Voderberg Trump Tiles

Modified Voderberg Tiles

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Original and modified standard Voderberg tiles

Standard Voderberg tiles admit periodic, rotational and spiral tilings of the plane.
More interesting is that two copies of a tile can surround one or two other copies.
The patch of tiles is a topological disk and two points of its boundary belong to all tiles.
Couples of Voderberg tiles that can surround more than 3 copies are not considered in this chapter.
Standard VT-tiles (Voderberg-Trump-tiles) are Voderberg tiles modified significantly by the author.

Voderberg Nonagons
Equilateral VT-Polygons
VT-Seahorse
VT-Swan

Surround number 2

The first tile with surround number 2 was found by Casey Mann in 2002.

Voderberg Mann Tile

VT-Dragons

Two copies of a VT-Dragon can surround another copy completely. That means:
There exists a patch of 3 congruent VT-Dragons that is a topological disk and
one Dragon has no point in common with the boundary of the patch.
Note, that the second condition is not satisfied by standard VT-tiles.
Additionally a VT-Dragon has to admit a tiling of the plane.
Rotational or spiral tilings of the plane are not possible.

First VT-Dragon
VT-Dragon 2
VT-Dragon 3
VT-Dragon 4