The convex polyhedron C2 of (1) cube C 1 with the center of each face as the vertex is a regular octahedron.

Its middle part (the interface vertically bisecting the line connecting the opposite vertices) is square,

The diagonal length of a square is equal to the side length of a cube.

So its side length a2=( 18 root number 2)/ root number 2= 18.

(2) The convex polyhedron C3 with the center of each face of octahedron C2 as the vertex is a cube.

The diagonal length of the C3 face of the cube is equal to 2/3 of the length of the C2 side (the distance from the center of the regular triangle to the opposite side is equal to 2/3 of the height),

So the diagonal is 12.

So a3= 12/ root number 2.

(3) By analogy, a4=a3/ radical number 2= 12/2=6.

A5=(2/3)a4/ radical number 2=4/ radical number 2, a6=a5/ radical number 2=2.

Enlightenment of this problem: In fact, we can find the law from it, and we can find a general term by discussing the odd and even terms. )