QuasiRegularPolyhedron - Maple Help

geom3d

 QuasiRegularPolyhedron
 define a quasi-regular polyhedron

 Calling Sequence QuasiRegularPolyhedron(gon, sch, o, r) cuboctahedron(gon, o, r) icosidodecahedron(gon, o, r)

Parameters

 gon - the name of the polyhedron to be created sch - Schlafli symbol o - point r - positive number, an equation

Description

 • 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).
 • There are two quasi-regular polyhedra: cuboctahedron and icosidodecahedron.
 • 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.
 • 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.
 • The Schlafli symbol can be one of the following:

 Maple's Schlafli Polyhedron type [[3],[4]] cuboctahedron [[3],[5]] icosidodecahedron

 • Another way to define a quasi-regular polyhedron is to use the command PolyhedronName(gon, o, r) where PolyhedronName is either cuboctahedron or icosidodecahedron.
 • To access the information relating to a quasi-regular polyhedron gon, use the following function calls:

 center(gon) returns the center of the circum-sphere 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 radius of the circum-sphere of gon. schlafli(gon) returns the Schlafli symbol of gon. sides(gon) returns the length of the edges of gon. vertices(gon) returns the coordinates of vertices of gon.

Examples

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

Define an icosidodecahedron with center (0,0,0), radius of the circum-sphere 1

 > $\mathrm{icosidodecahedron}\left(t,\mathrm{point}\left(o,0,0,0\right),1\right)$
 ${t}$ (1)

Access information relating to the icosidodecahedron $t$:

 > $\mathrm{center}\left(t\right)$
 ${o}$ (2)
 > $\mathrm{form}\left(t\right)$
 ${\mathrm{icosidodecahedron3d}}$ (3)
 > $\mathrm{radius}\left(t\right)$
 ${1}$ (4)
 > $\mathrm{schlafli}\left(t\right)$
 $\left[\left[{3}\right]{,}\left[{5}\right]\right]$ (5)
 > $\mathrm{sides}\left(t\right)$
 $\frac{{2}{}\sqrt{{5}}}{{5}{+}\sqrt{{5}}}$ (6)

Define a cuboctahedron with center (1,1,1), radius $\sqrt{2}$

 > $\mathrm{QuasiRegularPolyhedron}\left(i,\left[\left[3\right],\left[4\right]\right],\mathrm{point}\left(o,1,1,1\right),1\right)$
 ${i}$ (7)
 > $\mathrm{form}\left(i\right)$
 ${\mathrm{cuboctahedron3d}}$ (8)