This week’s post is special for a few reasons, the most important one being: there may not be another until sometime in the spring!  My wife and I depart next week for a two-month trip.  Originally, I had planned to write a number of posts in advance so that there could still be regular material appearing on the site during my absence. Unfortunately the preparation for this trip FAR exceeded my expectations and I simply ran out of time!

Ways To Stay Involved

However, fear not, for I shall not leave you empty-handed!  Here are five different ways you can stay involved with Geometric Arts during and after this little hiatus:

1. Subscribe to the post feed, either through your RSS Reader or by getting email updates.  This way you will know immediately when the posts resume, and who knows, if I find the time, the means, and have something interesting to write about, I just may squeeze out a post or two during my trip!
2. Subscribe to the newsletter on the newsletter page (or at the right).  This bimonthly email includes extra material not found on the site, and although it, too, will be on hold while I’m away, you will get the first one upon my return – another way to know Geometric Arts is back in action.
3. Read 2011 posts in more depth. In 2011 I wrote 25 posts totaling almost 19,000 words – so now would be a great time to go back and catch up on any you may have missed or not had the time to read in full. See the full list here.
4. Suggest future post topics.  I’m always looking for new ideas, so if there’s something you think would be cool for me to write about, use the contact form to let me know. It would be sweet to come back from my trip with a basket full of new ideas!
5. Enjoy the links below.  As a way to substitute for the lack of posts in coming weeks, I’m sharing below a number of links that should give you plenty of material to tickly your geometric fancy throughout the inwter months.

As always, thanks for reading, and I’ll see you in late March!

Phil

Winter Links (As Promised)

• Hoberman.com – Web site of Chuck Hoberman’s company – the guy that invented those expandable sphere toys you’ve surely seen!
• Worldofescher.com – a fun place to shop for all things with Escher prints on them
• Mathematica Graphics Gallery – images created using the Mathematics software package – a fest for the eyes!
• George W. Hart’s “Pavilion of Polyhedrality” – a launching spot with dozens of other links – hours of entertainment!
• Wolfram MathWorld – Geometry – in case you want to explore some fundamental geometric concepts
• The Geometry Junkyard – a quirky but LARGE collection of links to all sorts of cool geometry stuff
• Spidrons – hard to explain, beautiful to look at.  Just Click.
• Pattern in Islamic Art – a large repository of Islamic patterns and photos

Holiday Star - copyright Phil Webster 2011

Pretty, don’t you think?  So, where did it come from?  Why don’t you study it for a moment before reading on.  See what you you can notice about it. For example:

• What different kinds of shapes can you see?
• Do they have anything in common?
• Is there any symmetry going on? Any asymmetry?

Inspiration Number One – The Starbucks Pattern

So, as my wife, brother, and sister-in-law will attest, around Thanksgiving time I became rather obsessed with a pattern that Starbucks is using pervasively in its holiday advertising. Now would be the time to go re-read the post title, groan a little, and then resume reading.

I mentioned this pattern in my last newsletter, but didn’t say much about it. That’s about to change. First of all, here is the pattern, which I copied off of a tumbler I purchased:

Starbucks pattern (dotted lines show repeat)

As the dotted lines show, the pattern does repeat, although with a long enough cycle that it’s not immediately obvious. For those who are interested, every other place I’ve checked (mugs, displays, even my Starbucks gold card!) the pattern is the same.

Deconstructing the Pattern – The Pieces

So, the first and most obvious interesting thing about the pattern is the pieces. It doesn’t take long to realize that they are all combinations of the sub-pieces you get if you take a pentagon and draw a five-sided star (pentagram) within it. My next step was to figure out how many different such pieces there are (remember, I said I was obsessed!). Here is my summary of every piece I could find, not counting reflections and rotations of the same piece:

Summary of possible pieces from subdivided pentagon

It’s worth noting that there are a couple of “filler pieces” in the pattern that are not from this set, though they’re closely related.  Can you find them??

