Introduction: Make a Pythagorean Dodecahedron
The star pentagon, sometimes called a pentagram is the shape of a five point star. The shape has interesting ratios of different segment. The golden ratio just keeps on popping up. It so fascinated the Pythagoreans so much that they used it as a sign of recognition.
When I was writing my Instructable on Snub Dodecahedrons I noticed in Step 2 that the assembly of one pentagon and five triangles could be replace with a single five point star.
This Instructable with show how to assemble 12 stars into a polyhedron. Included are the patterns in SVG and PDF.
Step 1: Prep Your Pieces
You are going to need 12 stars. The pattern has two stars so you will need to make six copies on standard letter size card stock. . Either print and cut (PDF) or laser cut (SVG) all 12 pieces. Print or cut on the less pristine side of the card stock.
For each star fold the tabs down and the star point up. Turn each other. They should look like the photo.
Step 2: Assemble Six Stars..... Twice
Take six of the stars and arrange them as shown in the 1st photo. All the gluing with be done on the left sides of the points. I mark the left side tabs with a dot. If you are not gluing a dotted tab to a dotted tab then you are doing something wrong. Glue to the center star the five satellites stars. Then glue the satellite stars together with the arrows shown in the 1st photo. When complete, flip it over. It should look like the 2nd photo.
Make another one of these with your remaining six stars.
Step 3: Assemble Two Halves
Here is the place in place sometime inside before you seal it up. (Maybe a smaller dodecahedron or icosahedron.)
Take the two halves and arrange them so you have dotted tabs aligned with dotted tabs. Carefully glue them together. It is complete.
These stars are 6½" from tip to tip and the completed dodecahedron is roughly 8" in diameter. Use these values to scale this design to whatever size you want.
Either as a table decoration and hanging mobile it will be a conversation piece.
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