Reciprocal Polyhedra of the Thirteen Archimedean Solids - Maple Programming Help

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Reciprocal Polyhedra of the Thirteen Archimedean Solids

 Calling Sequence TriakisTetrahedron(gon, o, r) TetrakisHexahedron(gon, o, r) TriakisOctahedron(gon, o, r) PentakisDodecahedron(gon, o, r) TriakisIcosahedron(gon, o, r) RhombicDodecahedron(gon, o, r) RhombicTriacontahedron(gon, o, r) TrapezoidalIcositetrahedron(gon, o, r) TrapezoidalHexecontahedron(gon, o, r) HexakisOctahedron(gon, o, r) HexakisIcosahedron(gon, o, r) PentagonalIcositetrahedron(gon, o, r) PentagonalHexacontahedron(gon, o, r)

Parameters

 gon - the name of the polyhedron to be created o - point r - positive number

Description

 • The functions are to define the reciprocal polyhedra of the thirteen Archimedean solids where o is the center of the polyhedron, and r the mid-radius.
 • To access the information relating to these particular type of polyhedra, use the following function calls:

 center(gon) returns the center of gon. 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. radius(gon) returns the mid-radius 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 a trapezoidal icositetrahedron with center (1,2,3), radius of the mid-sphere 3

 > $\mathrm{HexakisIcosahedron}\left(t,\mathrm{point}\left(o,1,2,3\right),3\right)$
 ${t}$ (1)

Access information relating to the tetrahedron t:

 > $\mathrm{coordinates}\left(\mathrm{center}\left(t\right)\right)$
 $\left[{1}{,}{2}{,}{3}\right]$ (2)
 > $\mathrm{form}\left(t\right)$
 ${\mathrm{HexakisIcosahedron3d}}$ (3)
 > $\mathrm{radius}\left(t\right)$
 ${3}$ (4)
 > $\mathrm{schlafli}\left(t\right)$
 ${\mathrm{dual}}{}\left({\mathrm{_t}}{}\left(\left[\left[{3}\right]{,}\left[{5}\right]\right]\right)\right)$ (5)

Plotting:

 > $\mathrm{draw}\left(t,\mathrm{style}=\mathrm{patch},\mathrm{lightmodel}=\mathrm{light3}\right)$