Fig. 415.22 Rational Volumes of Tetrahedroning:
- The cube may be formed by placing four 1/8-octahedra
with their equilateral faces on the faces of a
tetrahedron. Since tetrahedron volume equals one, and
1/8-octahedron equals 1/2, the volume of the
cube will be: 1 + 4(1/2) =3.
- The rhombic dodecahedron may be formed by placing
eight 1/4-tetrahedra with their equilateral faces
on the faces of an octahedron. Since the octahedron
volume equals four and 1/4-tetrahedron equals
1/4, the volume of the rhombic dodecahedron will be:
4 + 8 (1/4) = 6.
|
