A Tetrahedron with Edges of Given Length

a

1

b

1

c

1

d

1

e

1

f

1

2D/3D

net	polyhedron

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This Demonstration constructs a tetrahedron with edges of given length using a Cayley–Menger determinant.

The Cayley–Menger determinant

Δ

d

gives the volume of a simplex in

d

dimensions.

Δ

2

gives the area for a plane triangle and is a form of Heron's formula.

Δ

3

gives the content of the 3-simplex, that is, the volume of the general tetrahedron.

Izidor Hafner