Deconstructing the Pattern – The Grid

So, knowing that (most) of the pieces fit inside pentagons, it seemed a natural next step to lay out the underlying pentagons to see if any pattern emerged:

Starbucks pattern with underlying pentagons (blue for upright, purple for inverted)

Lo and behold, when you remove the pattern itself, suddenly more underlying order is revelaed than is immediately apparent:

Grid of pentagons underneath the Starbucks pattern

Inspiration Number Two – My College Doodle

So, having set that all aside a few weeks ago, the other day an old college friend reminded me of an elaborate doodle I had once created during a mind-numbing lecture we were in.

The Doodle

I haven’t found the original doodle but remembered it well enough to recreate it quickly:

My college doodle - "Pentagon Rosette" copyright 1986 Phil Webster

OK, I’m sure you see where I’m headed with this now…

The Star Variation

Knowing I wanted to create something holiday related, I first modified my original doodle into a star shape, and added the shading I used for the Starbucks grid, in order to create my foundation:

Pentagon grid for my Holiday Star

Putting It All Together

From here, it was just a matter of laying in some of the possible tiles onto the grid, while trying to maintain a nice sense of overall balance, make sure the gaps between tiles were nice shapes, and make the outside border conform to something nice. The result is my Holiday Star for 2011, shown at the top of the post.

How It “Bucks the Trend”

While it’s true that I titled the post mostly just to make the horrible pun, it is also true that my star “bucks the trend” set by the Starbucks pattern in a few ways. Namely:

• I used a few tiles from the pentagon-pentagram set that Starbucks did not. Can you find them?
• My pattern has rotational symmetry, while theirs has translational (“glide”) symmetry
• Due to the nature of my grid, I used a different “filler piece” (piece not derived from the pentagon-pentagram system) than they did. Again., can you spot it?

Special Thanks

That’s about it, except that I would be remiss without offering some special thanks to:

• My wife Jen, brother Brian, and sister-in-law Katy for putting up with my ranting about “this awesome pattern… look, it repeats!… check out the grid!…”
• My buddy Barak for reminding my of that college doodle
• The staff of my local Starbucks (where I sat to write this post), not only for their awesome friendly service, but for letting my take some of their holiday-patterned display pieces now that they’re done with them!

(For a detailed explanation of the rating system, see the end of the review.)

Review

Introduction

Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology (Wooden Books) may possibly be the most efficient little book I’ve ever purchased.  By this I mean that the amount of information, illustration, and insight packed into its 416 6″x7″ pages is mind blowing. Another in the series of Wooden Books (I previously reviewed Platonic and Archimedean Solids, another in this series), it is, in fact, an artful compilation of six (!) of their other books, each of which sell for a similar price. So, in a way, it’s like hitting a six-for-the-price-of-one sale!

About the Title

Quad-what?!  I’m sure most of you are wondering, as I did, what the word “quadrivium” means. The term arises from ancient Greece, and refers to four (“quad-“) areas of studies related to Number. The foreword of the book explains this better than I can:

The Quadrivium arises out of the most revered of all subjects available to the human mind – Number. The first of these disciplines we call Arithmetic, the second is Geometry or the order of space as Number in Space, the third is Harmony which for Plato meant Number in Time, and the fourth is Astronomy, or Number in Space and Time.

This is a fascinating way of conceiving of these areas of study. What this book does is to assemble six other Wooden Books that together cover these four areas in great detail (geometry and music are each covered in two books, hence six books instead of four!).

Walkthrough

There is so much information in this book that a complete walkthrough would take many, many paragraphs.  Instead, let me walk you through it by listing the six “sub-books” and a little description of what each one covers.

[NOTE: All images below are courtesy of and © Wooden Books.]

Book I: Sacred Number (Miranda Lundy)

This book discusses the study of numbers as it has evolved in many cultures over many centuries. In essence, it approaches numbers from a philosophical or mystical point of view, musing on what each number represents, symbolizes, or embodies in the larger world. For example: one = unity, two = duality and opposites, three = the trinity, four = the elements (air, fire, water, earth), etc. Although very different from our modern “scientific” view of numbers, it offers a rich, beautiful, and intriguing exploration of the world of numbers.

