The development of variable-stiffness systems is key to the advance of compact engineering solutions in a number of fields. Rigidizable structures exhibit variable-stiffness based on external stimuli. This function is necessary for deployable structures, such as inflatable space antennas, where the deployed structure is semi-permanent. Rigidization is also useful for a wide range of applications, such as prosthetics and exoskeletons, to help support external loads. In general, variable-stiffness designs suffer from a tradeoff between the magnitude of stiffness change and the ability of the structure to resist mechanical failure at any stiffness state. This paper presents the design, analysis, and fabrication of a rigidizable structure based on inflatable octet-truss cells. An octet-truss is a lattice-like configuration of elements, traditionally beams, arranged in a geometry reminiscent of that of the FCC lattice found in many metals; namely, the truss elements are arranged to form a single interior octahedral cell surrounded by eight tetrahedral cells. The interior octahedral cell is the core of the octet-truss unit cell, and is used as the main structure for examining the mechanics of the unit as a whole. In this work, the elements of the inflatable octet truss are pneumatic air muscles, also called McKibben actuators. Generalized McKibben actuators are a type of tubular pneumatic actuator that possess the ability to either contract or expand axially due to an applied pressure. Their unique kinematics are achieved by using a fiber wrap around an isotropic elastomeric shell. Under normal conditions, pressurizing the isotropic shell causes expansion in all directions, like a balloon. The fiber wrap constrains the ability of the shell to freely expand, due to the fiber stiffness. The wrap geometry thus guides the extensile/contractile motion of the actuator by controlling its kinematics. It is their ability to contract under pressure that makes McKibben actuators unique, and consequently they are of great interest presently to the robotics community due to their similitude to organic muscles. Kinematic analysis from constrained maximization of the shell volume during pressurization is used to obtain relations between the input work due to applied pressure and the resulting shape change due to strain energy. Analytical results are presented to describe the truss stiffness as a function of the McKibben geometry at varying pressures.