A polyhedron is said to be uniform if its faces are regular while its vertices are all alike, i.e., every vertex can be transformed into any other by a symmetry operation.

Archimedean solids are uniform polyhedra with faces of at least two kinds. Besides the infinite families of prisms and antiprisms, there are thirteen Archimedean solids.

In Maple, one can define an Archimedean solid by using the command Archimedean(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 Archimedean solid to be constructed.

The Schlafli symbol can be one of the following:

Another way to define an Archimedean solid is to use the command PolyhedronName(gon,o,r) where PolyhedronName is one of TruncatedTetrahedron, TruncatedOctahedron, TruncatedHexahedron, TruncatedIcosahedron, TruncatedDodecahedron, SmallRhombicuboctahedron, SmallRhombiicosidodecahedron, GreatRhombicuboctahedron, TruncatedCuboctahedron, GreatRhombiicosidodecahedron, TruncatedIcosidodecahedron, SnubCube, cuboctahedron, or icosidodecahedron.

To access the information relating to an Archimedean solid gon, use the following function calls:

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

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

$t$

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

$o$

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

$\left[\left[\left[\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\right]\right]\,\left[\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\right]\,\left[\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\right]\,\left[\left[\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\right]\right]\,\left[\left[\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\right]\right]\,\left[\left[\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\right]\right]\,\left[\left[\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\right]\,\left[\left[\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{33}\,-\frac{\sqrt{33}\sqrt{3}}{11}\right]\,\left[-\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\,-\frac{\sqrt{33}\sqrt{3}}{33}\right]\,\left[\frac{\sqrt{33}\sqrt{3}}{33}\,\frac{\sqrt{33}\sqrt{3}}{11}\,\frac{\sqrt{33}\sqrt{3}}{33}\right]\right]\right]$

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

$\mathrm{TruncatedTetrahedron3d}$

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

$\frac{\sqrt{6}\sqrt{33}\sqrt{2}}{22}$

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

$1$

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

$\mathrm{\_t}\left(\left[3\,3\right]\right)$

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

$\frac{2\sqrt{6}\sqrt{33}}{33}$

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

$i$

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

$\mathrm{SmallRhombicuboctahedron3d}$