define a stellation of a given polyhedron
stellate(gon, core, n)
the name of the stellated polyhedron to be created
the core polyhedron
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).
the only lines are the faces itself. Hence, there is only one possible value of n, namely 0.
possible values of n are 0, 1 (the core octahedron and the stella octangula).
4 possible values of n: 0 to 3 (the core dodecahedron, the small stellated dodecahedron, the great stellated dodecahedron and the great dodecahedron).
59 possible values of n: 0 to 58.
5 possible values of n: 0 to 4.
19 possible values of n: 0 to 18.
To access the information relating to a stellated polyhedron gon, use the following function calls:
returns the center of the core polyhedron core.
returns the faces of gon, each face is represented as a list of coordinates of its vertices.
returns the form of gon.
returns the ``Schlafli'' symbol of gon.
returns the coordinates of vertices of gon.
Define the 22-nd stellation of an icosahedron with center (1,1,1) radius 2
draw⁡i1,style=patch,orientation=−90,145,lightmodel=light4,title=`stellated icosahedron - 22`
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