Book II: Sacred Geometry (Miranda Lundy)

This book “charts the unfolding of number in space” as the introduction puts it. Starting from basic concepts of point, line, vertex, circle, and so on, it works up through arrangements of circles, then three dimensional solids and regular tesselations, all the time relating these back to their “sacred” connotations throughout history, as well as their use in the designs of church windows, sacred stone circles, Celtic spirals, Islamic tilings, etc.

Highlights

As with every Wooden Book I’ve ever picked up, I’d have to give the nod to the plentiful and wonderful illustrations.  Part of how they are able to pack so much information into these little gems is by including beautiful, information-rich illustrations on (literally) every other page of the book.  You could not read a single word and still have a wonderful time and glean a lot of what the books have to say!

Conclusion

Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology (Wooden Books) is an incredible treasure trove of information on these four ancient areas of study, packed into an incredibly compact book for an incredibly reasonable price. I can’t recommend it highly enough for anyone interested in these areas and their interrelationships.

Feedback

Please let me know what you think about this review – the rating scales, the format, the content, anything!  I want to make sure these reviews are as useful and informative as possible, and only you can help me do that! Thanks.

Rating Format

To keep things consistent, I have decided to give each book I review a rating from 1-5 stars on each of several scales, pertaining to their usefulness and desirability for the library of someone interested in geometric art. Here are the rating scales I will be using:

I imagine many of us are getting to that point of last-minute holiday shopping.  I, of course, am always drawn to fun geometric items at holiday time! So, if you’re struggling to find those last few gifts, here are some fun geometrically-themed gift ideas for 2011.

Toys, Games, and Puzzles

There are, of course, hundreds of toys, games, and puzzles based on geometric shapes.  Here are just a handful of my favorites (all of which I own myself!)

Zometool
For building and exploring polyhedral objects

Buckyballs
An insanely addictive magnetic desk toy

Ball of Whacks
Another fun magnetic toy

Fractiles
7-fold geometric tiles for making patterns and pictures

Rubik’s Cube
An oldie but a goodie!

QJ megaminx II
The dodecahedral version of Rubik’s cube. Don’t ask me where the stupid name comes from!

Books

Here are all the books I’ve reviewed this year on the site (click here to see the posts themselves, or click below to see individual books on Amazon)…

Islamic Geometric Patterns

M.C. Escher: His Life and Complete Graphic Work

Origami Tessellations: Awe-Inspiring Geometric Designs

Platonic & Archimedean Solids

… a couple of others I’ve mentioned in posts along the way …

Origami in Action : Paper Toys That Fly, Flap, Gobble, and Inflate

Zome Geometry

…and here are a few I haven’t gotten to yet, but which I highly recommend:

Arabic Geometrical Pattern and Design
Just got this one myself – nothing but pages and pages of Islamic tiling with construction hints!

The Beauty of Fractals
The most beautiful book of fractal images I’ve run across

Decorative Objects

Last but not least, here are a handful of decor and other miscellaneous items that will appeal to geometric art fans.

Akaasa 2 Sun 10 step Puzzle Box
One of many, many puzzle boxes with various patterns and levels of difficulty

ThinkBamboo Printed Pattern Bamboo Placemats with Matching Coasters
The name kinda says it all!

Italian Geometric Lacquer Blue Box
Pricy, but beautiful!

Coral Stone Paperweight
Stone paperweight shaped like a cuboctahedron – also available in green onyx and black marble

Laser Cut and Engraved Wood Christmas Tree Ornament
And if all else fails, why not an ornament for their tree?!

Swarovski 2011 Annual Ornament
It turns out Swarovski went geo this year!

Note: Many of the links above are affiliate links, meaning that if you click through them to purchase I will earn a small commission. There will be no extra cost to you, and you will be indirectly supporting this web site by supporting its author.

