Tetrahedral Packing

Tetrahedral-PackingThat’s tetrahedral packing — not “packaging,” although, really, I want to talk about both subjects.

What are we looking at here? According to a 2009 paper from the University of Michigan, the upper polyhedron is a pentagonal dipyramid “built from tetrahedral dice stuck together with modelling putty.” (Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra)

According to the same paper, the lower polyhedron made from red dice is a “quasicrystal with packing fraction φ = 0.8324.” (The lower photo is from The Ann Arbor Chronicle)

The big breakthrough in tetrahedral packing was Elizabeth Chen’s 2008 research uncovering substantially denser packing arrangements than previously thought possible.

We’ve speculated before on the structural packaging implications of “close-packing” and of “space filling” polyhedra.

Tetrahedral packing is interesting precisely because tetrahedrons cannot pack together perfectly. Although, Aristotle believed that they did…

In 1972 Stanislav Ulam, a Polish-American mathematician who worked on the Manhattan Project, conjectured that spheres were the worst-packing of all convex bodies. So from Ulam’s conjecture, it should follow that tetrahedra should pack denser than 0.74048.  But in the mid-2000s, investigations of tetrahedron packing that used computer simulations, as well as experiments using  physical tetrahedral dice, could not establish any configuration of tetrahedron packing that clearly surpassed the 0.74048 for spheres. Maybe tetrahedra were worse-packing than spheres?

Was Ulam wrong? No. We’ll get to that in a moment. Now’s a good chance to think about how very wrong Aristotle had been – wrong about tetrahedra and their ability to completely fill space. How did he manage to massively miss that one?

Part of the reason could have been that Aristotle had no ready source of tetrahedral dice and gummi putty to try pasting models of tetrahedra together – the way that Elizabeth Chen asked the audience of her thesis defense to do. Once you have them in your hands, it’s easy to paste together models and convince yourself that they will fill less than all of space – a pastes-great-less-filling experience.

Dave Askins, Packing Pyramids: UM and Ann Arbor
The Ann Arbor Chronicle, February 14, 2010

 (See also NY Times article, Packing Tetrahedrons, and Closing In on a Perfect Fit)

What’s the “packaging” take away? If you’re not designing a package for tetrahedral dice, why should you even care about tetrahedral packing?

Well, as we’ve shown recently, there are some tetrahedron shaped packages out there. (See: ModissaАбажурус, and Tetra-Pak)  Denser, more efficient packing arrangements might lower the cubic space taken up by such packages in a shipping container.

And the remaining gaps between the tetrahedrons, might, in some way be exploited as a feature. (More about that in a future post.)

Real World Branding: Dead Horse Bay

Dead Horse Bay is a small body of water located in Brooklyn on the southwest shore of Barren Island. It got it's name from more than two dozen horse rendering plants which were situated there between 1850 and 1930. As cars became more plentiful, the rendering plants disappeared and the city began to use the area as a landfill which was capped by 1930. In the 1950's, the cap burst, flooding the beach with garbage. Today the beach is a veritable museum of bottles, old shoes, wig hair, nylon stockings and pieces of horse bone from the 20's and 30's. The sounds of the waves blend with the tinkling of the bottles and the wailing of the gulls.
photo: Debby Davis

Dead Horse Bay is a small body of water located in Brooklyn on the southwest shore of Barren Island. It got it’s name from more than two dozen horse rendering plants which were situated there between 1850 and 1930. As cars became more plentiful, the rendering plants disappeared and the city began to use the area as a landfill which was capped by 1930. In the 1950’s, the cap burst, flooding the beach with garbage.

Today the beach is a veritable museum of bottles, old shoes, wig hair, nylon stockings and pieces of horse bone from the 20’s and 30’s. The sounds of the waves blend with the tinkling of the bottles and the wailing of the gulls.

For more Dead Horse Bay branding, see: Bottle Beach, Bottles from Dead Horse Bay, “Uncapped Landfill Jars” #1, #2, #3, #4 and “Uncapped Landfill Bottles” #1, #2, #3, #4, #5, #6

Michael Wang: neutralizing brand rivalries

Michael Wang, PGUN

I saw Michael Wang’s recent “Rivals” exhibition a couple months ago. Competing products lined up on white, powder-coated aluminum shelves. At first I thought that it was a straightforward presentation of brand rivalries.

In the piece above 27 packages of “Old Spice” deodorant alternate with 28 packages of “Axe” deodorant. Not quite 50/50. And the proportions in the other pieces were even more unequal…


After checking out Wang’s accompanying text and charts, I realized that the proportions were based on market share. I was assuming a false equivalency of brands.

What exactly is he up to here? Beginning with a quote by Milton Friedman, Wang takes us through it, step by step…

There is one and only one social responsibility of business–to use its resources and engage in activities designed to increase its profits so long as it stays within the rules of the game, which is to say, engages in open and free competition, without deception or fraud.

—Milton Friedman, Capitalism and Freedom

Using Coke and Pepsi to illustrate his points, Wang continues his “Rivals” presentation with a series of 15 chart and diagrams.

