I love snowflakes. Their shape is determined by temperature and humidity, but you can draw them any way you imagine. This handmade glass snowflake is manually drafted and an original design.

You can draw any snowflake with geometry. If you understand the math behind the shapes formed by the interlocking snowflake branches, then you can easily create your own patterns.

Supplies

Tools

Some of the tools used for this project are specific to cutting glass and can be purchased online at stores like Amazon, Delphi Glass, Bullseye Glass, or at a local hobby store.

Cutting Mat
Heavy Duty Running Pliers
Wheeled Nippers
Pistol Grip Glass Cutter
Glass Cleaner
Straight Edge
Tweezers
Pointy Tool
Safety Glasses
Band-aids
Graph Paper
Tracing Paper
Quilter's Rule
Pencils
Compass for drawing circles
Elmer's Glue
Plastic Drawing Template
Protractor
LED Lightbox
Square Ceramic Kiln Shelf, 10 inch x 10 inch x 1/2 inch thick
Fiber Paper, 1/2 inch x 1/2 inch x 1/8 inch thick
Bullseye ThinFire Shelf Paper, 10 inch x 10 inch

1 Jewelry Connector Jump Ring in silver-plated brass, 12mm round and 16 gauge (not shown)
Sharpie Fine line Marker (not shown)

Kiln

The kiln is a model called the Bonnie Glo and is made by Jen-Ken Kilns. It is an all fiber kiln with a digital 3 button controller. The interior measures 15 inches in circumference and 6 inches deep. It runs on 120 volts.

Glass

One piece - 6 inches x 10 inches. I used hand-rolled, fusible art glass made by Bullseye Glass Company. This piece is a double-rolled, 3mm, 2-color streaky sheet mix in light turquoise and true blue. It originally measured 10 inch by 10 inch and is Bullseye code 002416-0030-F-1010.

Step 1: Creating a Polar Graph

Polar graphs are an easy start to get the basic snowflake shape drawn. Snowflakes are 6 sided, so I divided my polar graph into 6 equal sections. You can buy polar graph paper, but I really enjoy the manual part of drafting. My construction is not perfect, but it serves to connect me with the geometry of the parts and how they work together as a whole.

Draw a 9-1/2 inch square and find the center.
Draw a circle with a 1 inch radius and centered in the square.

Using a ruler, spread the arms of the compass to 1 inch.
Set the metal tip of the compass in the square's marked center.
Tilt the compass at an angle so the pencil end just touches the paper.
Gently swing the pencil end in a circle and mark the paper.
Make sure to keep the metal tip in the center.

Now draw 7 more concentric circles at 1/2 inch intervals.

Using a ruler, spread the arms of the compass to 1-1/2 inches.
Set the metal tip of the compass in the square's marked center.
Tilt the compass at an angle so the pencil end just touches the paper.
Gently swing the pencil end in a circle and mark the paper.
Make sure to keep the metal tip in the center.
Repeat for circles with radius of 2 inch, 2-1/2 inch, 3 inch, 3-1/2 inch, 4 inch, 4-1/2 inch.
As each circle is drawn, the metal tip of the compass makes a hole at the center. That's okay.

Divide the 1 inch inner circle into 6 equal segments.

Using a ruler, spread the arms of the compass to 1 inch.
Set the metal tip of the compass at the 6 o'clock point of the circle.
Tilt the compass at an angle so the pencil end just touches the paper.
Gently swing the pencil end in an arc and mark the paper where it intersects the circle circumference.
Now set the metal tip of your compass on the just drawn intersection.
Again, gently swing the pencil end in an arc and mark the paper where it intersects the circle circumference.
Repeat until you have 6 sections.

Divide the 1-1/2 inch second circle into 6 equal segments.

Using a ruler, spread the arms of the compass to 1-1/2 inches.
Set the metal tip of the compass at the 9 o'clock point of this circle.
Tilt the compass at an angle so the pencil end just touches the paper.
Gently swing the pencil end in an arc and mark the paper where it intersects the circle circumference.
Now set the metal tip of your compass on the just drawn intersection.
Again, gently swing the pencil end in an arc and mark the paper where it intersects the circle circumference.
Repeat until you have 6 sections.

Draw the vertical axis, the horizontal axis and the rays.

Using a ruler, draw a vertical line through the center of the circles. This is the vertical or y-axis.
With a ruler, draw a horizontal line through the center of the circles. This is the horizontal or x-axis.
Starting at the center, draw each ray as it passes through the first and second circles and continue to the edge of the square.

