Conway polyhedron notation
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In geometry and topology, Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified by various prefix
Rhombic dodecahedron jC = jO = oT
Triakis octahedron kO
Tetrakis hexahedron kC = mT
Deltoidal icositetrahedron oC = oO
Dual polyhedron
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In geometry, every polyhedron is associated with a second dual structure, wherein the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to
Conway polyhedron notation
…symmetry. For example, tC represents a truncated cube, and taC, parsed as t(aC), is (topologically) a truncated cuboctahedron. The simplest operator dual swaps vertex and face elements; e.g., a dual cube is an octahedron: dC = O. Applied in a series, these operators allow many higher order polyhedra to…
The dual of a Platonic solid can be constructed by connecting the face centers. In general this creates only a topological dual. Images from Kepler's Harmonice Mundi (1619)