Right-Angled Tetrahedron
Right-Angled Tetrahedron
Let be a tetrahedron with the three plane angles at all right angles, that is, . (This is more explicitly known as a trirectangular tetrahedron.) Let , , . Then . The lines that join the midpoints of opposite edges are equal and meet at a point. The proof, outlined in the Details, implies that these three lines are diagonals of a rectangular prism, intersecting at the center.
T=ABCD
D
∠ADB=∠BDC=∠CDA=90°
α=∠CAD
β=∠CBD
ϕ=∠ACB
cosϕ=sinαsinβ