Figures at a glance

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FIGURE 1

Figure 1: Original Penrose tile

FIGURE 2

Figure 2: A regular pentagonal pattern with five decagonal on each side, (a) Bloated, (b) slim

FIGURE 3

Figure 3: The examples of bottom-to-bottom opposite direction coupling type, (3a) Shows a simple skin perfectly coupling

FIGURE 4

Figure 3b: Deeper coupling, with outer three layers involved, 3b1: coupling before revision remaining mismatched regions and figure (3b2) is after revision, (3c) shows an even deeper coupling, covers almost all the region slim type tile, (3c1) before revision, (3c2) after revision

FIGURE 5

Figure 3d: Completed coupling (3d1) before and (3d2) after revision revealed a circular Penrose tile.

FIGURE 6

Figure 3e: A slanted shift coupling

FIGURE 7

Figure 4: The examples vertex- to-vertex opposite direction coupling type Figure 4a1: Result of a deep coupling before revision, Figure 4a2: After revision.

FIGURE 8

Figure 5: Bottom-vertex coupling in the same direction type. 5a1: Before revision 5a2: After revision, (5b) A deeper coupling after revision, (5c) Slant shift coupling after revision

FIGURE 9

Figure 6: Coupled pairs can be translational (or slanted shift) coupled by their self as shown in figure 6 a,b

FIGURE 10

Figure 7: 7a: Tile in figure 3c2 self-coupled to infinity, Figure 7b: Anunit cell extracted from tile in figure 7c

FIGURE 11

Figure 8: Unit cell can be tessellated to construct a translational periodic Penrose tiling