### V. Other Polygonal Prototiles

The f-tilings are specified as described in the Introduction. The figures available for each f-tiling are listed as links. These are grouped by families, where the general tile shape and construction algorithm are the same within each family. A thumbnail example is given for each family.
A. There are two distinct f-tilings in this family. If the midpoint between the line segment of double length on the prototile is considered a vertex, then the tilings would be edge to edge. (In this case, the prototile can be considered a 12-gon rather than an 11-gon.)
• (p11, r3, g3, s.5, m0)
• (p11, r4, g4, s.5, m0)

B. The first two f-tilings in an infinite family of edge-to-edge f-tilings are shown.

• (p12, r2, g3, s.414, m0)
• (p12, r2, g3, s.382, m0)

C. The first two f-tilings in an infinite family of edge-to-edge f-tilingsare shown.

• (p15, r2, g4, s.333, m0)
• (p15, r2, g4, s.293, m0)

D. This infinite family is related to the first family based on hexagonal prototiles. These f-tilings are broken into two branches.
D1. In the first branch, the prototiles possess bilateral symmetry.

• (p10, r8, g13, s.147, m2)
• (p10, r12, g21, s.134, m2)
D2. In the second branch, the prototiles do not possess bilateral symmetry. If the midpoint between the line segment of double length on the prototile is considered a vertex, then the f-tilings would be edge to edge. (In this case, the prototile would be considered a 10-gon rather than an 9-gon.)

• (p9, r6, g13, s.167, m0)
• (p9, r8, g17, s.147, m0)
• (p9, r12, g25, s.134, m0)

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