facet - Maple Help

geom3d

 facet
 define a faceting of a given polyhedron

 Calling Sequence facet(gon, case, n)

Parameters

 gon - the name of the facetted polyhedron to be created case - the case polyhedron n - non-negative integer

Description

 • 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:

 center(gon); returns the center of the case polyhedron case. faces(gon); returns the faces of gon, each face is represented as a list of coordinates of its vertices. form(gon); returns the form of gon. schlafli(gon); returns the Schlafli symbol of gon. vertices(gon); returns the coordinates of vertices of gon.

Examples

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

Define the 1-st faceting of a cuboctahedron with center (0,0,0) radius 2

 > $\mathrm{facet}\left(\mathrm{i1},\mathrm{cuboctahedron}\left(c,\mathrm{point}\left(o,0,0,0\right),2\right),1\right)$
 ${\mathrm{i1}}$ (1)
 > $\mathrm{coordinates}\left(\mathrm{center}\left(\mathrm{i1}\right)\right)$
 $\left[{0}{,}{0}{,}{0}\right]$ (2)
 > $\mathrm{form}\left(\mathrm{i1}\right)$
 ${\mathrm{facetted_cuboctahedron3d}}$ (3)
 > $\mathrm{schlafli}\left(\mathrm{i1}\right)$
 ${\mathrm{facetted}}{}\left(\left[\left[{3}\right]{,}\left[{4}\right]\right]\right)$ (4)

Plotting:

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