Plumbing the Depths of the Lowly Cube

One day almost 12 years ago I got to wondering, “I wonder how many ways there are to divide a cube into two identical halves?”  The literal answer is “infinitely many” – for example, just take a straight slice through the center of the cube from any direction whatsoever. So I guess the real question was, “how many interesting / beautiful / surprising ways are there to divide a cube into two identical halves?” This page of sketches shows that I came up with over thirty options in one sitting:

Halved Cubes sketch - Phil Webster, 1990

And a few of the more interesting ones I went on to prototype in cardboard – see the pictures below as we go along…

In the course of creating those sketches, you can see that I identified several “families” or “themes” for how to generate ideas.  Let’s take a quick look at each group.

Categories for Halving a Cube

Single Plane

This is the simplest approach: simply slice the cube in half using a single straight cut. Even so, there are at least six different ways to do this that are qualitatively different from each other (1-6 in sketch). Number 7 is a variation on 3 which is no longer a single plane cut, so it doesn’t really belong in this category. Oh well!

8-Cube and Derivatives

If you imagine a cube being cut in half in all three direction you get 8 “sub-cubes”. Combining these in different groups of 4 leads to possibilities 8-11. Numbers 10 and 11 are in parentheses because they only work on paper, because they’re attached only along edges.  In the case of 11, you’d have to pass the two halves through each other to reassemble the cube! Here is Number 12, which also incorporates some diagonal elements:

"Halved Cubes #12" by Phil Webster

Main Diagonal

The “main diagonals” of a cube (each cube has four of them) run from one corner to the corner at the far opposite end of the cube. Number 19 and 20 are built using these diagonals, and number 21 is actually a hybrid with the last category, using the main diagonals of the 8 sub-cubes.

Tetrahedral

Every cube has two tetrahedra “hidden inside” it by connecting two sets of the four diagonals on the faces of the cube. Numbers 22-26 explore halves that use some or all of these tetrahedral edges in their construction. Here is my model of Number 22 (an especially cool one in my opinion!):

"Halved Cubes #22" by Phil Webster

Rectangular Prism

In the same way that you can split a cube into 8 sub-cubes, you can use other combinations of division along each of the three directions to divide the cube into rectangular prisms (a.k.a. boxes!) instead. Number 27 looks at a possibility if you cut the cube in 3 along two sides and in half along the third, creating 18 sub-boxes. Number 28 takes an entirely different approach, imagining boxes or “columns” within the cube connected by slanty surfaces. Number 29 is frankly out of place – it doesn’t seem to have anything to do with prisms at all!!

Donut

What if each half had a “hole” all the way through it, forming a “donut” (or in math terms, a “torus”)? Number 30 is an example of this with the goal of the hole being in the center of the face of the cube.  This model is one of the ones I built and it’s great fun because if you present it to someone assembled:

"Halved Cubes #30" (assembled) by Phil lWebster

and ask them to guess what the halves will look like, most people are surprised by what they find when they pull it apart:

"Halved Cubes #30" by Phil Webster (separation sequence)

Fractal

Number 31 explores the idea of a “fractal” or self-repeating approach. This category is technically unbuildable since the parts become infinitely small, but of course you could build an approximation of the one I sketched given enough time and patience. But I never did.

A Few New Possibilities

That completes the tour of this sketch “from the archives.” But before I sign off, here are a few new possibilities that occurred to me as I looked through these old sketches – mostly extensions of the existing ideas above.

N-cubed Cubes

If you take the 8-Cube idea and divide the original cube into 3, 4, 5… along each direction instead of just 2, you get 27 (3x3x3) sub-cubes, 64 (4x4x4) sub-cubes, 125 (5x5x5) sub-cubes, etc. In fact, on closer inspection, Numbers 13 and 14 are already based on the 4x4x4 case. The odd-numbered ones tend to be a little less elegant because the central sub-cube has to get split in half (can you figure out why?), so here is Number 13 extended to the 6x6x6 case (anyone remember Qbert?!):

Halved Cubes - 6x6x6 example

Zig-Zag Cuts

Instead of the single-plane cut of the first category, we could instead use 3 cuts in a “zig-zag” fashion like this:

Halved Cubes - "zig-zag" example

This could be extended even further by adding more zigs and zags to make a “lightning bolt” cut:

Halved Cubes - "lightning bolt" example

Curved Cuts

And finally… every example above limits itself to straight edges and faces. But why not use curves?:

Halved Cubes - "curved cut" example

Whoa, that really opens up the possibilities…  Can you think of any others? If so, leave them in the comments below!

