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Snowflake Globe

by kennyp1369, published

Snowflake Globe by kennyp1369 Jan 20, 2018
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Snowflake Globe by kennyp1369 is licensed under the Creative Commons - Attribution license.

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Thing Statistics

1035Views 152Downloads Found in Math Art

Summary

The Snowflake Globe is a sphere made out snowflakes. The whole thing was made by translating, mirroring, and rotating shapes inside of loops. The snowflake I designed was projected out onto the surface of a sphere and rotated to each face of an icosahedron. There are 20 hexagonal snowflakes on the surface and 12 pentagonal spaces between the snowflakes. All of the design was done in BlocksCAD. The design was printed in a friend’s office at Western Washington University on a Flashforge Creator Pro (Thank you for the printing time Reza Afshari).

Print Settings

Printer Brand:

FlashForge

Printer:

Rafts:

Yes

Supports:

Yes

Resolution:

.2 mm

Infill:

100 %

Post-Printing

The design was printed on a Flashforge Creator Pro, using natural PLA filament. There were plenty of supports, but they all came out.

How I Designed This

I had a great time designing for the BlocksCAD Snowflake Challenge and learning BlocksCAD. Trying different things was easy, and I learned how to make changes in my design by duplicating and collapsing blocks, and defining variables.

I parameterized 1/12 of a hexagonal snowflake to begin with. Spheres were translated inside a loop and hulled together to create each line. I parameterized each line by using the vector equation for a line r = v0 +t(v1 - v0), where v0 and v1 are the beginning and ending points of the line.

It was mirrored across the YZ plane and rotated inside a loop into the six points of a snowflake.

The whole thing was scaled up, the radii of the spheres were made larger, and a couple lines were disabled to make the design more printable.

The lines were all projected out onto the surface of a sphere. I gave them a Z coordinate by solving for Z in the equation of a sphere: x^2 + y^2 + z^2 = r^2.

I rotated and mirrored the snowflake to get four snowflakes that would be copied around the sphere to all 20 faces of an icosahedron.

To rotate around a line in the X-Z plane, I first rotated around the Y axis to get that line on top of the Z axis. Then I could just rotate around the Z axis alone. I found how much to rotate by calculating the dihedral angle of an icosahedron.

By rotating the snowflake in a loop around the Z axis, I was able to distribute 20 equally spaced snowflakes across the surface of a sphere.

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Beautiful model. Great print.

That level of support looked like a pain to print and clean. Not familiar with that printer but is it soluble support?

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