Running the z parameter past 1/2 (vanishing volume and area) out to 𝟇/2 indicates that the stellated icosahedron is an extreme pyritohedron: http://gosper.org/pyredohedra.gif --rwg On Mon, Sep 30, 2013 at 11:01 PM, Bill Gosper <billgosper@gmail.com> wrote:
Oops, gosper.org/dodex.gif was already something else. Mgif renamed to http://gosper.org/pyritodex.gif . Also, the animator can be further condensed:
ListAnimate[ Table[Graphics3D[ Polygon[Join[#, -#] &@ Join[#, Map[RotateLeft, #, {2}], Map[RotateRight, #, {2}]] &@{#, {-1, 1, -1}*# & /@ #} &@{{-1/2 + 2 z^2, -1/2 + z, 0}, {-1/2, -1/2, -1/2}, {0, -1/2 + 2 z^2, -1/2 + z}, {1/2, -1/2, -1/2}, {1/2 - 2 z^2, -1/2 + z, 0}}]] /. z -> (5*Sin[t] + Sin[5*t])/12, {t, -π/2, π/2, π/30}], AnimationRunning -> True, AnimationDirection -> ForwardBackward] --rwg