What is the Sri Yantra?

You have probably seen a Sri Yantra even if you haven’t heard the name for it. It looks like this:

And is often surrounded by additional ornamentation representing lotus petals, etc. like this:

This symbol (both the basic form and the full ornamented form above) is laden with many layers of meaning in Hindu philosophy, which you can read about in the Wikipedia article on Sri Yantra. However, I’m going to focus on the geometry, as you might expect.

An Acknowledgement

Before I dive in I want to note that much of what I am presenting (including a number of the images) I found a wonderful site called Sri Yantra Geometry Research (www.sriyantraresearch.com).  If you enjoy this post, you must go to this site, where you can spend hours (as I did!) learning all the finer details about this amazing figure.

Sri Yantra Basic Definitions

So, what make a Sri Yantra a Sri Yantra?  In short, it is a figure composed of nine triangles and a central point (called the bindhi) such that:

• Four triangles point up and five point down
• The corners of the two biggest triangles all touch the same outer circle
• For all the other triangles, the uppermost or lowermost point touches the base of an opposite-pointing triangle
• At eighteen different points, three triangles cross at a mutual point!
• The central bindhi is located at the geometric center of the innermost triangle (formed by the crossing of two of the downward-pointing triangles)

Sri Yantra Variations

So, which one is the “right one”??

The “Optimal” Sri Yantra

It turns out that an optimal figure has three important properties:

Concurrency = Everything Touches/Intersects Perfectly

A concurrency error - lines don't intersect

Concentricity = Centers Match

A concentricity error - centers don't match

Equilaterality = Center Triangle Has Equal Sides

An equilaterality error - center angles are not 60 degrees

Can It Be Done?

But this time around I had a “mission” — to look for and connect with artists using geometry in their art. Out of what I’d guess to be some 200+ artists, I encountered 5-10 whose work (or at least some of whose work) was substantially geometric in nature. I found all of them wonderful to talk to (I hope to do some interviews in the future!), and I can’t wait to share their work with you.

Here are the five who I connected with the most, listed in (roughly) increasing order of how “geometric” their work is as a whole.

Cheryl and Don Olney

Website: http://www.louisesdaughter.com/

I ended up chatting with Cheryl for quite a while – it turns out that she and Don live in Rochester, NY — my home town!  When you first arrive at their site you won’t think “geometric art” because most of what they do really isn’t.  However, if you scroll down, you’ll find what caught my geometric eye.  They (specifically, Cheryl’s husband Don) make these very clever little business-card sized kinetic pieces with tiny wooden gears inside. I picked one up and haven’t been able to stop playing with it!!  Here is an example:

"Gear Card" by Don Olney

Although you can’t see it in action, you can probably get a sense of how clever and cool an idea it is!

Ann Salk Rosenberg

Website: http://www.rosenbergartstudio.com/

Ann is a lovely lady who paints large, bright canvases. Most of her work is only geometric “around the edges” in that she uses a lot of checkerboard grids and other repeating patterns as textures within the whole piece.  However, she recently completed a series of 5 paintings called “Babylonian Voices” which tell the story of the Tower of Babel using entirely geometric shapes. They are all bold and beautiful.  I especially like #2 which features lots of circles intersecting with an underlying grid:

"Babylonian Voices #2" by Ann Salk Rosenberg

Nathan Macomber

Website: http://www.macomberglass.com/

Nathan does a variety of glass work, including some cool, creepy, not-so-geometric spiders!!  But what caught my eye were his beautiful glass disks.  He uses a variety of methods of his own design to achieve patterns of glass bubbles and spirals of color that make these glass discs really stand out. Most are mounted individually on metal stands, but some are combined into larger works, like this one that took center stage at his booth:

Large glass work by Nathan Macomber

Raj Kommineni

Website: http://kommineniartglass.com/

Raj also works in glass, and among other things, does one of my favorite forms of glass – small spheres with beautiful patterns inside.  In addition to the (sometimes) geometric nature of the colored glass inside the globe, many of Raj’s spheres also include a somewhat polyhedral aspect in that he sandblasts the outside and then grinds out clear “windows” around the outside:

Glass sphere by Raj Kommineni

Beautiful!!

