November 1, 2023

As soon as the process of producing 21st Century Pattern Blocks had begun, I thought of Hana Murray. I’d been enjoying her pattern block masterpieces for some time, and I couldn’t wait to see what she might do with this collection of new shapes. I shipped her four sets.

She produced a deluge of artistic and mathematical inspiration. The images she shared became one of the brightest spots on my social media feed, and something I always looked forward to seeing. Her creations are stunning, visually and mathematically.

Below, Hana shares reflections on her process and discoveries from playing with 21st Century Pattern Blocks. I hope you enjoy reading it as much as I did!

-Dan

PS If you’d like your own set of 21st Century Pattern Blocks, you can get them on Amazon and learn more about them on our website here. We also have bulk educational discounts; write us at orders@mathforlove.com to learn more.

by Hana Murray

“Just make a mark and see where it takes you.” — The Dot by Peter H. Reynolds

The beauty of the 21st Century Pattern Blocks are in their inherent invitation to play. When I first opened the pattern blocks boxes I was immediately lured in by the colorful assortment of blocks. I couldn’t help but reach out for the eye-catching blocks and begin arranging them into intricate patterns. My first designs with the 21st Century Pattern Blocks emerged from this joyful play. The more I created, the more unexpected discoveries I made. I began noticing various composite shapes that emerged and repeated in my pattern block play. This is how I first noticed the irregular heptagon!

The idea to explore heptagons came from the design above that I initially posted on Twitter on April 2, 2023. It is a radial design that is centered around a hexagon made of six kites, using four types of blocks (kites, darts, rhombuses, and concave hexagons). If you look closely, you can spot the six irregular heptagons in the largest design. Little did I know that this exploration would keep me busy for almost two months!

Once I noticed the heptagon shape, I wondered what other block combinations I could make. I was delighted to see that there were indeed many possibilities.  The above image shows some of the first irregular heptagons that I made.

I loved the one-line symmetry of this heptagon and I thought it would be a suitable shape for tiling. I recreated the shape online, so I could manipulate it easily and noticed a way to tessellate it around the middle hexagon with rhombuses to fill the gaps.

The image above is the first design that I created with the heptagons. I loved the way the three heptagons came together to create a beautiful star. The outline below shows the structure I used to make these designs, showing the first layer of heptagons pointing away from the center.

I was pleased with the outcomes of the designs. The images below show some of the designs with this structure.

I continued playing with the heptagons and kept noticing and wondering. I wondered whether there may be a way to tile the heptagons differently. Indeed there was! I came across another way to tile the heptagons around the center hexagon. This time the first layer of heptagons points towards the center, instead of away.  This design uses darts and rhombuses to fill in the gaps.

Once I came across the two ways of tiling the heptagons, I decided to build the two designs and display them side by side to note how the designs changed, looking for similarities and differences.

I could have stopped after finding the two different ways of tiling these heptagons. But I didn’t. I changed the heptagon tiling structure once more. Instead of having the first layer of heptagons pointing towards the center or away from the center, I arranged them to point slightly to the side. The designs use darts to fill in the gaps.

Below is a complete set of the three variations. This may be my favorite set of designs that uses only two types of pattern blocks (darts and rhombuses). I love how using the same heptagon composition changes the design when tiled differently.

As I continued my explorations with the heptagons, more questions arose. What would the design look like if I used different heptagon block compositions in one design?

What would happen if I reflected the heptagons in one design?

Start with play, notice, wonder and see where it takes you.  Only your imagination is the limit to what you can create!

#### Notes

1. 21st Century Pattern Blocks were created by Christopher Danielson, and produced by us at Math for Love. You can learn more about them at mathforlove.com/games/century.
2. If you would like to see more of Hana’s (@MurrayH83) pattern block designs,  you can view her work on X (Twitter) here.

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