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Half icosahedron, Platonic Solids

77621d171ae8d68dccb3981ac03649fc_preview_featured.jpg Half icosahedron, Platonic Solids
28ce60cfb9c6c210fac92a0625e87d10_preview_featured.jpg Half icosahedron, Platonic Solids
d7cc510be0080ab2eeea63a13d681f49_preview_featured.jpg Half icosahedron, Platonic Solids
dbee0ed917b6d246c1d24280bbc17880_preview_featured.jpg Half icosahedron, Platonic Solids
Icosahedron_Half_20mm.stl Half icosahedron, Platonic Solids
Icosahedron_Half_25mm.stl Half icosahedron, Platonic Solids
Icosahedron_Half_30mm.stl Half icosahedron, Platonic Solids
Icosahedron_Half_40mm.stl Half icosahedron, Platonic Solids
Icosahedron_Half_50mm.stl Half icosahedron, Platonic Solids
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Creation quality: 5.0/5 (1 vote)
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3D design format
STL Folder details Close
  • Icosahedron_Half_20mm.stl
  • Icosahedron_Half_25mm.stl
  • Icosahedron_Half_30mm.stl
  • Icosahedron_Half_40mm.stl
  • Icosahedron_Half_50mm.stl

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Publication date 2018-04-16 at 09:54
Design number 24103
LGBU

LGBU

3D printer file info

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.

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