Challenge 3: Why a Face Requires a Closed Loop of Edges — Solution Walkthrough

The answer:

Per this chapter's own material, a face is a flat, filled surface
bounded by a closed loop of edges — the same underlying requirement
Vector Graphics described for a closed path needing to hold a fill.
Just as an open path in Vector Graphics has no bounded interior for a
fill to occupy, an incomplete loop of edges in Blender has no
fully-enclosed region for a face to fill.

Why this parallel holds up directly:

In both cases, "closed" means the boundary connects all the way back
to where it started, with no gap. A Vector Graphics path with a gap
can't hold a fill because there's no enclosed interior; a Blender edge
loop with a gap can't form a face for the same underlying reason —
there's simply no bounded region for either a 2D fill or a 3D surface
to occupy.

Why this connects to this chapter's own broader framing:

This chapter frames vertices, edges, and faces as the same underlying
building-block concept as Vector Graphics' own anchor points and
paths, just one dimension higher. This specific requirement — needing
a closed boundary to hold a filled interior — is one of the clearest,
most direct instances of that shared underlying logic between the two
courses.

WHY THIS WORKS AS AN ANSWER
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This exercise checks that a face's own closed-loop requirement is
correctly traced back to the same underlying principle as Vector
Graphics' own closed-path-for-a-fill requirement, one dimension
higher.