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The case of a star-polyhedron or compound is the smallest convex solid that can contain it. The star-polyhedron or compound may be constructed by faceting its case which involves removal of solid pieces. Note that it can also be constructed by stellating its core. See the geom3d:-stellate command for more information.

Maple currently supports faceting process to the five polyhedra: octahedron, cuboctahedron, icosidodecahedron, small rhombicuboctahedron and small rhombiicosidodecahedron.

For the octahedron, there are two values of n: 0 and 1.

For the other four polyhedra, there are three values of n: 0, 1 and 2.

To access the information relating to a facetted polyhedron gon, use the following function calls:

$\mathrm{with}\left(\mathrm{geom3d}\right)\:$

$\mathrm{facet}\left(\mathrm{i1}\,\mathrm{cuboctahedron}\left(c\,\mathrm{point}\left(o\,0\,0\,0\right)\,2\right)\,1\right)$

$\mathrm{i1}$

$\mathrm{coordinates}\left(\mathrm{center}\left(\mathrm{i1}\right)\right)$

$\left[0\,0\,0\right]$

$\mathrm{form}\left(\mathrm{i1}\right)$

$\mathrm{facetted\_cuboctahedron3d}$

$\mathrm{schlafli}\left(\mathrm{i1}\right)$

$\mathrm{facetted}\left(\left[\left[3\right]\,\left[4\right]\right]\right)$

$\mathrm{draw}\left(\mathrm{i1}\,\mathrm{style}=\mathrm{patch}\,\mathrm{orientation}=\left[-145\,132\right]\,\mathrm{lightmodel}=\mathrm{light4}\,\mathrm{shading}=\mathrm{XY}\,\mathrm{title}=\mathrm{`facetted\; cuboctahedron\; -\; 1`}\right)$