Polymorf - Knowhere - Octahedron symmetry

Demonstrating that the octahedron is symmetrically identical to the cube

Inscribing the octahedron in the cube demonstrates that they are symmetrically

identical. Rotating the construction about the [100], [110], and [111] axes reveals


Fig. 6a - Octahedron sliced by	Fig. 6b - Octahedron
(100) cubic planes	inscribed in a cube
Required parts
8 large triangles, 24 right triangles	8 large triangles, 24 small squares
18 pinges	2 right triangles, 60 pinges

Fig. 6 - Inscribing the octahedron in the cube

that the octahedron possesses the same rotational axes and planes as does the

cube. Likewise the octahedron is demonstrated to possess the same cubic (100)

and (110) mirror planes dividing it into two identical halves.

Exercise: Combine Fig. 6a and 6b into one model

Page 5 Geometry rules! - Symmetry association by inscription