The inconvenience of orthogonal illumination, which certainly gives better results, is avoided in the **coaxial** apparatus.

The other case of importance is that of two **coaxial** cylinders.

It has 6 octagonal faces (belonging to the original cube), and 8 triangular ones (belonging to the **coaxial** octahedron).

The snub cube is a 38-faced solid having at each corner 4 triangles and I square; 6 faces belong to a cube, 8 to the **coaxial** octahedron, and the remaining 24 to no regular solid.

It is enclosed by 6 square and 8 triangular faces, the latter belonging to a **coaxial** octahedron.

It is enclosed by 20 triangular faces belonging to the original icosahedron, and 12 pentagonal faces belonging to the **coaxial** dodecahedron.

It is therefore enclosed by 20 hexagonal faces belonging to the icosahedron, and 12 pentagonal faces belonging to the **coaxial** dodecahedron.

The truncated dodecahedron is formed by truncating the vertices of a dodecahedron parallel to the faces of the **coaxial** icosahedron so as to leave the former decagons.

Capacity of two concentric spheres, of two **coaxial** cylinders and of two parallel planes.

The same arrangement can be supplied to a pair of **coaxial** cylinders.