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The tetrahedron is a "self-dual". The vertices and faces of one can be
juxtaposed |
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with another to
form two completely interpenetrating tetrahedra. This is called a |
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stellated
tetrahedron or stella octangula. The stella octangula itself can be inscribed in |
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the cube to
demonstrate its symmetry. Stellating the tetrahedron restores all of the |
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Fig. 9a - large
stella octangula |
Fig. 9b - small
stella octangula |
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Required
parts |
s.o. - 32 large
triangles, 36 pinges |
s.o. - 32 small
triangles, 36 pinges |
cube - 48 right
triangles, 48 pinges |
cube - 24 right
triangles, 12 pinges |
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Fig. 9 -
Alternative models of a stella octangula inscribed in a cube |
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cubic symmetry
elements that were lacking in the tetrahedron alone. Therefore the |
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stella
octangula possesses full cubic symmetry. |
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Exercise: Explain why the
tetrahedron is missing some cubic |
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symmetry elements and why they are
restored when it is stellated. |
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Geometry rules! - Symmetry association by inscription |