- The
vertex figure of a tiling is the pattern of polygons surrounding a vertex
point. Use the table in #16 to
determine all of the possible vertex figures of regular polygons with at
most 12 sides. There are 16
possibilities.
- In
addition to the vertex figures of #19, exactly five others are possible,
each involving one polygon with more than 12 sides. These many-sided polygons have 15, 18,
20, 24, and 42 sides. Determine the
other polygons in these vertex figures.
Unfortunately, none of these vertex figures will tile the plane.