Swannies Fourth Theorem: A theorem for the areas of Squares on a trirectangular tetrahedron.
A Square and three smaller squares -
Definition: The sum of the areas of squares on the rectangular faces of a trirectangular tetrahedron equals the area of a square on its base provided the length of a shorter side of a rectangular projection of a square on the base onto a rectangular face is used as the length of the side of the square on the face.
The photograph on the left: What you get if you don't use the circle in the method given above. In the photograph below on the right EF = DG/AD x BC.
Swannies Fifth Theorem: A theorem for the volumes of Cuboids on a trirectangular tetrahedron. A Cube and three cuboids -
the side of the cube. (Sorry no model yet. Also wish to turn them all into cubes without my calculation trick -
Below on the righ: Just to fill the space. A 'which is more' -