# Meaning of MeshCells for CantorMesh?

Let

    cantor2 = CantorMesh[2]


As expected:

    RegionBounds[cantor2]
(* {{0., 1.}} *)


And as expected:

    Flatten@Rationalize@MeshCoordinates[cantor2]
(* {0, 1/9, 2/9, 1/3, 2/3, 7/9, 8/9, 1} *)


Then what is the meaning of the output below?

    MeshCells[cantor2, RegionDimension[cantor2]]
(* {Line[{1, 2}], Line[{3, 4}], Line[{5, 6}], Line[{7, 8}]} *)


I expected it to be a list of lines with endpoints the various rational numbers in the interval from 0 to 1.

• You want MeshPrimitives[]: MeshPrimitives[CantorMesh[2], 1] // Rationalize. See the second bullet point under "Details" in the MeshCells[] doc page. Jun 4 at 21:40
• @J.M.: OK, that gives what I want. But what then does MeshCells[CantorMesh[2], RegionDimension[CantorMesh[2]]] mean? Jun 4 at 21:45
• The integers are indices into the MeshCoordinates[] similar to GraphicsComplex[]. Jun 4 at 21:57