
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 


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Geometry rules!  Symmetry association by inscription 