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.