Interactive Problem 859: Tetrahedron Inscribed in a Unit Cube

• How many tetrahedra (i.e. trilateral pyramids) can be formed with vertices of the unit cube?

• How many different types exist, that cannot be mapped onto each other by rotation, reflection, or translation?

• What are the possible volumes of the tetrahedra?

Answer:

Number of the tetrahedra:
Number of the different types:
Possible volumes:

(The results should be correct to four decimal places.)