Polyominoes (Pentominoes)

thingiverse

<P><B>Polyominoes</B>, also known as Pentominoes, date back to ancient times and gained popularity around 1907. They were first thoroughly discussed by Solomon W. Golomb, an American mathematician and electrical engineer, in 1953, and later featured in Arthur C. Clarke's science fiction novel <I>Imperial Earth</I> in 1974.</P> <P>The following are the 12 unique pieces that comprise all possible shapes made by combining FIVE squares into a single piece such that each square touches an adjacent square with the full length of a side. These 12 shapes are unique because they cannot be duplicated through any rotation or mirroring.</P> <P>As a mental exercise, try drawing them on graph paper before examining the shapes closely here. All 12 shapes are provided as individual .stl files plus a single file that 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 />\r\nIt fits all of the pieces in a neat 3 x 4 x 5 box, and how they fit is left for you to solve.</P> <B>PUZZLE</B><br /> <P>Each of the 12 pieces measures 5 cubes in size or a total of 60 cubes (5 x 12). They can 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.</P> <P><B>Printing Notes...</B><br />\r\nThese were originally designed using 10mm cubes 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. This allows for easy nesting. CAUTION... These parts will only print well if your X and Y axis values are well calibrated and equal.</P>