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:

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

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

$\mathrm{i1}$

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

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

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

$\mathrm{stellated\_icosahedron3d}$

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

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

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