High strength and high toughness are usually mutually exclusive in engineering materials. Improving the toughness of strong but brittle materials like ceramics thus relies on the introduction of a metallic or polymeric ductile phase to dissipate energy, which conversely decreases the strength, stiffness, and the ability to operate at high temperature. In many natural materials, toughness is achieved through a combination of multiple mechanisms operating at different length scales but such structures have been extremely difficult to replicate. Building upon such biological structures, we demonstrate a simple approach that yields bulk ceramics characterized by a unique combination of high strength (470 MPa), high toughness (22 MPa.m1/2), and high stiffness (290 GPa) without the assistance of a ductile phase. Because only mineral constituents were used, this material retains its mechanical properties at high temperature (600{\deg}C). The bioinspired, material-independent design presented here is a specific but relevant example of a strong, tough, and stiff material, in great need for structural, transportations, and energy-related applications. ; Comment: 27 pages, 4 figures, supplementary data, 47 references