We show that the hypercube has a face-unfolding that tiles space, and that unfolding has an edge-unfolding that tiles the plane. So the hypercube is a “dimension-descending tiler.” We also show that the hypercube cross unfolding made famous by Dali tiles space, but we leave open the question of whether or not it has an edge-unfolding that tiles the plane.

We first prove that solving Mahjong Solitaire boards with peeking is NPcomplete, even if one only allows isolated stacks of the forms aab and abb. We subsequently show that layouts of isolated stacks of heights one and two can always be solved with peeking, and that doing so is in P, as well as finding an optimal algorithm for such layouts without peeking. Next, we describe a practical algorith...

We give a simple set of two tiles that can only tile aperiodically | that is no tiling with these tiles is invariant under any in nite cyclic group of isometries. Although general constructions for producing aperiodic sets of tiles are nally appearing, simple aperiodic sets are fairly rare. This set is among the smallest sets ever found. A tiling is non-periodic if there is no in nite cyclic gr...

This case report describes a simple method for identifying the citizenship of a denture wearer by marking the telephone country code number inside the denture base. A wax pattern for the denture framework was prepared on the refractory cast. A piece of embossing tape, containing the country code (81, Japan), Japanese prefectural code, and abbreviation of the dental clinic where the denture was ...

LINKED EDITORIALS This Editorial is part of a series. To view the other Editorials in this series, visit: http://onlinelibrary.wiley.com/doi/10.1111/bph.12956/abstract; http://onlinelibrary.wiley.com/doi/10.1111/bph.12954/abstract; http://onlinelibrary.wiley.com/doi/10.1111/bph.12955/abstract and http://onlinelibrary.wiley.com/doi/10.1111/bph.12856/abstract. VIDEO To view the video on the IUP...

A new aperiodic tile set containing 11 Wang tiles on 4 colors is presented. This tile set is minimal in the sense that no Wang set with less than 11 tiles is aperiodic, and no Wang set with less than 4 colors is aperiodic. Wang tiles are square tiles with colored edges. A tiling of the plane by Wang tiles consists in putting a Wang tile in each cell of the grid Z so that contiguous edges share ...

We investigated the effect of augmenting a chat-based learning system, with a lowand high-quality video link, on the focus (factual vs. abstract) of a case-based learning discussion. Efficient learning with cases requires discussion on the case as well as on the meaning of abstract knowledge. We find that students who first experience chat + high-quality video, focus significantly more on abstr...

Many complex signals, such as point distributions and textures, cannot efficiently be synthesized and stored. In this work we present tile-based methods to solve this problem. Instead of synthesizing a complex signal when needed, the signal is synthesized on forehand over a small set of tiles. Arbitrary large amounts of that signal can then efficiently be generated when needed by generating a s...