Why Do Snow Crystals Have Six Sides, and When Do Their Arms Match?

People Were Asking Why Snowflakes Have Six Corners More Than 400 Years Ago

In 1611 the astronomer Johannes Kepler gave a friend and patron a New Year’s present that cost him nothing: a short essay on why snowflakes have six corners. He tried several ideas. He compared the shape to the hexagonal cells of a beehive and to the way pomegranate seeds pack together, and he wondered whether packing like that might be the reason. He never settled it, and he ended the essay with the words “nothing follows” [1].

One word needs care before we go on. In everyday speech a snowflake is anything white that falls. A snowflake can be one ice crystal or a clump of several stuck together [2]. This note is about the single crystals, which scientists call snow crystals. They grow from water vapor, the invisible gas form of water, rather than from frozen drops [3].

Six Corners Come From How Water Molecules Are Arranged Inside Ice

The modern answer starts with what ice is made of. The core of a snow crystal is a single crystal of ordinary ice, called hexagonal ice, the first of 17 known kinds of ice to be worked out. Its structure has a hexagon in it: one water molecule surrounded by a ring of six others [4]. The physicist Kenneth Libbrecht, who has studied and photographed snow crystals for decades, puts it directly: the six-fold symmetry of a snow crystal arises from the arrangement of water molecules in the ice crystal lattice [5].

So the tiny pattern of molecules is repeated over and over, and a crystal that is built from it ends up with flat faces that meet at six corners. This explains why six, but not why water chooses this arrangement in the first place. The sources I could read state the structure; they do not go further into the chemistry of that choice, so I will not either.

Kepler guessed that packing mattered, and in a loose sense the guess points the right way, because the shape of the whole comes from how the smallest pieces fit together. A simple way to picture it is to lay a coin on a table and see how many same-sized coins can touch it. That is a picture, not the real explanation: ice is built from molecules, not coins, and the activity at the end of this note lets you try it.

Temperature Decides Whether a Tiny Hexagon Grows Into a Plate, a Needle or a Star

A snow crystal starts as a very small hexagonal piece of ice, and what it grows into depends on the air around it. In the 1930s the Japanese physicist Ukichiro Nakaya grew snow crystals in his laboratory and found how shape depends on temperature and humidity. A chart of this is now called the Nakaya diagram, or the snow crystal morphology diagram [5].

The temperature pattern is surprising because it does not move in one direction. Reading it as the air gets colder: thin plates near −2 °C (28 °F), then long needles or slender columns around −5 to −6 °C (21–23 °F), then large thin plates again near −15 °C (5 °F), and thicker plates and columns around −25 °C (−13 °F) [4] [6]. The shape flips from plate to needle and back to plate over a few steps of cooling. The exact temperature for needles differs a little between sources, and the chart values are approximate guides, not sharp lines.

Humidity then decides how fancy the crystal gets. When the air is dry the crystal grows slowly and stays simple. When it is humid the crystal grows fast and sprouts branches [6]. The large star-shaped crystals people draw, called stellar crystals, form best around −15 °C [5].

Here is the honest part: Libbrecht writes that science still cannot explain why crystals grow as thin plates or slender columns depending on temperature, because the physics of the ice surface is complicated [6].

Arms Match When All Six Take the Same Trip Through the Cloud

Now the second question. A star-shaped crystal begins as a small hexagonal plate, and branches grow from its six corners. The final shape depends on the exact path the crystal took through the cloud. But the six arms all took the same path, so each felt the same changes in temperature and humidity at the same times. They grow in step, and the result is complex but symmetrical [5].

Nothing has to pass messages between the arms. Libbrecht compares it to six people who each reach for an umbrella when it rains, without talking to one another [5]. A physics review says the same thing from another angle: across something as tiny as a snow crystal, conditions in the air are nearly constant, so growth is essentially perfectly symmetric [4]. When a branch picks up an imperfection and turns, it goes off at 60 degrees, which follows the hexagon built into the ice [4].

The same rule tells you when matching fails. Libbrecht notes that snow crystal symmetry needs symmetrical growth conditions, and if the six arms meet different surroundings they grow differently [7]. In a laboratory, with temperature, humidity and airflow carefully controlled, he has grown pairs of “identical-twin” crystals. They are clearly very similar, although not precisely identical [7].

Matching Arms Are the Exception: Most Real Snow Crystals Are Lopsided

If matching arms are so natural, why do you rarely see them? Libbrecht answers bluntly: the vast majority of snow crystals are not very symmetrical, and irregular crystals are by far the most common type, so do not be fooled by the pictures [5]. The perfect stars in photographs were picked out from among many ordinary ones.

Even the pretty ones are rarely perfect. In fern-like stellar crystals, the side branches on one arm are not quite the same as on the others [8]. And six is not a strict limit on what you can find. Two small six-branched crystals that collide in the air can stick together and grow into a twelve-branched snowflake, and there are small triangular crystals shaped like truncated triangles [8].

So the two questions have one answer in two parts. The ice gives every crystal a six-fold pattern to build on. The cloud then decides how much of that pattern survives, and the pictures you see are the cases where the whole crystal had the same journey.

Try It Yourself With Coins Now, and With Snow When It Falls

Any day: the coin picture. Take seven coins of the same size. Put one on a table and try to place others so each touches it and its neighbors. Exactly six fit around it, each touching the center coin and its two neighbors. Look at the shape the outer six make. Remember this is only a picture of packing, which is what Kepler wondered about, and not how ice works.

When it snows: count the arms. If it is snowing where you live and an adult is with you, step outside for a few minutes, hold a dark piece of cloth such as a scarf or a dark glove, catch a few flakes on it and look with a magnifying glass if you have one. If it is not snowing, look at photographs of snow crystals instead. The largest crystal ever photographed measured about 10 mm (0.4 inches) tip to tip [9], and most are much smaller, so a close look helps. Count the arms. Are there six? Do the arms match? Do not be disappointed if they do not: you now know that most do not. Dress warmly, and stay somewhere safe, away from traffic and slippery ground, while you look.

Sources

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