Tetrahedron from its vertices

Draw the tetrahedron with vertices A(7, 2, 5), B(20, 10, 4), C(12, 17, 5) and D(18, 8, 13). Find its volume.

Step-by-step solution

Check that the four points are not coplanar: if they were, they would not form a body.
Join each pair of vertices sharing a face; the faces are triangles.
Draw visible edges with a continuous line and hidden ones dashed.
The volume of the tetrahedron is |(AB × AC) · AD| / 6.

Result: volume 229.17 u³; 4 triangular faces, 6 edges and 4 vertices.

Four coplanar points do not form a tetrahedron: that is the first check.