The surface area and radiative properties of an object influence the rate of radiative emission from the object's surface and the rate of radiative absorption into the surface. Control of these variables would allow for the radiative heat transfer behavior of the surface to be manipulated in real time. Origami tessellations, being a repeated pattern of linked, dynamic surfaces, provide a framework by which dynamic control of apparent radiative properties and surface area is possible. The panels within a tessellation form cavities whose aspect ratio varies as the device actuates. The cavity effect suggests that the apparent radiative properties of the cavity openings will vary as a function of aspect ratio. The apparent absorptivity of an accordion tessellation formed from folded shim stock is shown experimentally to increase by 10x as the tessellation actuates from fully extended to within 10\% of a completely-folded state. Analytical models and Monte Carlo ray tracing are used to quantify the apparent radiative properties of an infinite V-groove for a variety of conditions, including specular or diffuse reflection and diffuse or collimated incident irradiation. For a diffuse V-groove, apparent radiative properties increase with increasing V-groove aspect ratio but do not approach unity. Highly reflective surfaces exhibit the largest relative increase in apparent radiative properties with actuation. Closed-form correlations achieve an average relative error of 2.0\% or less. For a specular V-groove, apparent radiative properties approach unity as the V-groove collapses towards an infinite aspect ratio. The apparent absorptivity for a V-groove exposed to collimated irradiation shows significant variations over small actuation distances, increasing by 5x over a small actuation range. For certain conditions the apparent absorptivity of a V-groove subject to collimated irradiation decreases as the aspect ratio increases.For an isothermal accordion tessellation the net radiative heat exchange continuously decreases as the surface is collapsed for most conditions, indicating that the reduction in apparent surface area generally dominates the increase in apparent radiative properties. Net radiative heat transfer values decrease by 7x for collimated irradiation and specular reflection over small actuation distances. Specular V-grooves subject to collimated irradiation occasionally show an increase in net radiative heat transfer as the device collapses. A non-isothermal dynamic radiative fin achieves a 3x reduction in heat transfer as the fin collapses; this value can be increased with the use of highly conductive materials and by increasing the length of the fin. The fin efficiency of a collapsible fin increases as the fin collapses. An experimental prototype of a collapsible fin is developed and tested in a vacuum environment, achieving a 1.32x reduction in heat transfer for a limited actuation range, where a numerical model suggests this prototype may achieve a 2.23x reduction in heat transfer over the full actuation range.