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


octahedron.gif (9381 bytes)

cube.gif (12062 bytes)

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.


page 4 of lesson

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

page 6 of lesson

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