[brtjfoni] Magic 600-cell

The Magic 8 Ball has an internal floating icosahedron, providing 20 different answer possibilities.

If we allow both square and equilateral triangular faces (but not anything larger, because then the face sizes seem aesthetically too different), the rhombicuboctahedron offers 26 faces, and the snub cube 38.

Catalan solids have up to 120 identical faces.

A geodesic dome offers an unlimited number of triangular faces.

The natural analogue to the icosahedron in 4D is the 600-cell.  Of course, a magic 600-cell cannot actually be built in 3D, but it could be interestingly dressed up in simulation: "The answer to your question comes from oracles living in the fourth dimension."  It has 600 tetrahedral cells, but it is hard to write within a 3D cell, as human writing systems are only 2D.  It offers 1200 triangular faces, which act like edges between the cells.

The omnisnub 24-cell, not a uniform polychoron, offers 2832 faces, a mix squares and equilateral triangles.  The rectified 600-cell offers 3600 triangular faces.

Like the Catalan solids, we now consider duals to convex (mostly) uniform polychora.  Assuming the edges dualize into faces in 4D, we seek polychora with many edges.  The onmitruncated 120-cell has 28800 edges.  The omnisnub 120-cell, not uniform, has 32400 edges.

Coming up with so many answer possibilities is left as an exercise for the reader.