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Figure 4.7. Gauss map examples.
Vertices also, by extension, map to the hull enclosed by adjacent faces' nor-
mals, which is a spherical polygon on
2 (see Figure 4.6(c)). Figure 4.6(d) shows
S
the full Gauss map of a cube.
The whole sphere is covered by a Gauss map and features overlap only at the
borders of their corresponding images. Vertex areas are bounded by edge arcs,
which have corresponding face points (normals) as their ends. See Figure 4.7 for
examples.
A Gauss map is not reversible. Figure 4.8 shows two Gauss maps generated
by six different polytopes.
Figure 4.8. Gauss map nonreversibility.
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