Polyominoes (Pentominoes)

thingiverse

<P><B>Polyominoes</B> (aka Pentominoes) date to antiquity and became popular circa 1907. They were first seriously discussed by Solomon W. Golomb. an American Mathematician and Electrical Engineer in 1953 and were later featured by Arthur C. Clarke in a Science Fiction novel, <I>Imperial Earth</I>, in 1974.</P> <P>Herewith are presented the 12 unique pieces which comprise ALL of the possible shapes made by combining FIVE squares into a single piece such that each square contacts an adjacent square with the full length of a side. These 12 shapes are unique in that they are not duplicated by any rotation or mirroring.</P> <P>As a mental exercise, you might try drawing them on graph paper before you examine the shapes too closely here. All 12 shapes are given as individual .stl files plus a single file which can print all of them at once, if you're confident in your printer. </P> <P>You will also find the Box here... https://www.thingiverse.com/make:460310<br /> It fits all of the pieces in a neat 3 x 4 x 5 box. How they fit is left for you to solve.</P> <B>PUZZLE</B><br /> <P>Each of the 12 pieces is 5 cubes in size or a total of 60 cubes (5 x 12). They may be arranged in perfect rectangles of 6 x 10, 5 x 12, 4 x 15, and 3 x 20. There are over 900,000 possible solutions in total but only TWO for the 3 x 20 rectangular shape. Have fun!</P> <P><B>Printing Notes...</B><br /> These were originally designed using 10mm cubes but in order to allow for interlocking and nesting, they were reduced to 9.75mm cubes and longer pieces at 19.5, 29.5 and 39.5mm lengths using a few 10mm recesses. All of this allows for easy nesting. <br /> CAUTION... These parts will only print well if your X and Y axis values are well calibrated and equal.</P>