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:

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:

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

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

$t$

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

$o$

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

$\mathrm{icosidodecahedron3d}$

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

$1$

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

$\left[\left[3\right]\,\left[5\right]\right]$

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

$\frac{2\sqrt{5}}{5+\sqrt{5}}$

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

$i$

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

$\mathrm{cuboctahedron3d}$