List the coordinates of a unit tetrahedron's vertices:

List the indices of a unit octahedron's edges:

Annotate the indices on the polyhedron:

List the indices of a unit cube's faces:

Annotate the indices on the polyhedron:

Give the regular octahedron as a Polyhedron object:

Visualize:

Convert to a region:

Return the polygons corresponding to the faces of the cube:

Visualize:

Return the lines corresponding to the edges of the octahedron:

Visualize:

Return the points corresponding to the vertices of the cube:

Visualize:

Show a 3D graphic of the dodecahedron:

Return a graphics complex for the icosahedron:

View as a 3D graphic:

Display a rasterized image of the cube:

Show a graphic of the cube and its dual:

Give the number of edges in an icosahedron:

Give the number of faces in a cuboctahedron:

Give the number of distinct nets of an icosahedron:

Count the number of vertices in a cuboctahedron:

Give the boundary mesh region of the small triambic icosahedron:

Return the coordinate bounds of the icosahedron:

Place a bounding box around the solid:

Use the bounds to plot the relevant region:

Give the implicit region of the cube:

Visualize:

Give the mesh region of the small triambic icosahedron:

Visualize the region of the small triambic icosahedron:

Give the region function of the tetrahedron:

Visualize the region by converting it to an ImplicitRegion:

Give the region function of the cuboctahedron as a pure function:

Give the region function of the cuboctahedron as a function of , , and coordinates:

Plot the region corresponding to the interior of the cuboctahedron:

Give the centroid of Dürer's solid:

Give the circumcenter of the unit tetrahedron:

Show the circumdiameter of the unit tetrahedron:

Show the circumradius of the unit tetrahedron:

Combine the two to get the circumsphere itself:

Show the circumsphere of the unit cube:

Show the Dehn invariant of the unit cube:

The Dehn invariant of a space-filling polyhedron is 0:

Show the dihedral angle rules of the unit cube:

Give the generalized diameter of the unit cube:

Give the incenter of the unit cube:

Give the normalized moment of inertia tensor of the Wolfram Language polyhedron:

Give the inradius of the unit cube:

Combine the two to get the insphere of the unit cube:

Give the midcenter of the unit cube:

Give the midradius of the unit cube:

Combine the two to get the midsphere of the unit cube:

Show the stable face of the Conway–Guy polyhedron:

Give the surface area of the unit cube:

Show the unstable faces of the Conway–Guy polyhedron:

Give rules for vertex subsets whose convex hulls form other solids:

Visualize the hulls:

Give the volume of the unit cube:

Give the mean cylindrical radius of the cube:

Give the mean spherical radius of the cube:

Give the mean interior line segment length of the cube:

Give the mean square cylindrical radius of the cube:

Give the mean square spherical radius of the cube:

Classes of which the cube is a member:

Notations describing the cube:

Amphichiral polyhedra:

Canonical polyhedra:

Chiral polyhedra:

Compound polyhedra:

Concave polyhedra:

Convex polyhedra:

Deltahedra:

Equilateral polyhedra:

Isohedra:

Parallelohedra:

Plesiohedra:

Self-dual polyhedra:

Space-filling polyhedra:

Stereohedra:

Polyhedra that are stellations:

Unistable polyhedra:

Zonohedra:

Archimedean solids:

Archimedean duals:

Johnson solids:

Kepler–Poinsot solids:

Platonic solids:

Platonic duals:

Same as the Platonic solids:

Trapezohedra:

Uniform solids:

Uniform duals:

Antiprisms:

Dipyramids:

Prisms:

Pyramids:

Zalgaller solids:

List the alternate English names of the cube:

List the alternate standard names for the octahedron:

Give the entity form of the cube:

Give the textual name of the cube:

Give the textual names of the cube:

Give rules for various notations for the cube:

Query the standard name of the 3-hypercube:

Show other alternate standard names corresponding to this standard name:

Show the common solid of the first cube 5-compound:

Return as a polyhedron:

Give the name and scale (relative to the named polyhedron) of the compound interior:

Visualize together with the original polyhedron:

Show the convex hull of the great icosahedron:

Return as a polyhedron:

Give the name and scale (relative to the named polyhedron) of the convex hull:

Visualize together with the original polyhedron:

Show the dihedral angles of the cuboctahedron:

Show as a list of rules mapping adjacent faces to angles:

Build the same list by hand:

Show a graphic of the dodecahedron dual:

Give the standard name of the dodecahedron dual:

Format as an entity:

Show the cube dual as a 3D graphic:

Return a graphics complex of the cube dual:

Visualize:

Show as an image:

Return the scale of the dual relative to the unit primary solid:

Show a graphic of the dodecahedron-dual compound:

Give the standard name of the dodecahedron-dual compound:

Format as an entity:

Show the cube-dual compound as a 3D graphic:

Return a graphics complex of the cube-dual compound:

Visualize:

Show as an image:

List the indices of the edges of the equilateral 5-prism:

Visualize the edge connectivity as a graph embedded in three dimensions:

Visualize the edges directly:

Return the number of edges as an annotation:

Do the same using the dedicated property:

Return edges as a graphics expression:

Return the underlying graphics expression:

Visualize:

Show an image of the edges:

Return a sorted list of unique edge lengths:

Give edge lengths of the deltoidal hexecontahedron:

Compute directly from lines:

Return edges as explicit line segments:

Explicitly request edge indices as a list of pairs:

Return edges as a list of indexed rules:

Plot using GraphPlot:

Return edges as a list of undirected edges:

Convert to a Graph expression: