The product of two line segments:

Visualize it:

The product of a disk and a line segment:

Visualize it:

The product of two BoundaryMeshRegion objects:

Define a tensor product mesh as the product of several 1D meshes:

Define a 1D mesh from a list of points:

Define a 2D tensor product mesh:

Define a 3D tensor product mesh:

Directly construct a MeshRegion representing a stage for the Cantor set. The set is defined by starting with the interval {0,1} and at each step removing the middle third:

The first few steps:

Use RegionProduct to produce Cantor dust:

Find the length of the Cantor set at each stage:

Guess the general formula:

Find the measure of the Cantor dust in 2D at each stage:

Find the measure of the Cantor dust in 3D at each stage:

The RegionEmbeddingDimension of a product is the sum of input embedding dimensions:

The RegionDimension of a product is the sum of input dimensions:

A RegionProduct of special regions is left unevaluated:

It is a region and can be used for computation:

A RegionProduct of formula regions is left unevaluated:

It is a region and can be used for computation:

A product of MeshRegion or BoundaryMeshRegion objects is itself a MeshRegion:

The RegionMeasure of a product is the product of the input measures:

The RegionCentroid of a product is the input centroids joined together:

A Rectangle is a product of two Line objects:

Show membership is equivalent:

A Cuboid is a product of three Line objects:

Show membership is equivalent:

A Cylinder is a product of a Disk and a Line:

Show membership is equivalent:

Define Cantor dust-like regions as products of Cantor sets:

Products of Cantor sets in 2D:

Products of Cantor sets in 3D: