The core of a star-polyhedron or compound is the largest convex solid that can be drawn inside it. The star-polyhedron or compound may be constructed by stellating its core. Note that it can also be constructed by faceting its case. See the geom3d:-facet command for more information.

In order to stellate a polyhedron, one has to extend its faces symmetrically until they again form a polyhedron. To investigate all possibilities, we consider the set of lines in which the plane of a particular face would be cut by all other faces ( sufficiently extended), and try to select regular polygons bounded by sets of these lines.

Maple currently supports stellation of the five Platonic solids and the two quasi-regular polyhedra (the cuboctahedron and the icosidodecahedron).

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

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

$\mathrm{stellate}\left(\mathrm{i1}\,\mathrm{icosahedron}\left(i\,\mathrm{point}\left(o\,1\,1\,1\right)\,2\right)\,22\right)$

$\mathrm{i1}$

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

$\left[1\,1\,1\right]$

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

$\mathrm{stellated\_icosahedron3d}$

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

$\mathrm{stellated}\left(\left[3\,5\right]\right)$

$\mathrm{draw}\left(\mathrm{i1}\,\mathrm{style}=\mathrm{patch}\,\mathrm{orientation}=\left[-90\,145\right]\,\mathrm{lightmodel}=\mathrm{light4}\,\mathrm{title}=\mathrm{`stellated\; icosahedron\; -\; 22`}\right)$