![]() ![]() In fact there areĩ possible ways to make a tessellating piece using these five moves. Is Move T on two sides and Move C on each of the remaining two sides. For example, Move T could beĭone on two opposite sides and Move G done on the other two sides. ![]() Putting the Moves Together for a Tessellating Piece – Heesch Typesĭifferent combinations of the five moves are possible. That two or more of the moves can be done on the same square piece of cardboard to get a This completes our presentation of the five moves. Perhaps an more natural way to visualize this move is by taking the cutout pieceĪnd flipping it over (as in Move G) and then rotating the flipped piece about theĬorner (as in move C 4). Side (along a diagonal glide reflection line going through the midpoints of the two Something is cut out of a side, a glide reflection carries the cutout to an adjacent This final move, like the last, involves a side and a touching or adjacent side. Move G ’’ (Glide Reflection, Adjacent sides): Move C 4 this cutout is rotated around a corner of the square and taped onto aĥ. Examples are given below.Īgain we again begin by cutting out something from one side of the square. However, as you may suspect, the pieces must be rotated around in Perhaps it is not so easy to see how a supply of these pieces can be fit together. Point of the side and taped onto the other half of the side. For this move, this cutout is rotated about the center Middle of one side of the cardboard square. This move is a little different since it involves only one side. Note that the pieces must be flipped over in order to fit together. Not be attached easily to the opposite side.Ī supply of these shapes could also be put together in an interlocking fashion but (not parallel to the side) – the wrong flip usually results in a cutout piece that can Note: The flip used here must be over a line perpendicular to the side of the square Thenįlip or reflect the cutout piece and slide it over and tape it to the opposite side of The top and translating it to the bottom (or vise versa).įor this move again cut some shape out of one side of the cardboard square. Together side by side like a puzzle? This move also works by cutting out part of Then slide or translate the cutout part over to the opposite side and tape itĬan you see that if you had a supply of tiles like this then you could put them So that the resulting shape is tessellating.įor the first move, translation, cut out part of the square along one side as pictured ![]() There are five “moves” (translation T, two kinds of glideĪnd two kinds of rotation C and C 4 ) which can be done to the square (See below for a discussion of more general shapes than a square which can be We will begin by cutting out a cardboard square which is the beginning of our tessellating Giving human or animal form to the abstract shapes is an opportunity for creativity andįive Moves for Making Our Own Tessellating Pieces The basic tile and how it was made and also reveals the symmetries of the design. AĬlassification, called the Heesch Type, will be presented. In this chapter we will describe ways we can make our own tessellating pieces. Is sometimes upright and sometimes upside down and sometimes facing right and Notice in the design below that the basic tile Sometimes the basic tile must be rotated or flipped over in order to fit together withĮxisting pieces as in the following example. We can imagine covering a bathroom floor with this type of design where many copies ofĪ basic tile or tessellating piece are placed side by side to form a tiling. These are examples of what we will call Escher Style Tessellations, patterns which canīe extended to the left, right, up and down to cover an entire wall. Escher have captured peoples’ imagination the world Every glide reflection has a mirror line and translation distance.The delightful designs by M. Every reflection has a mirror line.Ī glide reflection is a mirror reflection followed by a translation parallel to the mirror. Every rotation has a rotocenter and an angle.Ī reflection fixes a mirror line in the plane and exchanges points from one side of the line with points on the other side of the mirror at the same distance from the mirror. Every translation has a direction and a distance.Ī rotation fixes one point (the rotocenter) and everything rotates by the same amount around that point. In a translation, everything is moved by the same amount and in the same direction. There are four types of rigid motions that we will consider: translation, rotation, reflection, and glide reflection. Any way of moving all the points in the plane such thatĪ) the relative distance between points stays the same andī) the relative position of the points stays the same.
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