Basic Examples (4) 

Retrieve the ResourceFunction:

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Get the boundary of a Simplex:

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Get the boundary of a simplicial complex, represented as a list of simplices:

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Get the boundary of a MeshRegion:

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Scope (2) 

By default, the boundary will be computed from simplices that match the dimension of the simplicial complex:

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A different dimension k can be specified, which will find the boundary of the k-skeleton of the complex:

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Generalizations and Extensions (1) 

Some other primitives can represent a simplex as well:

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Applications (2) 

Find holes in a 3D model:

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Highlight the boundary edges:

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Properties and Relations (3) 

Orientation is preserved:

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The boundary of a boundary is always empty:

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A graph can be considered a one-dimensional simplicial complex:

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The boundary can give you information about degree of vertices:

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Possible Issues (5) 

Not all graphics primitives are valid simplices:

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They can often be converted to simplicial complexes using DiscretizeGraphics that are reasonable approximations:

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Valid n-dimensional simplices must have n+1 vertices:

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Mesh regions are not necessarily composed of simplices:

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TriangulateMesh can often be used to create a valid simplicial complex:

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Vertices must be unique:

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If orientations are not consistent within a simplicial complex, the boundary will not have consistent orientations, either:

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Interactive Examples (1) 

One can visualize 4D shapes by rotating and projecting the boundary into 3D. Here is an example using a hexadecachoron:

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Neat Examples (2) 

The boundary of an annulus is two circles, while the boundary of a Moebius strip is a single circle:

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Get text outlines:

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