The tetrahedron is a "self-dual".  The vertices and faces of one can be juxtaposed


with another to form two completely interpenetrating tetrahedra.  This is called a


stellated tetrahedron or stella octangula.  The stella octangula itself can be inscribed in


the cube to demonstrate its symmetry.  Stellating the tetrahedron restores all of the


stella_octangula.gif (14596 bytes)

stella_octangula.gif (11697 bytes)

Fig. 9a - large stella octangula

Fig. 9b - small stella octangula


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



Fig. 9 - Alternative models of a stella octangula inscribed in a cube

. .

cubic symmetry elements that were lacking in the tetrahedron alone.  Therefore the


stella octangula possesses full cubic symmetry.


page 7 of lesson

Exercise:  Explain why the tetrahedron is missing some cubic

page 9 of lesson

symmetry elements and why they are restored when it is stellated.

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