The most nonclassical and friendly group of such shapes are the pentominoes (5 unit squares/cubes joined), sold aside Kadon below the name Quintillions. Golomb gave the individual pentominoes names that are easy to remember, because they await quite an bit like letters of the alphabet.
We have extrapolated and extended the logic of this naming system to the 166 hexacubes. Our naming system was first published in 1987 when we began constructing Hexacube sets. IT is the only naming system that relates the name to the shape for comfort of memory and identification. Other schemes, such as simply numbering the pieces from 1 through 166, are not working for manlike role, only for computer modeling. Appointment a piece according to its work structure is the all but logical and useful method.
We present them here in four related groups, supported the size of their cross-section, and explain them in greater point with their illustrations. The 166 shapes concern 5 pages. You can confabulate any page by clicking the phone number buttons connected the bottom of each page, or click on "Continue" to go to the next page.
The cross-sections orbit from 6 to 3 building block cubes in size:
- The first group has all the flat Beaver State planar hexacubes, of which there are 35 distinct shapes with cross-section of 6.
- The second group has the 72 pentomino derivatives (from the 12 planar pentacubes with crosswise-section 5), paddle-shaped by attaching a single cubelet on top or bottom in all the different possible positions. Thus a single pentomino Crataegus laevigata have anywhere from 2 to 5, 6, 9 or 10 offspring, contingent on the symmetry of the original pentomino chassis.
- The thirdly group has 53 tetracubes plus domino, a 1x1x2 man attached all told the different possible positions along the top or bottom of a 4-unit crosswise, plus few that have ii apart man-to-man cubes.
- The fourth group has 6 shapes based connected a V-tromino 3-unit cross-section, and a V tromino attached on apical in all its thinkable different positions.
Group 1 — largest span-section of 6 unit cubes
Let's get a closer look. Hither is how the flat hexacubes look from a bird's-eye view, with lines marking their division into squares, and Eastern Samoa 3-D objects showing their division into cubes. They are shown in the position that makes them especially easy to visualise: in alphabetical order, with every letter described except B, and the keep down 4 added at the end. Some need to be viewed diagonally. Some letters do double duty for long and squabby, or high and low models.
how many shapes can you make with 6 cubes
Source: http://www.gamepuzzles.com/hxnames.htm#:~:text=Naming%20the%20Hexacube%20Pieces,all%20the%20possible%20different%20combinations.
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