E. Douglas Wunder

Website: http://www.edouglaswunder.com/

E. Dougles Wunder was one of two artists I spoke to whose art is almost entirely geometrically inspired. He creates very distinctive metal jewelry (primarily out of titanium) using a particular process he developed himself.  He carefully drafts out his designs in advance and then stacks several layers, using wire and spacers to keep the layers stacked nicely on top of one another. Here is an example of one of his bracelets:

"Square Segmented Bracelet" by E. Douglas Wunder

Valerie Hector

Website: http://www.valeriehector.com/

Last but not least, Valerie Hector was perhaps the most geometrically inclined of the artists I spoke to, and works in a medium I never would have thought could be used in a geometric way: beads!  She creates beaded jewelry almost all of which is in the shape of various polyhedra! What really astounded me about her pieces (besides the fact that they existed at all, and how beautiful they are!) is that they are incredibly rigid — not “floppy” the way most beaded work I’ve run across tends to be. I could pick up these little bead polyhedra and squeeze and they hardly budged! I had to ask Valerie three times to confirm that she used thread, not wire, to string the beads.  Here is a necklace that features multiple polyhedral shapes:

"China Spring" necklace by Valerie Hector

Conclusion

All in all, I am SO GLAD that I took the time and energy to travel to this show!  It made for a long day, but I made some new friends, took in loads of fabulous art, and walked away reinvigorated and inspired to keep creating my own art.

(For a detailed explanation of the rating system, see the end of the review.)

Review

Introduction

This week I have another fabulous “how to” book to share.  This one is called Islamic Geometric Patterns and is written by Eric Broug, who is a designer focusing exclusively on Islamic geometrical design in his work. It is a modestly sized book that is jam-packed with illustrations showing how to construct by hand almost 20 different patterns found in actual Islamic buildings throughout the world.

Walkthrough

The non-nonsense approach of this book is reflected by the fact that it only has two “chapters” entitled The Basics and Step-by-Step Construction. The former discusses the basic building blocks of the designs (hexagons, pentagons, and squares) plus a few design tips. The latter, which comprises the majority of the book, offers (as promised) detailed instructions for constructing a number of different patterns.

The patterns are grouped into three difficulty levels (Easy, Intermediate, and Difficult). Each pattern begins with a page offering:

• the name of the building or artwork in which the pattern is featured
• the city, country, and date of construction of the building or artwork
• an illustration showing the full repeating pattern, with one “cell” highlighted (this is what you will be taught how to draw)
• a paragraph or two describing the history or other interesting features of the building or artwork in question

After this introductory page, the following 2-10 pages (depending on the complexity) show numbered steps, 4 to a page, showing how to build up the design using simple steps.

Highlights

One of the things that makes this book stand out is the simplicity and clarity of the instructional steps, as well as the fact that no mathematical knowledge whatsoever is required to follow the instructions!  At each stage, you are simply identifying existing points or lines you have already drawn and drawing new lines or circular arcs, which then create more points. This is in keeping with a point the author makes in the introduction, which is that the original creators of these designs used nothing more than a straight edge and a fixed-width compass (i.e. circles of a single size), often in the form of a simple rope! It is incredible to contemplate that such complexity was achieved using such basic tools.

Conclusion

Islamic Geometric Patterns is a meticulously presented, non-mathematical introduction to the construction of Islamic geometric patterns. It encourages the reader to grab a pencil, ruler, and compass and create some of these astonishing patterns, deepening one’s understanding through the act of drawing.  Unlike many other books in this genre, there are no photographs and only minimal descriptive text. Instead, this book focuses on the patterns themselves and how to construct them.

If you are interested in understanding these patterns more deeply and understanding how they are derived and designed, I can think of no better source.

