# Convex Polyhedra with Largest Constant Dihedral Angle for Given Number of Faces

Which $20$ faced convex polyhedron has the largest constant dihedral angle?

Which $24$ faced convex polyhedron has the largest constant dihedral angle?

Also, what about $30$ or $32$ faced polyhedra? How does one go about finding them?

(Note: this is a repost of a question on Math stack exchange)

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You should wait more than a few hours after posting on math.stackexchange before posting here. What do you mean by "constant dihedral angle?" All dihedral angles are constant, and they can be arbitrarily close to $\pi$. Do you mean you want to maximize the minimal dihedral angle? – Douglas Zare Mar 4 '13 at 23:27
@Douglas: I would guess the question means: among those convex icosahedra whose dihedral angles are all equal, which one maximises this dihedral angle? – Matt Fayers Mar 5 '13 at 11:16