tetrahedron calculator.
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.

The source code file for this html page contains the complete JavaScript program. It will be of interest to those who want to see what formulae were used, or who want to adapt the calculator to other purposes.

input
specifying vertices  xyz
A
B
C
D
specifying edge lengths AB
AC
CD
BD
BC

output
volume
distance of vertex from origin A
B
C
D
solid angle at vertex A
B
C
D
total
altitude between vertex and face A & BCD
B & ACD
C & ABD
D & ABC
dihedral angle between faces ABC & ABD
ABC & ACD
ABD & ACD
total
ACD & BCD
ABD & BCD
ABC & BCD
distance between lines in which skew edges lie AB & CD
AC & BD
angle between skew edges AB & CD
AC & BD
area of face ABC
ABD
ACD
BCD
total
angle between cofacial edges AB & CB
BA & DA
DC & BC
BC & AC
DB & AB
DA & CA
BD & CD
CA & BA
AC & DC
CB & DB
altitude between vertex and edge A & BC
B & AC
C & AB
D & AB
A & BD
D & AC
A & CD
B & CD
C & BD
D & BC
xyz
cartesian coördinates of a unit vector normal to faceABC
ABD
ACD
BCD