Feedback

Please let me know what you think about this review – the rating scales, the format, the content, anything!  I want to make sure these reviews are as useful and informative as possible, and only you can help me do that! Thanks.

Rating Format

To keep things consistent, I have decided to give each book I review a rating from 1-5 stars on each of several scales, pertaining to their usefulness and desirability for the library of someone interested in geometric art. Here are the rating scales I will be using:

I asked you all to offer other ideas and examples, and as promised, I am publishing some of them this week for us all to enjoy. The real standout for the reader challenge was Nancy Webster (disclaimer: she’s my mom!) who sent me at least a dozen examples across many categories, several of which are featured below.  Thanks, mom!

So, without further ado, here are…

Examples of “Useful” Geometric Art

Note: I’ve offered at least two examples under each of my original top level categories. Each example includes a thumbnail image and a link in case you want to find out more about the particular example.  Enjoy!

Furniture

Chair:

http://www.homedit.com/chair-one-by-konstanian-grcic/

Coffee Table:
 
http://www.2modern.com/designer/Arktura/Arktura-Quadra-Coffee-Table

Home Furnishings

Wallpaper:

http://www.2modern.com/designer/Piet-Hein-Eek

Rug:

http://www.2modern.com/designer/Gandia-Blasco/Gandia-Blasco-Caleido-Wool-Rug

Lamp:

http://www.2modern.com/designer/Stig-Hansen/Stig-Hansen-IQ-Light_2

Bedspread:

http://www.kaboodle.com/reviews/geometric-polyhedra-bedspread–collectible-vintage-scarves-bedding

Kitchen

Coasters:

http://www.zazzle.com/black_white_circles_pattern_coaster-174974371988592381

Potholder:

http://www.panamola.com/index.php?route=product/product&product_id=34

Boxes

Puzzle Box:

http://www.seriouspuzzles.com/i11273.asp

Jewelry Box:

http://www.forzieri.com/usa/product_view.asp?l=usa&c=usa&dept_id=28&sku=fz36459-007-00&popup=0

Architecture

Modern House:

http://www.interiorarcade.com/home-design-house-design/modern-home-designs/geometric-home-design/

Swedish “Turning Torso” building:

http://en.wikipedia.org/wiki/Turning_Torso

Desktop Items

Paperweight:

http://www.corporate-awards.com/Faceted-Cube-Hexagon-Etched-Crystal-Paperweights

Desk Organizer:

http://stores.photolarkgallery.com/-strse-388/desk-organizer-pattern-black/Detail.bok

Clothing

Dress (this one is wild!):

http://randommization.com/2010/11/14/wearable-geometry/geometric-clothing_3/

Jacket:

http://www.stylehive.com/bookmark/geometric-print-jacket-623209

Clothing Accessories

Necklace:

http://www.designformankind.com/2010/07/one-geometric-necklace/

Bracelet:

http://www.thisnext.com/tag/geometric-jewelry/

Phil’s List

Here are 51 items (not counting the top level categories) I came up with in about 10 minutes of brainstorming:

• Furniture
• Chairs
• Overall shape
• Upholstery
• Tables
• Bases
• Tops
• Couches
• Cabinets
• Chests
• Overall shape
• Surface decoration
• Beds (esp. headboards)
• Desks
• Home Furnishings
• Carpets
• Tiled floors
• Wallpaper
• Mirrors
• Lamps
• Vases
• Clocks
• Kitchen
• Trivets
• Coasters
• Racks
• Wine racks
• Spice racks
• Hanging racks
• Dish towels
• Plates
• Silverware
• Boxes
• Jewelry boxes
• Puzzle boxes
• Architecture
• Building/room layout
• Façades
• Surface decoration
• Desktop Items
• Paperweights
• Picture frames
• Inboxes
• Desk organizers
• Clothing
• Pants
• Shirts/blouses
• Skirts
• Shoes
• Socks
• Clothing Accessories
• Jewelry
• Necklaces
• Earrings
• Bracelets
• Rings
• Belts
• Scarves
• Handbags

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