There are several ways to construct the dual
of a polyhedron
. Roughly speaking,
and
switch faces and vertices and the edges flip around. The dual of
is
.
Here is a combinatorial definition. The vertices
of
are the centers of the faces
of
. An edge of
joins
and
if their corresponding faces
and
were adjacent in
. Each face
of
corresponds to a vertex
of
: if
was a vertex of the faces
,
, … of
, then
is the polygon with vertices
,
, …. This definition leads to skew polygonal faces if
is not concave or has holes.
The dual can be constructed by various geometric operations on
: truncating either at vertices or edges, augmenting faces, or by stellation.
The number of edges of
and of
are the same. Could the edges of
be transformed to form
? Yes: by rotating each edge about the axis from the center of
to the midpoint of the edge.
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