Conway polyhedron notation

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Conway polyhedron notation is used to describe polyhedra based on a seed polyhedron modified by various operators. The seed polyhedra are the Platonic solids, represented by their first letter of their name (T,O,C,I,D); the prisms (Pn), antiprisms (An) and pyramids (Yn). Any convex polyhedron can serve as a seed, as long as the operations can be executed on it.

Operations on polyhedra consist of:

• d - the dual of the seed polyhedron
• tn - truncates all the n-fold vertices; if n is omitted, truncates all vertices
• kn - "kis" operator raises a pyramid on each n-gonal face; if n is omitted, elevates all faces
• a - "ambo" truncates to the edge midpoints, rectifying the polyhedron
• e - "expand" (cantellate)
• s - "snub"
• r - "reflect" (an extension by George Hart) makes the mirror image of the seed; it has no effect unless the seed was made with s
• p - "propellor" (an extension by George Hart)

Some frequent combinations of operators have a shorter alternate notation:

• j - "join": jX = daX
• g - "gyro": gX = dsX
• b - "bevel": bX = taX
• o - "ortho": oX = deX
• m - "meta": mX = dbX = kjX

The operators are applied like functions from right to left. For example:

• the dual of a tetrahedron is dT;
• the truncation of a cube is t3C or tC;
• the truncation of a Cuboctahedron is t4aC or taC.

[edit] External Links and References

• George Hart's Conway interpreter: generates polyhedra in VRML, taking Conway notation as input
• Conway Polyhedron Notation at Mathworld