# Platonic solid in Euclidean geometry / Platonische Koerper

## by nischi, published Dec 14, 2012

Platonic solid in Euclidean geometry / Platonische Koerper by nischi Dec 14, 2012

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# Summary

The five great platonic solids

Tetrahedron (four faces)
Cube or hexahedron (six faces)
Octahedron (eight faces)
Dodecahedron (twelve faces)
Icosahedron (twenty faces)

In Euclidean geometry, a Platonic solid is a regular, convex polyhedron. The faces are congruent, regular polygons, with the same number of faces meeting at each vertex. There are exactly five solids which meet those criteria; each is named according to its number of faces.

Geometers have studied the mathematical beauty and symmetry of the Platonic solids for thousands of years. They are named for the ancient Greek philosopher Plato who theorized in his dialogue, the Timaeus, that the classical elements were made of these regular solids.[

http://www.ichdruck3d.de/platonische-koerper/

# Instructions

In Euclidean geometry, a Platonic solid is a regular, convex polyhedron. The faces are congruent, regular polygons, with the same number of faces meeting at each vertex. There are exactly five solids which meet those criteria; each is named according to its number of faces.

German:

In der Geometrie bezeichnet man mit den platonischen Koerpern (nach dem griechischen Philosophen Platon) vollkommen regelmaeszige Polyeder (dreidimensionale Koerper, die von Polygonen (Vielecken) als Seitenflaechen begrenzt sind).

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These are wonderful, thanks for modeling and sharing them!

im looking for someone to make me th following:
4 tetrahedrons [type 3 pyramids, th 1st platonic solid]
&
6 type 4 pyramids. a type 4 pyramid is 1/2 of an octahedron [th 3rd platonic solid]
all th edges must be th same length for all 10 objects. i dont have a 3D printer but will pay a reasonable price.
let me know if you are interested.
[email protected]

There is a bug in the Dodecahedron of this Thing, so I created a new one to fix this: http://www.thingiverse.com/thing:261258http://www.thingiverse.com/thi...

Dodekaeder
by took
nischi - in reply to took

hi,

thanks. that was one area which was not exactly leveled.
interesting: http://www.ichdruck3d.de/platonische-koerper/http://www.ichdruck3d.de/plato...

best wishes,

``     alex``

Any chance we will see a 10 sided solid added to the collection?

nischi - in reply to BrianMinister

No, sorry! There is abolutly no chance for a platonic solid with 10 faces!

Here you can see the definition:
In Euclidean geometry, a Platonic solid is a regular, convex polyhedron with congruent faces of regular polygons and the same number of faces meeting at each vertex. Five solids meet those criteria, and each is named after its number of faces.
http://en.wikipedia.org/wiki/Platonic_solidhttp://en.wikipedia.org/wiki/P...

BrianMinister - in reply to nischi

Thx for the link. Now I am clear on the term. surprised myself for not knowing this.
Now for the return trivia, since it is only fair. As far as many of us old folks go, we recognize these first as D4, D6, D8, D12, and D20 dice for Dungeons and Dragons. So the only missing die is D10. :) Though I suspect this isn't new trivia for you. It more illustrates what went through my head when I saw the images. :) I am nerd that way.

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