Discover art and science at play with Zometool; the intelligence-building toy made for kids and used by Nobel-Prize winners! · Guaranteed for life· All components are inter compatible.· More parts = more fun!

“The mind, once stretched by a new idea, never regains it’s original dimensions.”

- Oliver Wendell Holmes

Snow is made up of a limitless number of tiny frozenworks of art - crystals! Each crystal is unique in itself. Ice crystals form different structures, depending on the surrounding temperature.With this Zometool kit, you can discover

that ice crystals have a six-sided basic structure,marvel

that, due to the composition of water molecules, only angles of 60° und 120° are possibleand create:

elegant stars, crystals and hybrid forms of manycrystal structures. With Zometool, you’ll experiencethese sparkling works of art in a completely new way.

Snow is made up of a limitless number of tiny frozenworks of art - crystals! Each crystal is unique in itself. Ice crystals form different structures, depending on the surrounding temperature.With this Zometool kit, you can discover

that ice crystals have a six-sided basic structure,marvel

that, due to the composition of water molecules, only angles of 60° und 120° are possible and create:

elegant stars, crystals and hybrid forms of many crystal structures. With Zometool, you’ll experience these sparkling works of art in a completely new way.

WARNING: CHOKING HAZARDThis produkt contains small parts,which could be swallowed.NOT for children under 3 years.

US Patents RE 33,785; 6,840,699 B2. Zometool is a registered trademark of Zometool Inc. and Zometool EuropaUG. Based on the 31-zone system, discovered by Steve Baer, Zomeworks Corp., USA © 2011

Parts: 9018 303012

art and science at play

ZOMETOOL®

In our day to day life, we are surroundedby crystals. For example, well-known typesof crystals are sugar, salt - and, of course,snow - but more about that later.

The atoms or molecules in a crystal are notrandomly arranged, in fact, they alwaysfollow regular patterns: so-called crystallattices. These are 3-dimensional patterns of(mathematical) points, whose sub-unit iscalled a “unit cell”. There are about 1.25 x1018 unit cells in a single grain of salt. Wecan depict these structures with Zometool:

The beauty of simplicity: this complex Zometool lattice struktur represents a single grain of salt!

Crystals

When we see a beautiful winter landscape,with white mountain tops and ski slopes,we know that snow has fallen. But what issnow?

Snow is “solid” rain. It forms when finedrops of very cold water attach themselvesto dust particles or to bacteria and thenfreeze. This situation occurs within clouds,at or below -12° Celcius. The minute icecrystals become heavier and heavier andbegin to fall. The surrounding temperature

Snowand humidity influence how each crystaldevelops. If it is very cold, with a high levelof humidity, six-sided hollow columns willform - if the weather is warmer, six-sidedstars will appear. Each and every crystalfollows its own particular path on its waydownwards and the tiniest fluctuations intemperature and humidity will have aneffect on its appearance.

The water molecules in an ice crystal formthemselves into a six-sided lattice, as inthe Zometool model below:

The Hexagon

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a2 x hydrogen +1 x oxygen= H2O

Ice crystals

Therefore we can see that snowflakes arenot frozen drops of water. Of course, somedrops of water do freeze as they fall to earth- these are called ice pellets, or sleet andhave no particular symmetry.

When we observe ice crystals closely, webecome aware of the unbelievable beautyof their structures - millions of individualworks of art, all falling from the sky. Theirdevelopment is determined by temperatureand humidity: the greater the humidity, themore delicate the “arms” of each crystal.

The movement of the ice crystals throughthe air causes them to melt and recrystaliseagain and again, which leads to the “growth”of increasingly complex hybrid forms. Thisgrowth only comes to a halt when the icecrystals have reached a point about 100 m.above the ground, with temperatures ofaround 0° C. The wind whirles the manyice crystals through the air and they collidewith each other, causing their “arms” to get tangled and stick together. A snowflake is born!

Each crystal is unique. As long ago as 1895,Wilson A. Bentley, a Canadian farmer, tookphotos of around 5,000 different forms. Theprobability is that there have never been twoidentically-shaped complex snowflakes, thereason lying in the great variety of possiblecombinations of all the different features ofcrystals. The number of possible forms ofcomplex ice crystals is greater than thenumber of atoms within the universe.

