Cubes and Things: Color and Construct your own geometric shapes!

Net Book Essentials:

The different patterns on each page of Cubes and Things welcome you into the wonderful world of a coloring book, but the good times get even better as you assemble your own geometric shapes! You will be fascinated watching the 2D design fold into a 3D form, and surprised at how easy they are to make.

For years I've been addicted to making these many faceted geometrical forms called polyhedra. And now I have a way to share this delightful creative experience though my new collection of nets. The term 'nets' refers to the different 2D plans, groups of connected polygons (triangles, squares, pentagons, etc), which fold up to become snazzy 3D shapes.

To construct your own polyhedron from a net: cut along the outer edges (keeping it all in one piece), then fold it along the inner edges, and tape it together. Once your form is completed, the next level of enjoyment begins as you contemplate the intriguing symmetries that the pattern creates around the form.

Symmetries in Pattern and Form:

In the center of the five images below is a diagram of an octahedron, which is made up of eight equilateral triangles. The other four pictures are of an octahedron with a pattern from Cubes and Things - Platonics Plus - Net Book #1. Each triangle has the same simple design, but as you rotate it you can see how it changes from different view points. The two pictures on the left show a four-fold symmetry and the two on the right are of a two-fold symmetry. Although I always support whimsical aesthetic additions, coloring these shapes is not only decorative. It emphasizes the different aspects of a shape and its pattern. Does seeing the same view with and without color, give you ideas of how you might color it differently? 

You can find plain nets to download for free from a number of different places. Here are links to three good sites:

http://www.mathsisfun.com/geometry/model-construction-tips.html

http://mathgeekmama.com/3-d-shapes-worksheets-free-printables/

http://www.senteacher.org/worksheet/12/NetsPolyhedra.html

Aesthetics Add Meaning: 

Most nets only give you the plain shape with low resolution lines. Putting my artistic skills to good use, I've developed nets that make every polyhedron into a special work of art. There is a thin grey line around all the polygon faces that acts as a spacer and a fold line. It accents each polygon face, making sure that every triangle or square is framed nicely to show it off. (Though I sometimes when coloring the net, I darken that grey line to emphasize the edges of the form, as I did with the octahedra above.)

The result is a cool sculpture that looks great wherever you place it around your home, which also teaches you about the shape's geometry. The fun and easily accessible parts of mathematics come from observations into the nature and qualities of an object. There is no need to find time to study, when you learn something of the 2D pattern and 3D form while you were coloring and constructing it —and then even more from looking at or playing with the completed shape!

Physical Details:

The net books are pads of paper glued along the top side for easy removal of whichever shape you want to make next. They are printed on a recycled card stock that feels nice in your hand and has a good flexibility for when you are building the shape, yet the finished form has the right rigidity to show off its fabulous geometry. The eco-friendly company who did the printing is called Greenerprinter. Here is a link to their website:

http://www.greenerprinter.com/grp/

I tried to make every page look lovely to entice you to start working on it. If all you do is color the page, it will still be neat to look at, but the real magic happens when you transform the 2D net into a 3D form. The next images are examples from Cubes and Things - Platonic & Archimedean - Net Book #2:

Net Books #1 & #2:

When I was first sharing my nets, I noticed two main preferences: either people wanted to make a simple shape that didn't take too much time or they asked for the most challenging one I had. In response to this, I compiled two different collections of nets:

Platonics Plus - Net Book #1 has 28 shapes on 19 pages. There are 10 different kinds of polyhedra.  Some are smaller with several nets on 1 page, others fill a page, and a few cover 2 pages.

Platonic & Archimedean - Net Book #2 has 32 shapes on 36 pages. It has the 10 polyhedra that are in Net Book #1, plus 8 more shapes. This net book has twice the pages because the additional shapes are bigger and more complicated.

For those who want to make as many shapes as they can and are thinking of getting both net books, all the polyhedra/pattern combinations in the two net books are unique. Though there are no duplications of a certain pattern on that same polyhedron, some tile designs are seen on several forms. As in the examples above, I was so entranced at how one pattern changed depending on the number of faces meeting at the vertex (mathematicians prefer that term for the corner) of a polyhedron.

