Polymorf - Knowhere - Octahedron symmetry

Compounding the cube and the octahedron is another way to show that they are

symmetrically identical. In doing so the vertex of one polyhedron is juxtapositioned


Fig. 7a - Compound cube/	Fig. 7b - 2, 3, and 4-fold
octahedron	symmetry of cube/octahedron
Required parts
32 large triangles, 6 large squares, 24 right triangles, 72 pinges
.

Fig. 7 - Compounding the cube and octahedron

with the face center of the other so that their rotational axes and mirror planes

coincide. As a result the octahedron is said to be the dual of the cube and v.v. See

that the compounded polyhedra are created by raising the center point of their faces

until they can be connected by a straight line that bisects the intervening edge.

Note that the faces of the cube and octahedron modeled in Fig. 7 interpenetrate

each other completely so that there is no ambiguity in the fact that the model was

compounded from two distinct and individual polyhedra.

Exercise: Demonstrate that the edges of the polyhedra are bisected

and that straight lines connect the raised center points of their faces.

Page 6 Geometry rules! - Symmetry association by inscription