When this shape is bisected along its longest edge two
mirrored parts are produced, a kind of SKEW
TETRAHEDRON, left and right oriented, like a pair of
shoes. This skew shoe can be bisected into two equal parts
which are HALF PYRAMIDS, and these are of course again
splitable into skew tetrahedra, and we have completed some
kind of cycle.
Twelve of these half pyramids will form a cube.
Taped together along the edges by the right angle, they
make a funny toy, that will flex into a lot of interesting shapes.
A model in plastic has been on the market for some years.
Of course there are other ways to split the cube, for instance,
into halves, along a plane, that bisects six zig-zagging
adjacent edges around the cube, producing a
HEXAGONAL BISECTIONED CUBE.
The geometrical proportions of the silver rectangle: 1: V2
with a diagonal V3 shows up again and again in these shapes
and very clearly emphasizes the close relationship between
the cube and the silver rectangle.
By all this, nothing new about the cube has been unveiled,
but 1 have amused myself in making these shapes by folding
only, and it might amuse others, who are foolishly
fond of folding.
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