Three-dimensional (3D) displays having regular-polyhedron structures are proposed and their imaging characteristics are analyzed. Four types of conceptual regular-polyhedron 3D displays, i.e., hexahedron, octahedron, dodecahedron, and icosahedrons, are considered. In principle, regular-polyhedron 3D display can present omnidirectional full parallax 3D images. Design conditions of structural factors such as viewing angle of facet panel and observation distance for 3D display with omnidirectional full parallax are studied. As a main issue, image volumes containing virtual 3D objects represented by the four types of regular-polyhedron displays are comparatively analyzed.