Explore three-dimensional geometry, ZOME construction, and tetrahedron trigonometry in this 59-minute lecture. Delve into rational trigonometry concepts, including quadrance and spread, in both affine and projective settings. Learn about the ZOME system and its applications in geometric constructions. Discover new rational formulas for 3D trigonometry, covering side quadrances, face spreads, dihedral edge spreads, solid spreads, and quadrume. Examine specific examples like the right isosceles tetrahedron and regular tetrahedron, unveiling the metrical structure of these fundamental objects. Gain insights into the educational implications of rational trigonometry for mathematics teaching and explore challenges in ZOME constructions.