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Golden Rhombohedra, Acute, Obtuse, Golden Ratio, Dodecahedron, Rhombic Triacontahedron

3D model description

Golden Rhombohedra
Starting from a golden rhombus, we can build a 30-faced rhombic triacontahedron, which can be further used to build a golden icosahedron, a golden (Bilinski) dodecahedron. Then, from a golden dodecahedron, we can obtain two types of golden rhombohedra (six-faced polyhedra)—the acute form the obtuse form. They are strange on the screen but look and fit together beautifully once you have them in your hands.

There are certainly other ways to make these. But that is what I went through. Simple and complex as they are, all children should have a chance to play with them, to get a feel for mathematics! The rich connections are everywhere in these wonderful mathematical gems! Two sizes (short diagonal of a rhombus) are included: 25mm and 50mm.

How to Play
2 acute ones + 2 obtuse ones => 1 golden dodecahedron;
10 acute ones + 10 obtuse ones => 1 golden rhombic triacontahedron.

References
http://www.cutoutfoldup.com/979-golden-rhombohedra.php
http://www.georgehart.com/virtual-polyhedra/dissection-rt.html
https://en.wikipedia.org/wiki/Rhombic_triacontahedron

3D printing settings

Rafts:

No

Supports:

No

Resolution:

.1 to .2mm

Infill:

5-20%

Notes:
Support does not seem to necessary for the obtuse one; but do consider it if your printer needs it.

  • 3D model format: STL

Creator

STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides: http://www.nsta.org/safety/.

LGBU Contact: LGBU@SIU.EDU

License

CC BY


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