Apropos the universe:Don’t the ray-shaped “arms” of an ice crystal remind you of stars?

In picture , each red ball represents ahydrogen atom and the white struts depictthe oxygen atoms. There are always twohydrogen atoms to each oxygen atom,thus giving us the chemical formular H2O.The symmetry of an ice crystal developsfrom the sixfold symmetry of an (ice) crystallattice and this is the reason why the basicstructure of an ice crystal is always six-sided.

Almost 500 years ago, Johannes Kepler(1571-1630) wrote a paper on the symmetryof snowflakes, in which he described thefact that a snowflake always looks the samewhen rotated 60° (sixfold symmetry). TheZometool kit “Kepler’s Kosmos”, exploresKepler’s view of the planets and their orbits.

Quite simply, snowflakes andsnow crystals are

made of ice: a snow crystal comprises onlyone single icecrystal, whereasa snowflake is

made up of anamalgamation of

ice crystals.2

a

Kepler’sKosmos

You can create interesting shadows withthe 3-dimensional models.

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Maybe your ice crystal will develop into abeautiful star? Use two Ice Crystals sets to

continue building in 3-D. The starsyou see here have two different “centrepieces”: an icosahedron

(20 faces) and a dodecahedron (12 faces).

Dodekahedron star -in the middle we havea regular Platonic solid;a dodecahedron. Wecan attach the 12 “rays”of the star onto thiscentrepiece.

We can build 2-dimensional ice crystalsand observe the sixfold symmetries whichoccur.

Use the blue struts to create 2-D crystals, making sure to note the position of the Zometool ball, with either a rectangle, a pentagon or a triangle pointing upwards:

ZOMETOOL RULES ICE CRYSTALS (2-D)

SHA

DO

WS

STARS (2-D) STARS (2-D) STARS (3-D)*

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2

3

2

4

5

2

3

4

5

If it works, it works perfectly ...... and if it doesn’t work, it doesn’t work at all.Don’t force Zometool components. You can benda strut to fit it into a tight spot, but struts in finishedmodels are always straight, never under tension.

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Hint: you can tell which strut fits between twoballs in a model by lining up the balls and lookingthrough the holes. The holes show you the shapeof the strut which fits!

Don’t break it apart, take it apart!Take models apart by grasping a strut with yourfingers and pushing the ball straight off with yourthumb. Twisting balls or pulling models apart orcrushing them can cause parts to break!*

To disassemble a largemodel quickly, remove allthe longest struts of onecolour first and work yourway down!

Leave the place cleaner than you found it.It’s always a good idea to clean up when you’redone, so the next person can enjoy Zometooltoo. If we work together, we can make the worldbetter for all.

*We replace accidentally broken parts for free:Europe: contact service@zometooleuropa.euOutside Europe: visit: www.zometool.com/warrantyfor details.

Our mission:· Make learning fun· Create value· Build a better world

Whether you want to ask better questions orlearn better answers, Zometool is your ticket todiscovery and fun. From numeracy to nanotech-nology, quasicrystals to quantum mechanics, thedestination is always the same: understanding ouramazing universe.

More under www.zometool.com

Zometool Project ‘Ice Crystals and Stars’: A-B. Paschen, idea; Paul Hildebrandt, Erwin Kotzab, concept and text; Dr. ScottVorthmann, software for illustrations; Photomicrographs of SnowCrystals, W.A. Bentley and W.J. Humpfreys, Dover Pub., NewYork, USA; Lyn Taylor, Anni Wildung, graphic design; PaulHildebrandt, concept und project management. Based on the 31-zone system, discovered by Steve Baer, Zomeworks Corp. USA.Contact: service@zometooleuropa.eu. ©2011 Zometool Inc.

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1. Depending on the shadow you wishto project, stick either a blue (2-fold),yellow (3-fold), or red (5-fold) strut inthe appropriate hole of one ball of thecompleted 3-D model.

2. Turn the strut in the direction of thelight source.

3. Make sure that the projection surface is at 90° to the light source.

* use 2 kits to build these 3-D stars!

art and science at play

ZOMETOOL®