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:

List the indices of a square pyramid's faces:

Visualize the faces:

Return a list of indices of adjacent faces:

Visualize the adjacent faces:

Return the number of faces as an annotation:

Do the same using the dedicated property:

Return a graphics expression containing the faces:

Return the underlying graphics expression:

Visualize:

Show an image of the faces:

Explicitly request faces as a list of indices:

Return faces as explicit polygons:

Do the same using the "Polygons" property:

Return a rule list of counts of faces with given numbers of sides:

Compute explicitly:

Show faces colored by numbers of sides:

Return the indices of polyhedra in a compound:

Show the five components:

Combine:

Color the component tetrahedra:

Show a styled graphics expression for the icosahedron net:

Do the same using the explicit "Graphics" annotation:

Show a net colored by face type:

Give the coordinates of the vertices of an icosahedron net:

Return the number of nonisomorphic nets for the cube:

Do the same using the dedicated property:

Return the net of the dodecahedron as a Graph object:

Show a graphic for the cuboctahedron net:

Give the faces in a net of the octahedron as a GraphicsComplex:

Give the edges of an icosahedron net as a GraphicsComplex:

Construct a graphic:

Give the indices of the faces of a net of the icosahedron:

Construct a graphic from the net faces:

Show an image of the net of the dodecahedron:

Return the net as a set of polygons:

Return the stella octangula solid as a Polyhedron:

Display as a region:

Return the skeleton graph of the dodecahedron:

Give the vertices of a skeleton of the dodecahedron:

Obtain the skeleton graph as an Entity:

Return the skeleton of the dodecahedron as a Graph object:

This is equivalent to the default output of "Skeleton":

Give the name of the skeleton graph of the cube:

Use the "Image" annotation:

Give dodecahedron skeleton graph edges as rules:

Visualize using GraphPlot:

Visualize using GraphPlot3D:

Return the skeleton graph edges as an UndirectedEdge list:

Visualize as a graph:

Show the symmetry group of the cube as a FiniteGroupData standard name:

Do the same using the explicit "Name" annotation:

Return the entity:

Return as an explicit permutation group:

Return notation for symmetry group:

List the indices of a unit tetrahedron's vertices:

Compare with the "VertexCoordinates" property:

Compare with the "Coordinates" annotation:

Visualize the vertices:

Do the same using the "Points" property:

Return the number of vertices as an annotation:

Do the same using the dedicated property:

Return a graphics expression containing the faces:

Return the underlying graphics expression:

Visualize:

Show an image of the vertices:

Explicitly request vertices as a list of indices:

Return vertices as explicit points: