- The dual of a solid is formed by joining the centers
of adjacent faces with straight lines. In the resulting dual solid,
each vertex of the dual corresponds to
a face on the original, each face on the dual to an original vertex,
while the edges match, one for one.
- The dual of a tessellation
is obtained by replacing each tile with a point at its center, and each
edge between tiles with an edge joining vertices. The dual of a regular
tessellation is a regular tessellation; the dual of a semi-regular tessellation
is not semi-regular.