Step 2: Drawing the Snowflake Template

I like to draw a snowflake template and then use that to design the glass version. The snowflake tracing template has 6 main arms (rays) plus side branches. Note that when the side branches meet each other, they form 6 pointed stars. Also, all branches extend from the arms at 60 degrees, which is also the interior angle of an equilateral triangle. I think it's neat that since all branches are drawn at 60 degrees, they are part of an equilateral triangle that is similar to a mirrored equilateral triangle that is part of a hexagon that fits inside the 1 inch circle.

Choose your 6 main arms. (Snowflake arms are called dendrites.)

The polar graph is drawn with 8 rays, a positive / negative horizontal axis, and a positive / negative vertical axis for a total of 12 prospective snowflake arms.
Label the 12 radiating arms with numbers 1-6 and letters A-F, alternating between letters and numbers as you travel around the circle.

Creating branches at the 1 inch circle.

Using a ruler, spread the arms of the drawing compass to 1 inch.
Set the metal tip of the compass where ray 4 intersects the circle with a 1 inch radius.
Tilt the compass and swing a small arc until it intersects ray C.
Set the metal tip of the compass where ray 3 intersects the circle with a 1 inch radius.
Tilt the compass and swing a small arc until it intersects ray C and then B.
Repeat for rays A, D, E and F.

Draw the branches.

Connect the dots and create a 6 pointed star.

Creating branches at the 2 inch circle.

You can use parallel lines to draw this set of branches, or continue with the compass. If you choose to use parallel lines, step 6 has more information.

Using a ruler, spread the arms of the compass to 1 inch.
Set the metal tip of the compass where ray 3 intersects the circle with a 2 inch radius.
Tilt the compass and swing a small arc, marking at approximately 60 degrees.
Set the metal tip of the compass where ray 3 intersects the circle with a 3 inch radius.
Tilt the compass and swing a small arc until it meets and crosses the previous arc, making a curvy x.
Repeat for the opposite side of ray 3.
Draw 2-1/2 inch lines from ray 3 that extend out and through the arc intersections.

Draw the branches.

Repeat 5 more times and create a total of 6 sets of branches and a larger 6 pointed star.

Add more fernlike branches.

All of the branches along a ray will be parallel to each other.
To add more branches, use a transparent quilting rule with parallel lines printed on it.
Looking through the quilter's rule, place the 1 inch line over any branch.
Draw a 1/2 inch line extending out from the arm.
Move the quilter's rule up a 1/2 inch and draw a 1 inch line extending out from the arm.
Move a 1/2 inch at a time, repeat for the desired number of branches.
Repeat the pattern on each arm around the snowflake to keep the symmetry.

Add more details.

Use a standard template (mine was for house planning) to add 1/2 inch diamonds at the tips.

Now you have a basic snowflake for a tracing template! Hurray!

Step 3: Developing the Snowflake Design

After paging through the book Snow Crystals by WA Bentley and WJ Humphreys, I chose a few favorite snowflakes as inspiration.

Place tracing paper over your tracing template and draw snowflake variations until you find the one that works for you. Take time to find the patterns within each snowflake formed by the interlocking side-branches. You can create diamonds within the 6-pointed stars and mini snowflakes at the end of each main arm. Make sure to repeat your patten on each of the six arms for symmetry.

Choose your favorite snowflake form. Place a new sheet of tracing paper on top of it to translate the pattern into something that will work in glass. Here are a few things to consider:

Size: make the main parts wider and other parts skinny to add visual interest

Glass Cutting: it is hard to cut pieces thinner than 1/4 inch

Construction: building is easier when components are supported evenly

Overlap: glass fusing requires an overlap of pieces so they stick together

Volume Control: surface tension of Bullseye glass at full fuse is about 1/4 inch or 2 layers of glass so glass only 1 layer thick will shrink a little and 2 layers will round

Once drawn, identify the main shapes:

Main arm
Inner hexagon
Inner Star
Outer Star
Branches

Now label each component:

Main arm
Inner hexagon
Inner star
Outer star
Main arm branch
Inner star connector
Outer star connector and Main arm top
Outer star cross piece and Main arm branch tips
Jump ring for hanging

Step 4: Shop Safety

Wear safety glasses!

Cutting glass can cause sharp flakes and glass bits to go flying. Make sure to always wear eye protection when cutting glass.

Be careful!

Cut and broken glass can be sharp so be careful to not cut yourself.

Step 5: Cutting the Glass

Always use shop safety. Be careful and wear safety glasses when working with glass. Cut glass is sharp so be careful and try not to get cut. Yellow glass was used for the photos because it was easier to see.

