Great polyhedra: What does "great" signify? 
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*Great Cubicuboctahedron

*Great Icosacronic Hexecontahedron

*Great Rhombic Triacontahedron

*Great Snub Icosidodecahedron

*Great Stellated Dodecahedron

*Great Triakis Octahedron

*...

There are many polyhedra with a rich variety of beautifully baroque names, often prefixed with "Great."

Q. What does "great" signify?

     

     The Great Rhombic Triacontahedron.
 A: There are two things “great” can refer to. The first, as Sam explained, is a specific kind of stellation. The second is to distinguish conjugates. Since they’d otherwise have the same name, one of them (usually the spikier one) is prefixed with “great” and the other with “small”. Note that not all pairs are distinguished this way. This usually happens when the polytopes in question are snubs, or one of them is convex, but there are other exceptions too, such as the disprismatotesseract and the prismatocubintercepted tesseract.
A: Quoting Wikipedia: https://en.wikipedia.org/wiki/Stellation#Naming_stellations

John Conway devised a terminology for stellated polygons, polyhedra and polychora (Coxeter 1974). In this system the process of extending edges to create a new figure is called stellation, that of extending faces is called greatening and that of extending cells is called aggrandizement (this last does not apply to polyhedra). This allows a systematic use of words such as 'stellated', 'great', and 'grand' in devising names for the resulting figures. For example Conway proposed some minor variations to the names of the Kepler–Poinsot polyhedra.

