The Tetrahedron, Cube, Octahedron, TruncatedTetrahedron, TruncatedOctahedron, and Cuboctahedron commands create polyhedral sets in three dimensions.  The calling sequence with no arguments, SetName(), uses the default coordinates for the set's ambient space.  Alternatively, the coordinates can be specified via SetName(coords) or generated as indexed variables with variable varname as their root via SetName(varname).

The tetrahedron, cube and octahedron are regular polyhedra.  The truncated tetrahedron, truncated octahedron and cuboctahedron are semiregular polyhedra, whose facets consist of different types of regular polygons.

The Tetrahedron, Cube, Octahedron, TruncatedTetrahedron, TruncatedOctahedron, and Cuboctahedron commands were introduced in Maple 2015.

For more information on Maple 2015 changes, see Updates in Maple 2015.

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

$\mathrm{with}\left(\mathrm{ExampleSets}\right)$

$\left[\mathrm{Cube}\,\mathrm{Cuboctahedron}\,\mathrm{EmptySet}\,\mathrm{Hypercube}\,\mathrm{Hyperoctant}\,\mathrm{Octahedron}\,\mathrm{RandomSet}\,\mathrm{RandomSolid}\,\mathrm{Simplex}\,\mathrm{Tetrahedron}\,\mathrm{TruncatedOctahedron}\,\mathrm{TruncatedTetrahedron}\,\mathrm{UniversalSet}\right]$

$t≔\mathrm{Tetrahedron}\left(\right)\;$$\mathrm{Plot}\left(t\right)$

$t≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[-x_1-x_2-x_3\le 1\,-x_1+x_2+x_3\le 1\,x_1-x_2+x_3\le 1\,x_1+x_2-x_3\le 1\right]\end{array}$

$c≔\mathrm{Cube}\left(\left[x\,y\,z\right]\right)\;$$\mathrm{Plot}\left(c\right)$

$c≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x\,y\,z\right]\\ \mathrm{Relations}& \:& \left[-z\le 1\,z\le 1\,-y\le 1\,y\le 1\,-x\le 1\,x\le 1\right]\end{array}$

$o≔\mathrm{Octahedron}\left(y\right)\;$$\mathrm{Plot}\left(o\right)$

$o≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[y_1\,y_2\,y_3\right]\\ \mathrm{Relations}& \:& \left[-y_1-y_2-y_3\le 1\,-y_1-y_2+y_3\le 1\,-y_1+y_2-y_3\le 1\,-y_1+y_2+y_3\le 1\,y_1-y_2-y_3\le 1\,y_1-y_2+y_3\le 1\,y_1+y_2-y_3\le 1\,y_1+y_2+y_3\le 1\right]\end{array}$

$\mathrm{tt}≔\mathrm{TruncatedTetrahedron}\left(y\right)\;$$\mathrm{Plot}\left(\mathrm{tt}\right)$

$\mathrm{tt}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[y_1\,y_2\,y_3\right]\\ \mathrm{Relations}& \:& \left[-y_1-y_2-y_3\le 1\,-y_1-y_2+y_3\le \frac{5}{3}\,-y_1+y_2-y_3\le \frac{5}{3}\,-y_1+y_2+y_3\le 1\,y_1-y_2-y_3\le \frac{5}{3}\,y_1-y_2+y_3\le 1\,y_1+y_2-y_3\le 1\,y_1+y_2+y_3\le \frac{5}{3}\right]\end{array}$

$\mathrm{tro}≔\mathrm{TruncatedOctahedron}\left(\right)\;$$\mathrm{Plot}\left(\mathrm{tro}\right)$

$\mathrm{tro}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[-x_3\le 1\,x_3\le 1\,-x_2\le 1\,x_2\le 1\,-x_1-x_2-x_3\le \frac{3}{2}\,-x_2+x_3-x_1\le \frac{3}{2}\,-x_1\le 1\,-x_3+x_2-x_1\le \frac{3}{2}\,-x_1+x_2+x_3\le \frac{3}{2}\,x_1-x_3-x_2\le \frac{3}{2}\,\mathrm{and\; 4\; more\; constraints}\right]\end{array}$

$\mathrm{co}≔\mathrm{Cuboctahedron}\left(\right)\;$$\mathrm{Plot}\left(\mathrm{co}\right)$

$\mathrm{co}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[-x_3\le 1\,x_3\le 1\,-x_2\le 1\,x_2\le 1\,-x_1-x_2-x_3\le 2\,-x_2+x_3-x_1\le 2\,-x_1\le 1\,-x_3+x_2-x_1\le 2\,-x_1+x_2+x_3\le 2\,x_1-x_3-x_2\le 2\,\mathrm{and\; 4\; more\; constraints}\right]\end{array}$