The first 6 pages of both books have information about the net books, polyhedra, construction advice, a list of shapes, and a color chart so you can compare the polyhedra in that net book. The color chart of forms in each net book and the list of shapes can be seen in the Cubes and Things store:

http://polyhedra.stacyspeyer.net/to-buy-books

To see charts of the Platonic and Archimedean solids from my book Polyhedra: Eye Candy to Feed the Mind, follow this link:

http://polyhedra.stacyspeyer.net/polyhedra-charts/

For more information about the Platonic and Archimedean Solids follow these links:

https://en.wikipedia.org/wiki/Platonic_solid

https://en.wikipedia.org/wiki/Archimedean_solid

That Tricky Last Piece:

Anyone who has tried to make a polyhedron will know how hard it can be to nicely join up that tricky last piece. An easy solution came to me from my textile background. Most people who work with fabric have a variety of pins around. I found the perfect pin that could help me attach that last piece. Below are the shaded drawings and directions from the net books on how to use the pin:

NetBook-LastPieceOctaC.jpg

▪If possible, leave the last piece only connected on one side (m). Put tape on all its remaining sides (with tape on the outside (n) or on the inside (o)). After you carefully press the piece into place, you can no longer apply pressure from the inside. This is when you use the attached pin. Poke it through the vertex and under the edge you are taping (p). Now you can secure the last pieces of tape by pressing your finger down on the outside and, (with the pin) up from the inside.

To start things off right, the first 200 net books will come with an attached pin!  

Polyhedra Parties:

Now that the work of completing the net books is done, I want to share this special experience with as many people as I can. Joining in with those looking for new ways to inspire a joy for learning in STEM & STEAM programs, I want to work with schools, summer camps, and after school programs to have Polyhedra Parties!

Polyhedra Parties are the perfect blend of focused play that gently moves towards learning math. The beauty of the shapes can make someone curious to learn a little bit about their geometry. This leads to the kind of thinking involved in understanding how to categorize these different shapes, which can open the door to the enquiring mind that is hungry to learn more. Also, the concepts of symmetry observable in polyhedra are a part of very high level and fascinating mathematical subjects.

If you know of a group in need of a Polyhedra Party (for kids or adults, academically focused or not) and who would like me to lead their event, send me an e-mail at cubesandthings@gmail.com. I can come well supplied with a stack of nets, markers, crayons, scissors, and tape, as well as examples of my art which led to my passion for polyhedra. My years of experience teaching art and my enthusiasm for polyhedra make it an excellent experience. Polyhedra Parties are so much fun!

Thank you for reading this and please let me know what you think of it!

Stacy

 

Why I like Polyhedra - Part 1 - Weaving & Numbers


Flame    5.5 x 11 feet, dyed & woven sewing thread 

Flame   5.5 x 11 feet, dyed & woven sewing thread 

Recently, one of my weaving students asked me why I liked polyhedra.  An original goal of my book, Polyhedra: Eye Candy to Feed the Mind, is to answer that question for my friends.  But she got me thinking and writing.  Here is the short synopsis: 

  1. Polyhedra are super cool objects to make & study. - See Polyhedra book to get hooked!
  2. A confession: my woven pieces were 30 foot algebra problems. - See below.
  3. I like beauty in art & equations. - See in next post.

Weaving & Numbers

Weaving transported me to a delightful place in a way nothing ever had in my life.  I like all the different steps of weaving: planning out the project (more about this below), warping (measuring out the lengths of vertical threads), marking & dyeing my yarn (washing out isn't fun, but seeing the excess dye swirling around the sink is beautiful), I even enjoy threading the reed & heddles (setting the order & structure for the fabric), winding on (feeling & watching all the vibrant threads pass through my fingers), and, when I finally get to weave the weft threads in, watching the fabric grow is fantastic!

This complicated process engaged me technically in so many fun ways, but the planning was where I really indulged my love of numbers.  A big piece, called Cycle, is 30 feet tall, 15 feet wide, with 4,500 threads, woven with double weave on an 8 foot wide loom, and hung in an open arc with an 8 foot diameter.  How many cones of cotton sewing thread are needed if I set it at 30 epi (ends per inch) and use the thread that comes on 6,000 yard cones or the softer thread at 28 epi from 12,000 yard cones or a blend of the two?  (To see Cycle and other woven pieces go to my weaving website and click on catalog.)

