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MeshRegion

A region given by coordinates and the cells between them, as ConvexHullMesh, DelaunayMesh and VoronoiMesh build it. The ordinary region functions read it, and exact coordinates keep exact answers.

$ wo 'RegionMeasure[ConvexHullMesh[{{0, 0}, {2, 0}, {0, 2}}]]'
2

$ wo 'Perimeter[ConvexHullMesh[{{0, 0}, {2, 0}, {0, 2}}]]'
4 + 2*Sqrt[2]

$ wo 'RegionCentroid[ConvexHullMesh[{{0, 0}, {2, 0}, {2, 2}, {0, 2}}]]'
{1, 1}

$ wo 'RegionMember[ConvexHullMesh[{{0, 0}, {2, 0}, {0, 2}}], {0.5, 0.5}]'
True

MeshCoordinates, MeshCells, MeshPrimitives and MeshCellCount read the object itself. Cells are named by the indices of the coordinates they join, and primitives write those coordinates out:

$ wo 'MeshCells[ConvexHullMesh[{{0, 0}, {2, 0}, {0, 2}}], 1]'
{Line[{1, 2}], Line[{2, 3}], Line[{3, 1}]}

$ wo 'MeshPrimitives[ConvexHullMesh[{{0, 0}, {2, 0}, {0, 2}}], 1]'
{Line[{{0, 0}, {2, 0}}], Line[{{2, 0}, {0, 2}}], Line[{{0, 2}, {0, 0}}]}

$ wo 'MeshCellCount[DelaunayMesh[{{0, 0}, {2, 0}, {0, 2}, {2, 2}}]]'
{4, 5, 2}

DelaunayMesh triangulates a point set:

$ wo 'RegionMeasure[DelaunayMesh[{{0, 0}, {2, 0}, {0, 2}, {2, 2}}]]'
4

$ wo 'Sort[Sort /@ MeshCells[DelaunayMesh[{{0, 0}, {2, 0}, {0, 2}, {2, 2}}], 2][[All, 1]]]'
{{1, 2, 3}, {2, 3, 4}}