts. We find PE orthorhombic crystals have strong anisotropy in their side-face interfacial tensions, which leads to a rather oblong crystal cross section under the Wulff construction, far from an idealized hexagonal or cylindrical crystal nucleus. We also investigate rotationally disordered "rotator" or "condis" phases in PE and iPP, which have smaller side-face tensions than their crystalline counterparts. This finding is consistent with Strobl's hypothesis that rotator phases have lower nucleation barriers and nucleate first in many common polymers including PE and iPP.