version of thursday 31 october 2013.
Dave Barber's other pages.
This calculates numerous measures of a tetrahedron that resides in an ordinary euclidean three-dimensional space.
Every tetrahedron has four vertices, here named A, B, C and D. Either of two methods of input can be used:
- Specifying the tetrahedron's vertices in cartesian coördinates in the familiar (x, y, z) format …
- This indicates not only the shape of the tetrahedron, but also its location in space.
- Any four points will do, but if they are coplanar, the volume of the tetrahedron will turn out to be zero.
- Upon calculation, edge lengths will appear in the lower set of input boxes.
- Specifying the lengths of the six edges, which must be positive numbers …
- While this indicates the shape of the tetrahedron, it does not designate the figure's location in space, so the calculator arbitrarily selects one. Upon calculation, cartesian coördinates for the vertices thus chosen will appear in the upper set of input boxes.
- Some combinations of edge lengths will not work, giving the NaN message among the results. In particular:
- Each face is a triangle. If one side of a triangle is longer than the sum of the other two, the triangle cannot exist.
- The three edges that meet at a vertex form three (planar) angles. If one of these angles is larger than the sum of the other two, the vertex cannot exist.
With output, plane angles are given in radians, and solid angles in steradians.