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Demonstrating
that the octahedron is symmetrically identical to the cube |
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Inscribing the octahedron in the cube demonstrates that they are symmetrically |
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identical.
Rotating the construction about the [100], [110], and [111] axes reveals |
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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 |
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Fig. 6 -
Inscribing the octahedron in the cube |
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that the octahedron possesses
the same rotational axes and planes as does the |
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cube. Likewise the
octahedron is demonstrated to possess the same cubic (100) |
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and (110)
mirror planes dividing it into two identical halves. |
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Exercise: Combine Fig. 6a and 6b into one model |
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Page 5
Geometry rules! - Symmetry association by inscription |