You can create various rhombohedra by tilting the four parallel edges of a cube or varying the face diagonals. This Demonstration focuses on the special case where the rhombohedron has four faces with diagonal ratio
and two faces with diagonal ratio
, where
is the golden ratio. Let the edge of a cube be
. Tilt four parallel edges by
degrees, then reduce the diagonal of two faces to
. One interesting feature of this polyhedron is that the distance between the two thin rhombi is the golden ratio. The half-diagonals of the thin rhombus are
and
. This illustrates an interesting relationship:
, that is,
.
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