The six symmetries of the equilateral triangle. FY FZ N R L FX name effect N N N R L FX FY FZ ( ) R R L N FY FZ FX R (XYZ) L (XZY) L L N R FZ FX FY FX (YZ) FX FX FZ FY N L R FY (XZ) FY FY FX FZ R N L FZ (XY) FZ FZ FY FX L R N

Cut off and cut out the small triangle

A B C A B C

D R R J R J J D D

M G G E G E E M M

B A A B C D C D Cut out just the small rectangle. Carefully mark the back. Find the four symmetries. Build the table. B A B D C A C D

B A A B C D C D Cut out just the small square. Carefully mark the back. Find the 8 symmetries Build the table. B D C A B A C D

A y D x B B B z z y D D B x x A D y z y C C x C C z A

y Sam x z z y Sol x x z y y x Will z Will Eva Sol Sol Sol Sam Sam Eva

pentominoes Build rectangles 512, 320,415, 610, www.johnrausch.com/PuzzlingWorld/chap02d.htm

Octahedron tabbed Cut out Lightly score lines Cut through dark slots Fold (big tabs inside) Octahedron tabbed

Fibonacci puzzle

Fibonacci puzzle 64 squares. Cut on dark lines. Rearrange to 5 13 = 65 squares! Where did the extra square come from?

A D B B B D D A D B C C C C A There are 12 symmetries Here are 3: ( ) (DCB)(A) (AC)(BD) Find them, find the rest, Build the table. Cut out and fold up the tetrahedron. Find all the ways to put it on the base. A D B B B D D A B D Imagine A on top C C C C A

D A C B

D A C B