Michael Wang on Brand Rivalry

(Some, but not all, of these steps follow, after the fold…) [Read more…]

Packaged (past tense): Zoomorphic Rainier Beer

Terry HecklerRainierLogo’s television ads for Rainier Beer during the 1970s and 80s made zoomorphic beer packaging an integral part of their brand. Using actors in beer bottle and beer can costumes, the zoomorphic Rainier Beer commercials created an alternate universe in which bottles and cans of Ranier Beer were wild animals.

Wildly popular at the time, the zoomorphic packaging costumes are still used by the brand for their quirky (now nostalgic) charm.

In a 2008 interview, Heckler describes their first proposed TV spot (shown above)…

“Rainier Beer contacted us,” Heckler said. “They must have been desperate.”

…Rainier, he said, had burned through every ad agency in Seattle to little effect. Founded in 1884 in Georgetown and with the big red, rooftop R so well-known it was a landmark for Interstate 5 traffic reports, the company fell on hard times, dying in its own market.

“They said ‘OK, what can you do for us?’ ” Heckler remembered. “We were their last resort. They wanted something different.”

So what Heckler and Associates did in 1971 was create an ad, now considered a local classic, that shows a through-the-windshield view of an off-screen couple and child driving through a national park. The wipers are like a metronome. Through the rain they see a “Beer Crossing” sign. Then, a family of 6-foot Rainiers (two bottles and a can) darts across the road.

“Oh! Oh! A whole herd of Rainier beers,” the woman says. “They’re just so fresh and friendly.”

The Rainier executives were not sure what to think.

But they approved the campaign. What followed over the next 16 years not only made Rainier Washington’s most popular beer once again…

Under the Needle: A vote for beer over politics
Mike Lewis, October 8, 2008, Seattle Post-Intelligencer

(Several more zoomorphic Rainier Beer spots, after the fold…) [Read more…]

Plagiarism as Self-Promotion

The “capabilities” page on 50 Foot Marketing & Design’s website shows text that was lifted from BEACH’s 2009 website

Continuing with part 2 of the good-news/bad-news story that we started yesterday (“Good things come in smart packages”) today’s post is the “bad news” part: plagiarism as self-promotion.

The highlighted promotional copy above, was something that I originally wrote for a “services” page on our 2007 website and then revised slightly in 2009. Later, when we relaunched a different version of our website in 2011, that page was no longer even included.

So imagine my surprised to discover that the text I wrote 8 years ago to promote our services, is being used today on other companies’ websites to promote their own creative services!

Seems counter-intuitive that a “creative” company would need to swipe someone else’s creative work in order to promote itself, right? It’s like their copywriter did plenty of copying, but not so much writing. (To say nothing of copy-rights.)

But I get it. It’s a daunting amount of work if you do it all yourself—the writing, the designing, the SEO. How tempting it is to just copy what someone else has already written.

Here now are 3 companies that have apparently succumbed to the temptation to do this bad thing:

1. Texas-based 50 Foot marketing & design’s “capabilities” page (shown above) is the most egregious example. They’ve taken seven consecutive sentences from our 2009 website, with no changes that I can see except for changing the word “packaging” to “package” and removing the word “regularly.”

Regarding the rest of the text on their page, a search on the plagiarism checking website, Copyscape, shows that 39% of that page matches the website of New-Zealand based Big Impressions. (I’ll leave it to someone else to figure out who is copying who there.)

(Two more companies and a word about my own motives, after the fold…)

[Read more…]

Re: “ Good things come in smart packages ”


Search online for “Good things come in smart packages” and Dow’s 2012 video (above) will dominate the results. But Dow was not the first to ever use this headline.

We came out with a series of promotional mailing cards in 2000, one of which used the same declarative sentence as a headline.

Based on the old figure of speech about good things coming in small packages, it’s not surprising that more than one person has thought of substituting the word “smart” for the word, “small.” As an idea, this is relatively low hanging fruit.

Still, 15 years later, it’s interesting to note who has used this idea and what they were selling.

Here’s a partial list of 10 “smart packagers” including BEACH:

1. Dow is selling their “performance packaging solutions” under their newish “Solutionism” trademark.

2. In BEACH’s case, we were selling our package design services. The message on the back of our card read:

Who says you can’t judge a book by its cover. Not us. We think that’s pretty much what customers do—they judge the product by its package. Your products may be ingenious, but how will your customers know this if the packaging looks like an afterthought.

In the battle for market share, good packaging is a smart weapon. Call us now to outsmart your competition.

Did we overplay the “smart” metaphor? Maybe. Even though we were careful to mention “ingenious” products, there was always something glib and vaguely dishonest in this line of reasoning. The idiom about “small” packages, after all, is a rather optimistic prediction about the quality of hidden contents. Small packages might contain good things, but aren’t they equally apt to contain bad things?

“Good things come in smart packages” is like something that an unreliable narrator might say. What promise is being made and to whom? Is it just a promise to consumers of good things ahead? Or is it also a promise to manufacturers that a customer will believe a “smart” package’s promise?

