HyperCard & Tessellations with Glide Reflections

Suzanne Alejandre

HyperCard Tips || HyperCard & Tessellations || Tessellations with Rotations || Where's the Math?

It is possible to use HyperCard to create tessellations from figures generated by reflections and translations [which would be a glide reflection], and then translate them.

Although I use HyperCard I believe it would be possible to adapt this procedure to any application that has paint tools.

Step One

Using the polygon tool, select the triangle. Draw a triangle. If the shift key is held down as the triangle is drawn, it will help control the drawing.

Step Two

Using the lasso, start at the top corner of the triangle, wiggle around as you are going down, and exit the lower, left-hand corner of the triangle. A section of the triangle will be selected.

Step Three

With the section selected (and blinking), go to "paint" in the menu and select,"flip vertical". The section will be reflected.

Step Four

Using the lasso and holding the "shift" key, slide the section to the right.
[This is a translation.]

Step Five

Use the pencil or paint brush (with the white pattern selected) to decorate the figure. Do not add anything to the outer edges of the silhouette.

Step Six

Use the lasso and position the figure up higher on the card. Hold option and slide the copied figure to the side. In HyperCard this is a faster method to copy/paste if work is being done on only one card.

Step Seven

Using the lasso, hold "option" down and "copy" by sliding one darker figure to the side. Lasso the lighter figure, hold "option" down, slide a light figure off, and fit it into position up against the dark figure.

When you have one row of white figures and another row of black figures, select the dark figures, go to "option," and "flip vertical." Fit the black row of figures into the white row of figures. Continue this procedure until you have created a tessellation. Hint: If they do not fit perfectly, review Steps 1 - 8 and try again.