Working out such math problems for art projects was a secret world of math that I couldn't share, even with my weaver friends.  Most people weren't thinking about making projects in this way, but I spent many happy weeks working out all the details.  The work existed both as a fun mathematical problem to solve and requiring artistic imagination to envision a huge installation of glowing colours that had a bold strength and a quiet delicacy.

My pleasure in playing with numbers and in reading layman's science books led to me to re-take College Algebra, 5 years after getting my MFA.  I enjoyed studying math, but it all didn't come easy to me.  Though I had to work at it, I was used to hard work from my weaving projects.  I went on to take Trigonometry, Pre-Calculus, and Calculus.  -You know you can't leave an artist alone in a room with math for long before they start making geometric forms.

The planning involved in working out geometric shapes fit right into my artistic process, but the creation of these forms was so fast & simple compared to my woven pieces.  Every night a new funny little geometric shape was added to the round table in the living room.  Their ever growing numbers were reminiscent of the Star Trek episode Trouble with Tribbles.  Though most forms were spherical, each one had its own structural story that fascinated me.  I had so much math to learn!

Always searching for related topics, I studied whatever I could understand enough to read.  George Hart's extensive website http://www.georgehart.com is where I really started to learn about this subject and Wikipedia taught me a bunch, too.  I became a regular at the UC Berkeley Math Library; gleaning as much information as I could!  The study of a simple 3D shape, like a polyhedron, is a tiny introductory part of higher math concepts that most math writers assume you can work out on your own.  Some books I keep going back to: slowly learning enough to read deeper into the book, while with others I couldn't get past the introduction.  

I've been in a self-directed math class with no teacher and no real point, save curiosity.  There was something so captivating about these abstract concepts.  Books that would put many people to sleep were keeping me up at night because I just had to try to learn this next idea!  So many new theories danced around my head in delightful way, similar to the early rough images of an art project.  Studying math took the place of planning weavings.


While you take time to digest that last bit, look below at a photograph my Dad took of my early woven reed experiments.  If you want to see more, go to http://www.stacyspeyer.net , click on tangents and then geometric forms.

In the next post, I'll see if I can explain how the math world's love of beauty matches my own creative inspiration.

Be well,

Stacy

Eleven Woven Reed Spheres   sizes vary from diameters of 1.5 to 10 inches

Eleven Woven Reed Spheres  sizes vary from diameters of 1.5 to 10 inches

Polyhedra Kickstarter - First Try


In March of 2015, I tried running a Kickstarter campaign in the hopes of raising funds for the offset printing of my first book.  (See more about the book on its own page in this website).  Although I did not reach my financial goal, so many other goals were reached that -for me personally- it was a great success!  Below are a few of the positive outcomes: 

  • The book is finished!  After about 4 years of researching, writing, and making diagrams, I got through the home stretch of the last 200 hours of re-doing the layout and editing.  I am still so happy to have the first copy in my hands!
  • As one of the rewards, I designed a collection of nets (the 2D patterns of polygons, which fold up into polyhedra) with patterns that reveal different symmetries of the shapes (see below).  I'm developing these 'net books' into something I can sell.  This has given me a bunch of ideas for other products.  -For an artist who often spent a year or more on one project, the idea of making small items that many people can enjoy is a shocking new head space to be in!
  • Inviting others to use my net designs turned into an experience I can share as a 'Polyhedra Party,' filmed in the Kickstarter video.  For years I've been wanting to find a way to bring my playful version of math into the lives of children & adults.  Along with my book, I can use the art of making to invite people to discover how fun math can be! 
  • I joined on-line communities where I connected with special friends and found places filled with cool information.  I am so excited to continue traveling in this virtual world and to see where these connections can lead!

I feel so changed by this whole experience, but it is just a beginning.  I want to give the Kickstarter a try again in a year, when I've had more time to promote the book, find more people & places interested in it, make deeper connections, and look into grants for partial funding of the project, too. 

Thank you for reading my very first blog post and please let me know if you have any suggestions.

Cheers,

Stacy