Who else has been touting smart packages? We have 8 more, after the fold… [Read more…]

Packaged (past tense): Modissa Tetrahedral Pack

Terahedral pack by Burton Kramer

This vintage tetrahedral pack for Modissa scarves was designed by Canadian designer, Burton Kramer.

Similar to Art Lebedev’s 2011 folding carton (that we featured on Tuesday), but Kramer’s similarly tetrahedral folding carton for Modissa was designed in 1965.

Described in GraphisPackaging 2” as:

Folding carton with carrier loop for silk scarves from a Swiss fashion store. Black lettering on die-cut white board.

An earlier 1963 scarf pack designed by Burton for Modissa, was a triangular prism shaped folding carton. In this structure, designed 2 years later, Burton expanded upon his triangular theme for Modissa.


What’s the story with the carton’s “carrier loop”?

That’s better explained by a description given on the The Centre for Contemporary Canadian Art’s “Canadian Art Database.” The caption there calls it the “Modissa Christmas ornament.”

It’s a gift box, designed to be hung on the tree like an ornament.

The die-cut holes, revealing the colors and patterns of the scarves contained inside, making these tetrahedral boxes all the more ornamental. (See also: Vance Jonson’s dice-shaped “packaging innovation”)

Can-Dew Mousetrap Race Car

MouseTrapRacerCanDew-CokeThe package design for Doc Fizzix’s “Can-Dew” mousetrap powered vehicle kit includes an illustration showing the car loaded with a red can of Coca-Cola.

Can-Dew-Packaging-designCertain online vendors, however, have chosen to photograph this mousetrap racer carrying a can of Coke’s rival cola, Pepsi. (I’m just saying.)

Can-Dew is designed to carry a full sized soda can in its specially engineered cargo bay over a 15 meters distance. The secret to Can-Dew’s success is the high torque gearing system that generates a tremendous amount of power output capable of caring heavy loads a great distances.

(The Can-Dew kits also appear to include a Victor brand mouse trap.)

Founded in 1995, by former science teacher, Alden J. Balmer…

Doc Fizzix (pronounced Doc Physics) was originally the nick-name given to Alden J. Balmer by his students and this nickname would eventually became the name of the company he founded… [He] is considered by many to be the worlds foremost mousetrap-vehicle expert.

Mousetrap racing cars are often used as science class projects, and the ability to convey a full can of soda is often a requirement of the assignment…

According to Jim Sparks, physics teacher, MHS, each small group of students has built a mousetrap car capable of carrying a full can of soda as far as possible only on the power of the mousetrap spring…

But wait, there’s more! [Read more…]

Tetrahedral Packaging: Абажурус


Tetrahedral packaging for “Абажурус” (or Abazhurus) hanging lamp kits from Art Lebedev Studio, designed by Pavel Kuleshin and Yevgeny Zorin.

A tetrahedron-shaped, “tipi” structure with its three, intersecting flaps, appears not to require gluing.

(Check out our archives for more tetrahedral packaging)

Below, the product is shown to be modular in nature.

tetrahedral packaging for Абажурус lamps

For more packaging from Art Lebedev Studio, see: Lemon Slices, Level Bottles, Figural Punts and the orthographically-projecting Pahila-750 telephone carton.

LaCroix Package Design: recommended?

Lacroix Package Design
Jason Nocito for The New York Times

The New York Times Magazine section has some new columns. One of which is called “Letter of Recommendation.” While the first two installments were cultural in nature, it was inevitable that some consumer packaged goods would also be recommended.

Mary HK Choi’s “Letter of Recommendation” in yesterday’s column is about LaCroix Sparkling Water. The thing about her piece that really caught my eye was that, although she likes the product, she does not love the LaCroix package design…

My initial reluctance was partly due to the cans’ hideousness. The first time I drank LaCroix, I half expected it to be filled with self-tanner. Or Axe body spray. The cans look somehow simultaneously obnoxious and earnest, as if they’re trying to appeal to Canadian ravers or the sort of people who have septum piercings and shop at Desigual. With its bootleg Van Gogh swirls and the not-quite Yves Klein blue logo, LaCroix would look right at home nestled in a neoprene koozie screen-printed to look like an acid-washed denim jacket. Everything about the can suggests trashy fun. The inside of my recycling bin has begun to look like a Cirque du Soleil poster.

I wonder how this critique is being received by Alchemy, Ltd., the design firm responsible…

After developing a complete branding overhaul for LaCroix sparkling water that helped generate double digit growth over a ten year span, the choice was obvious. LaCroix again chose Alchemy to draft the sequel.

Our team proposed a strategy for elevating the brand with a line extension designed to disrupt and engage new followers rather than diluting the company’s iconic presence at retail.

LaCroix’s new offerings featured a lively blend of fruit essences, and a playful attitude that was launched with an integrated program developed by Alchemy. LaCroix’s new branding, packaging, POS, OOH, and digital have premiered to rave reviews!

One fundamental tenet of market research is that the consumer’s aesthetic sensibilities don’t really count for much at the cash register. The “hideous” design that Choi critiques was also the design considered the “least appealing” by LaCroix. Until MAi Research recommended it as the best choice. (More details about this, after the fold…) [Read more…]