This paper describes the development of a pair of adult male and adult female computational phantoms that are compatible with anatomical parameters for the 50th percentile population as specified by the International Commission on Radiological Protection (ICRP). The phantoms were designed entirely using polygonal mesh surfaces--a Boundary REPresentation (BREP) geometry that affords the ability to efficiently deform the shape and size of individual organs, as well as the body posture. A set of surface mesh models, from Anatomium 3D P1 V2.0, including 140 organs (out of 500 available) was adopted to supply the basic anatomical representation at the organ level. The organ masses were carefully adjusted to agree within 0.5% relative error with the reference values provided in the ICRP Publication 89. The finalized phantoms have been designated the RPI adult male (RPI-AM) and adult female (RPI-AF) phantoms. For the purposes of organ dose calculations using the MCNPX Monte Carlo code, these phantoms were subsequently converted to voxel formats. Monoenergetic photons between 10 keV and 10 MeV in six standard external photon source geometries were considered in this study: four parallel beams (anterior-posterior, posterior-anterior, left lateral and right lateral), one rotational and one isotropic. The results are tabulated as fluence-to-organ-absorbed-dose conversion coefficients and fluence-to-effective-dose conversion coefficients and compared against those derived from the ICRP computational phantoms, REX and REGINA. A general agreement was found for the effective dose from these two sets of phantoms for photon energies greater than about 300 keV. However, for low-energy photons and certain individual organs, the absorbed doses exhibit profound differences due to specific anatomical features. For example, the position of the arms affects the dose to the lung by more than 20% below 300 keV in the lateral source directions, and the vertical position of the testes affects the dose by more than 80% below 150 keV in the PA source direction. The deformability and adjustability of organs and posture in the RPI adult phantoms may prove useful not only for average workers or patients for radiation protection purposes, but also in studies involving anatomical and posture variability that is important in future radiation protection dosimetry.