making pentagonal tiles

STEP 1

In a unit square, choose a point (F) and reflect [icon]/images/ggb/toolbar/mode_mirroratpoint.png[/icon] it in the centre of the square. Join these two points to the vertices to make 5 segments. This will be a basic unit for rotating about a vertex of the square. The 5 segments [color=#0000ff](a to e)[/color] can be grouped as a list, which can be transformed as a single object. [br][br]Drag point F to change the segments.

figure 1 (5 segments)

STEP 2

To group the 5 segments (a to e) as a list and call it 'cell1', input:[br][color=#ff0000]cell1={a,b,c,d,e}[/color][br][br]Now, we can rotate cell1 about, say, point A, by 90[math]\deg[/math], input:[br][color=#ff0000]cell2=rotate[cell1, [math]90\deg[/math], A][/color][br][br]The two lists (cell1 and cell2) can be further combined as a new list, and we call it 'tile':[br][color=#ff0000]tile={cell1, cell2}[/color][br][br]Note that tile is not shown in the graphic view.

figure 2 (group the segments)

STEP 3

Translate the 'tile' by the vectors[icon]/images/ggb/toolbar/mode_vector.png[/icon] AC (u) and DB (v). We can use the sequence command to repeat a translation.[br][color=#ff0000]sequence[translate[tile, n*u], n, -3, 3][/color][br][br]This sequence of translation generates a new list ([color=#ff00ff]list1[/color]), which can then be translated in another direction v.[br]For example, you can input "[color=red]translate[list1, 2v][/color]" to make a new list by translating [color=#ff00ff]list1[/color] with the vector 2v.[br][br]Drag point F to change the tiling.

figure 3 (translate the tile)

STEP 3 (alternative)

The translation in two directions can be combined into a single input:[br][color=#ff0000]sequence[sequence[translate[tile, n*u+m*v], n, -3, 3], m, -3, 3][/color][br][br]Drag point F to change the tiling.