
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 quasiregular 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 quasiregular polyhedra: cuboctahedron and icosidodecahedron.

•

In Maple, one can define a quasiregular 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 circumsphere. When r is an equation, the lefthand side is one of radius, side, or mid_radius, and the righthand side specifies the radius of the circumsphere, the side, or the midradius (respectively) of the quasiregular 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 quasiregular polyhedron is to use the command PolyhedronName(gon, o, r) where PolyhedronName is either cuboctahedron or icosidodecahedron.

•

To access the information relating to a quasiregular polyhedron gon, use the following function calls:

center(gon)

returns the center of the circumsphere 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 circumsphere 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 circumsphere 1
>

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

Access information relating to the icosidodecahedron $t$:
>

$\mathrm{center}\left(t\right)$

>

$\mathrm{form}\left(t\right)$

${\mathrm{icosidodecahedron3d}}$
 (3) 
>

$\mathrm{radius}\left(t\right)$

>

$\mathrm{schlafli}\left(t\right)$

$\left[\left[{3}\right]{\,}\left[{5}\right]\right]$
 (5) 
>

$\mathrm{sides}\left(t\right)$

$\frac{{2}{}\sqrt{{5}}}{{5}{+}\sqrt{{5}}}$
 (6) 
Define a cuboctahedron with center (1,1,1), radius $\sqrt{2}$
>

$\mathrm{QuasiRegularPolyhedron}\left(i\,\left[\left[3\right]\,\left[4\right]\right]\,\mathrm{point}\left(o\,1\,1\,1\right)\,1\right)$

>

$\mathrm{form}\left(i\right)$

${\mathrm{cuboctahedron3d}}$
 (8) 


