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geom3d[facet] - define a faceting of a given polyhedron
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Calling Sequence
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facet(gon, case, n)
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Parameters
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gon
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the name of the facetted polyhedron to be created
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case
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the case polyhedron
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n
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non-negative integer
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Description
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The core of a star-polyhedron or compound is the largest convex solid that can be drawn inside it, and the case is the smallest convex solid that can contain it.
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The compound or star-polyhedron may be constructed either by stellating its core, or by faceting its case which involves removal of solid pieces.
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Maple currently supports faceting process to the five polyhedra: octahedron, cuboctahedron, icosidodecahedron, small rhombicuboctahedron and small rhombiicosidodecahedron.
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For the octahedron, there are two values of n: 0 and 1.
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For the other four polyhedra, there are three values of n: 0, 1 and 2.
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To access the information relating to a facetted polyhedron gon, use the following function calls:
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center(gon);
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returns the center of the case polyhedron case.
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faces(gon);
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returns the faces of gon, each face is represented
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as a list of coordinates of its vertices.
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form(gon);
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returns the form of gon.
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schlafli(gon);
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returns the ``Schlafli'' symbol of gon.
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vertices(gon);
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returns the coordinates of vertices of gon.
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Examples
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>
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Define the 1-st faceting of a cuboctahedron with center (0,0,0) radius 2
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![[0, 0, 0]](/support/helpjp/helpview.aspx?si=5961/file04006/math162.png)
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| (3) |
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![facetted([[3], [4]])](/support/helpjp/helpview.aspx?si=5961/file04006/math176.png)
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Plotting:
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![draw(i1, style = patch, orientation = [-145, 132], lightmodel = light4, shading = XY, title = `facetted cuboctahedron - 1`)](/support/helpjp/helpview.aspx?si=5961/file04006/math182.png)
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