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Half icosahedron, Platonic Solids

3D model description

I got a challenge from two children (3rd and 4th graders). They made two congruent solids using some snap triangles (polydrons, see figures). They thought it should be half a regular icosahedron but could not put them together to make one. Is it really half a regular icosahedron?

No. They are close but not half an icosahedron in terms of the 3D solid. But the surface is indeed true. The dihedral angle of a regular tetrahedron is about 70.53 degrees; that of a regular icosahedron is 138.19 degrees. The former is close to 1/2 of the latter but is not exactly one half. That is why the children's models are so close.

How could I explain it to them? I made a real half icosahedron. It is easy to show where they are correct and where they are wrong! It turns out to be a nice problem to me, too.

Sizes: Edge Lengths: 20mm, 25mm, 30mm, 40mm, 50mm.

Reference
https://en.wikipedia.org/wiki/Table_of_polyhedron_dihedral_angles

3D printing settings

Rafts:

No

Supports:

No

Resolution:

0.15-.2mm

Infill:

5-25%

Notes:
It takes two copies to make a whole regular icosahedron, of course.

  • 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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