New pentagon in town!

Unsurprisingly, several people reached out to me to say HEY NEW PENTAGON AMY, DID YOU SEE? I love you. You know me well. 

There are two kinds of people fascinated with the idea of finding shapes that can fill a two-dimensional plane: geometry professors, and quilters. What's weird, and sad, is that they aren't really talking to each other. I've corresponded with a few of them, and as far as I can tell, there are quite a few mathematicians who are working on these problems, but the number of quilters playing with the end results likely can be numbered on my fingers and toes.

This is sad -- and fixable.

So what came out this week? It's a newly-found irregular pentagon with very specific angles (60°, 135°, 105°, 90°, 150°) that can tile the plane with no gaps. This pentagon, published by Casey Mann, Jennifer McLoud and David Von Derau, marks the 15th tilable pentagon found, and the first one found since 1985:

An image of the new tiling published by Casey Mann, Jennifer McLoud and David Von Derau in August 2015. The angles are 60°, 135°, 105°, 90°, 150°. Screenshot made from the tiling app made available by Jaap Scherphuis at www.jaapsch.net/tilings/ Details available at www.theguardian.com/science/alexs-adventures-in-numberlan...Pentagon #15, zoomed in
 by domesticat.

An image of the new tiling published by Casey Mann, Jennifer McLoud and David Von Derau in August 2015. The angles are 60°, 135°, 105°, 90°, 150°. Screenshot made from the tiling app made available by Jaap Scherphuis at www.jaapsch.net/tilings/ Details available at www.theguardian.com/science/alexs-adventures-in-numberlan...Pentagon #15, zoomed out
 by domesticat.

I don't have a way of rendering the tiling in a vector format, to get the perfect shape. However, I worked backward using the .png image that Jaap Scherphuis' Java applet created, plus the published information about the angles. I've got a shape that's likely very close. It's likely close enough for quilting; if you're curious to try it, let me know and I can try turning it into something that's printable. (I'm reachable at amy@ [this site], and let me know what size paper. If I can make it into a usable PDF file, I'll share it with you. I'll update the post if I do.)

This tiling is best suited for English paper piecing. Explaining how to do it is far past the scope of what I want to write on a perfectly good Saturday afternoon, but suffice it to say, it works very well for shapes that are irregular and don't join up into long seams. EPP makes it easy to preserve the angles of these pieces and get the accuracy you want when showing off a project like this.

If the idea of doing something odd and pentagonal has your interest, though, let me take a moment to recommend a different tiling that is more widely available. There's a book I wrote about a few years ago (2011: "Save me, interlibrary loan!") that's worth quoting here. It is only available in German, but the grids at the back of the book need no translation.

It translates to 'Liesel's Pentagons: Inspiration and Instructions for pentagon projects.' Pentagons just don't show up much in quilting because -- as any geometry enthusiast will tell you -- they just don't appear often in repeating patterns. ISBN: 9783000189036. I checked WorldCat, and not a single library in the United States has this book available for loan. Of course, it IS in German. I was so intrigued with the photos that I decided to order the book, sight unseen.Front cover: 'Liesels Fünfecke'
 by domesticat.

It translates to 'Liesel's Pentagons: Inspiration and Instructions for pentagon projects.' Pentagons just don't show up much in quilting because -- as any geometry enthusiast will tell you -- they just don't appear often in repeating patterns. ISBN: 9783000189036. In German: Handnäherinnen öffnet die grandiose Musterfülle von Liesels Fünfecken eine regelrechte Schatzkiste. In diesem reichhaltigen Buch finden Sie über 50 Projekte, von Quilts über Kleinigkeiten bis zu Wandbildern. Es gibe ausführliche Hinweise zum Nacharbeiten, viele Variationsvorschläge, sowie Inspiration und Ermutigung für eigene Entwürfe. Liesels Fünfecke sind unregelmäßige Fünfecke, die zue ebenen Fläche zusammengefügt werden können. * * * Die Musterungen sind eingeteilt in die drei Abschnitte reine Fünfeckfläche, Kombinationen mit Rauten und ringförmige Anordnungen. Nach dem großen Erfold von Liesels Sechsecken-Technik ist dies das zweite Buch der Autorinnen Hilde Klatt und Liesel Niesner. Inspiration & Anleitung Der Schwerpunkt dieses Bandes liegt auf den Mustermöglichkeiten, die die mosaikartigen, über Papierschablone genähten Patchworkflächen bieten. Liesels Fünfecke gehören - wie Sechsecken - zu den Musterungen, die man vorzüglich von Hand nähen kann. Eine Anleitung für die Technik ist Bestandteil dieses Buches, das sowohl sehr gut für Anfänger geeignet ist als auch Fortgeschrittenen eine dauerhafte Fundgrube bieten wird. The gist, in English: A veritable treasure chest of patterns with Liesel's pentagons. Includes more than 50 projects ranging from quilts to wall hangings to small items. It gives detailed instructions for rework, variations, as well as inspiration and encouragement for your own designs. Liesel's pentagons are irregular pentagons, but they sew together flat. * * * * The patterns are divided into three sections: just pentagons, pentagons and diamonds, and circular arrangements. This book is the second for authors Hilde Klatt and Liesel Niesner, following their great book on hexagon techniques. This book focuses on the possibilities of mosaic-like patchwork sewn using English paper piecing. Liesel's pentagons can be hand-sewn just like hexagons. Well-suited for beginners and advanced quilters.Back cover: 'Liesels Fünfecke'
 by domesticat.

Title: Liesels Fünfecke, by Liesel Niesner and Hilde Klatt
ISBN: 978-3000189036
Format: Paperback
Published: 2006
(buy it at Amazon)

I haven't gone trawling in a few years to see if many people have made quilts from this book. When I last looked in 2011, I couldn't find any libraries in the US who had this book available for interlibrary loan, but that may have changed since then. 

I've done a scrap / sampler quilt using these pentagons, which -- since I worked on it partially in Washington DC -- I had to name "Pentagon Papers" --

Somehow, I don't know how, but I deleted the only finished photo I had of my quilt, Pentagon Papers. Took a few months to arrange getting my hands on it, but I finally got it re-photographed.Pentagon Papers, re-photographed
 by domesticat.

and because I'm a Giant Nerd, the backing is from a Doctor Who duvet cover I disassembled:

Jacob is a huge fan of Doctor Who. For the back, it seemed a shame not to use part of the Doctor Who duvet cover I'd ordered from the UK. It meant both sides were interesting, which I like.Pentagon Papers: the back
 by domesticat.

Here's hoping I can help encourage a few quilters to help move English paper piecing past hexagons.

all tags: 
quilting
tilings
pentagons

Comments

On , Amy said...

Love this. I'm always looking at different shapes for epp

On , domesticat said...

Your best bet is to skip the quilting books and go to the geometry / tiling books instead. They also try to sell you less crap.