Cut List:

Main arm : six - 4 inch x 1/2 inch
Inner hexagon : six - 7/8 inch x 1/4 inch
Inner star : twelve - 7/8 inch x 1/4 inch
Outer star : twelve - 1 and 5/8 inch x 1/4 inch
Main arm branch : twelve - 1 and 1/2 inch x 3/8 inch
Inner star connector : six - 3/8 inch x 3/8 inch
Outer star connector and Main arm top : twelve - 1/2 inch x 1/2 inch
Outer star cross piece and Main arm branch tips : forty-eight - 1/2 inch x 1/4 inch

Using the wheeled nippers, cut the smallest 1//8 inch triangle off of one corner of only 6 of your inner star pieces. Leave 6 inner star pieces uncut.

Cutting The Glass:

Check and make sure your safety glasses are on!

Clean your glass with glass cleaner and wipe dry. Using a fine line sharpie marker, mark the desired width on the glass.

Place the sheet glass on a cutting mat. Score the glass with the pistol grip glass cutter and break the strips apart with the running pliers.
My glass cutter has a pistol grip filled with a little oil, but any kind of glass cutter will work. A glass cutter scores the glass with its carbide wheel, this scoring of the surface tells the fragment where to break. The wheel is centered at the tip so make sure the wheel is on your marked line, not the edge of the tip that holds the scoring wheel. Now pressing firmly, take your glass cutter and score in one pass. A straight edge helps to keep everything square.
The running pliers will actually break the glass along the score. Take a moment and look at the ends of the jaws of the running pliers. They are curved, so hold them with the front edge of the jaws curving down or frowning and the score centered on the black mark. It is best to score and break from the middle out, so you have equal amounts of material on either side of the score. Place the scored glass in the mouth of the running pliers and gently squeeze until you hear a pop. Sometimes it helps to repeat this gentle squeeze on either end of the score. When the center of the bottom jaw pushes up, the outside of the top jaw pushes down and the glass breaks on the scored line. This is called running the break.

I had trouble photographing the transparent glass on the black cutting mat, so I took a few extra photos and a short video clip of cutting 1/4 inch strips out of yellow art glass. I didn't use any yellow in this project. Here is a clip of scoring and cutting 1/4 inch strips:

https://youtu.be/Y6bXhz3Lq4c

Step 6: Assembling the Snowflake

Place your completed snowflake pattern on the lightbox and lay the Bullseye ThinFire Shelf Paper over it. Make sure the printed side of the ThinFire is face down. With the lightbox on, trace the snowflake onto the ThinFire. Transfer the ThinFire to the top of the ceramic kiln shelf with the drawing face up.

Find the components for the first layer of the snowflake, the 6 main arms, 6 inner star connectors, 6 outer star connectors, and the 48 cross pieces and branch tips.
Using the tiniest drop of glue, attach these glass pieces to the ThinFire. Be careful to only use a small drop of glue so none squishes out. This glue is only to stabilize the pieces during assembly and keep everything together when transferring to the kiln. Now glue the square of fiber paper to the ThinFire just at the outside end of one of the main arms. This will be for the jump ring. Allow the glue to dry for a few minutes.
Next glue, with a small dot, the 12 main arm branches, the 12 inner star parts, and the 12 outer star parts. When placing the inner star glass components, alternate the 6 pieces missing the tiny triangle with the 6 uncut pieces. This allows both to fit on the inner star connector. Allow the glue to dry.
Take a moment to look at the jump ring, it is split in one place. This split must be completely encased in glass for hanging. Place a tiny glue dot about a 1/4 inch from the end of the arm with the fiber paper. Lay the jump ring opening over this glue dot, centered on the width of the arm. The jump ring should be half on the glass and half on the fiber paper. Allow the glue to dry.
Now fix the glass main arm top squares with a dot of glue. Make sure to gently balance the square over the jump ring. Also glue the inner hexagon. Let the glue dry.

Step 7: Firing the Kiln

Carefully move the shelf with the snowflake to the kiln. Now it is time to fire the kiln and fuse the snowflake together.

A little more math. I heat my glass in an electric kiln with a programmable controller. I use a timed schedule with very specific temperature increases and holds over a set period to get both the finished look I want and also to keep the glass from cracking due to thermal shock. All glass brands are different, please check the manufacturer for recommended fusing guidance. Be sure to test your glass and see how it will behave in your kiln.

A glass firing schedule is done in segments with each segment in three parts. These parts are:

ramp: speed of temperature change, degrees Fahrenheit per hour
temperature: set temperature to reach, degrees Fahrenheit
hold: amount of time to stay at that temperature, minutes

Here are the 6 segments of the schedule I use for fusing glass snowflakes. I have included a photo of the firing schedule graph in the photos to better see what is happening.