Hexdominoes: some surprising variations

The set
Matching patches
Polyhex patches
Symmetry patterns
Symmetries from Syracuse
More daisies and symmetries
Maximum groupings
Hard to categorize

 

The set

We knew Hexdominoes would be a winner, with hundreds of patterns, color themes, easy and difficult challenges. And now we keep discovering more and more beautiful designs of symmetry, color fields that spin before your eyes—the "playable art" aspect is transcendental.

These are the tiles that do all this and more — a hexagonal set of dominoes with every combination of 6 colors, plus one of each color as a single hex:

We show here a growing collection of results and solutions contributed by happy players. To our great delight, some are as young as 8 years old.


Matching patches

All same size and same shape color regions divide each color into two groups of 4 hexes. The first person ever to find such a solution was Emily Clark, on August 29, 2009, in Ye Olde Gamery at the Maryland Renaissance Festival in Crownsville, MD. Here is Emily with her history-making solution, "12 Eggs":

Soon other solvers got the idea and expanded the search to other patches of 4 hexes in size. See how neat and regular each packing looks.

 

 

 




Polyhex patches

Here each patch is different in size or shape and models polyhexes from 1 to 5 in area. Compare these to the pieces of the Hexnut Jr. set.

 




Symmetry patterns

Look carefully at each design to see how the colors have a rotational symmetry, or how some colors are opposite others.


At Hexdominoes' world premiere at the 2009 Maryland Renaissance Festival, Marty Roger was the very first solver to create a rotational design, and he's only 8 years old. Here he holds his amazing solution.



 


Nancy Koles visited Ye Olde Gamery at the Maryland Renaissance Festival on September 12, 2010, and created this amazing wheel of triangles:




Daniel Austin created this series of symmetry designs, each more elegant than the last, while working as a member of Ye Olde Gamery's crew during the 2009 and 2010 seasons. Thus he has many opportunities to surprise the rest of us with exquisite new designs. It's gratifying to see our products' full potential emerge in the hands of a skillful solver. Dan has also become adept at many of our strategy games and can teach them to visitors who are looking for competitive thrills.

 

 

 

Daniel's ever more sophisticated rotational symmetries and color groupings:

 

 




Symmetries from Syracuse

Two wonderful puzzle solvers Kate met at an art show in Syracuse, NY, have contributed their own elegant symmetries. Sue Edwards and Lisa Miller sent us these. Sue teaches violin and music theory to children and grownups; Lisa is a scientist and computer guru. Check out the subtle perfections of their Hexdominoes designs:

 

 

Sue keeps her Hexdominoes set around her music studio for her students to try out, too. Here's a great arrangement of lots of daisies by Joshua:




More daisies and symmetries

In this solution (left) by Kate, all 5 daisies have the same-color center, and lots of symmetry of the colors. At right, four colors are symmetrical and the last two, fully grouped, mirror each other.

 


Here's a round robin of 5 "pears" all pointing clockwise, with a rotation of colors in the same order at their centers, and the sixth color filling the gaps:


This solution has special properties: three colors are grouped in symmetrical shapes and occupy rotationally symmetrical places around the border. The other three colors are paired in all the different ways and make congruent and rotationally symmetrical patches.

Here's a pattern created by Meshele Merchant and solved by Kate, assisted by Steve Zeve. Three colors are grouped as rotationally symmetrical number 3's, and the remaining colors orbiting around them symmetrically:




Maximum groupings

These solutions by Kate came from a search for the extreme: grouping colors into their largest patches, and with symmetry. We start with six congruent groups of seven of each color, then move on to three colors fully grouped and the other three with 5, 6 or even 7 joined, leaving just a few loose hexes dancing symmetrically.

 

 

 

 

 

Can it get better than this? Well, yes, we can fully join 4 colors and pursue various symmetries, rotational and reflective, and congruent shapes. Here's a nice progression from three to four congruent groups, with interesting internal symmetries:

 

 

 

 

 

The search for maximum connectedness with total symmetry goes on.




Hard to categorize

More solutions by Kate pushing the limits. Left: Color pairs fold to form 6 triangles (outlined in white). Each triangle is composed of a different color trio. Only the pairs on the border are the actual color double tiles. Right: The maximum possible number of dominoes all facing the same direction: 22, with just four singles remaining. Below: Six horizontal stripes in rainbow order, bordered by all single colors with maximum symmetry.

 

 




Your turn

We'll continue to post new patterns with unusual characteristics here as they are discovered. And if you come up with any special solutions, please send them to us to include in this gallery. Digital images preferred, email to: Hexdominoes Gallery. Drawings on paper, snailmail to: Kadon Enterprises, Inc., 1227 Lorene Dr., Suite 16, Pasadena, MD 21122.


www.hexdominoes.com

Hexdominoes have proven themselves so amazing, so rich in design possibilities, that we've given them their own domain name and webpage. We're planning to expand it with new challenges and features. To begin with, both rule books and 19 actual-size grids are contained on this dedicated Hexdominoes site. One of the books even includes games for 2 to 5 players. Check back occasionally for future developments.

To order Hexdominoes, please visit any of the showrooms linked below.



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