Midpoint Augmentation

Midpoint augmentation, a term introduced here, is a variant of conventional augmentation in which each facial polygon is replaced by a triangular polygon joining vertices with the neighboring edge midpoints, and then constructing a pyramid with the base determined by the face's midpoints. Midpoint augmentation allows compounds of Archimedean solids and Archimedean duals to be easily constructed.

Archimedean solid	dual	face 1	face 2
cuboctahedron	rhombic dodecahedron	3:	4:
icosidodecahedron	rhombic triacontahedron	3:	5:
small rhombicuboctahedron	deltoidal icositetrahedron	3:	4:
truncated cube	small triakis octahedron	3:	8:
truncated dodecahedron	triakis icosahedron	3:	10:
truncated icosahedron	pentakis dodecahedron	5:	6:
truncated octahedron	tetrakis hexahedron	4:	6:
truncated tetrahedron	triakis tetrahedron	3:	6: