## 3D Wulff Net

A Wulff net is a 2D projection of a sphere onto a flat plane. On that plane are symbols of symmetry that help visualize the 3D shape is represents.

• Squares represent 4-fold symmetry.
• Triangles represent 3-fold symmetry.
• Ovals represent 2-fold symmetry.

This can be used to visualize the crystal structure of materials with the help of X-ray diffraction.

In this project, I converted a Wulff net of a cube into a 3D model and used Platonic solids to represent the symmetry.

• Faces → 4-fold symmetry → cubes
• Corners → 3-fold symmetry → tetrahedrons
• Edges → 2-fold symmetry → octahedrons

## Dodecahedron

The dodecahedron is the fifth Platonic solid made by having 3 regular pentagons meet at every corner.

Plato described this shape as the building block of the heavens, and even today, we can learn to appreciate its mystery.

A regular pentagon is in large part defined by the Golden Ratio, which occurs when the ratio of two numbers are the same as the ratio of their sum to the larger number.

So, if a > b > 0, then a is to b as (a+b) is to a.

In this project, I used the Golden Ratio to construct 3 rectangles and align each to one Cartesian axis.

I extended each rectangle's area by a square whose sides are equal to the rectangles' shorter sides.

Finally, I placed that structure in the middle of a cube whose sides are equal to the rectangle's longer sides prior to the addition of the squares.

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