geom3d[QuasiRegularPolyhedron] - define a quasi-regular polyhedron
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Calling Sequence
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QuasiRegularPolyhedron(gon, sch, o, r)
cuboctahedron(gon, o, r)
icosidodecahedron(gon, o, r)
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Parameters
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gon
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the name of the polyhedron to be created
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sch
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Schlafli symbol
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o
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-
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point
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r
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-
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positive number, an equation
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Description
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A quasi-regular polyhedron is defined as having regular faces, while its vertex figures, though not regular, are cyclic and equiangular (that is, has alternate sides and can be inscribed in circles).
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There are two quasi-regular polyhedra: cuboctahedron and icosidodecahedron.
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In Maple, one can define a quasi-regular polyhedron by using the command QuasiRegularPolyhedron(gon, sch, o, r) where gon is the name of the polyhedron to be defined, sch the Schlafli symbol, o the center of the polyhedron.
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When r is a positive number, it specifies the radius of the circum-sphere. When r is an equation, the left-hand side is one of radius, side, or mid_radius, and the right-hand side specifies the radius of the circum-sphere, the side, or the mid-radius (respectively) of the quasi-regular polyhedron to be constructed.
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The Schlafli symbol can be one of the following:
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Maple's Schlafli
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Polyhedron type
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[[3],[4]]
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cuboctahedron
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[[3],[5]]
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icosidodecahedron
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Another way to define a quasi-regular polyhedron is to use the command PolyhedronName(gon, o, r) where PolyhedronName is either cuboctahedron or icosidodecahedron.
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To access the information relating to a quasi-regular polyhedron gon, use the following function calls:
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center(gon)
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returns the center of the circum-sphere of gon.
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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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radius(gon)
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returns the radius of the circum-sphere of gon.
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schlafli(gon)
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returns the Schlafli symbol of gon.
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sides(gon)
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returns the length of the edges 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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Define an icosidodecahedron with center (0,0,0), radius of the circum-sphere 1
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Access information relating to the icosidodecahedron t:
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Define a cuboctahedron with center (1,1,1), radius sqrt(2)
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