Platonic solids [solved]

[NoeOM]

Hi,

I would like to know how to model the five platonic solids:

Platonic solid

Obviously, the faces involving more than 4 vertices (ngons) can be made up of tris or quads, no problem as long as you don’t notice it after rendering.

Thanks in advance.

[NoeOM]

Well, the hexahedron is a simple cube, and the icosahedron can be modelled with a icosphere with just one subdivisions.

Just three of them left… any help?

[DolorSitAmet]

The tetrahedron can be obtained from a cube, by creating a face-diagonal in each face of the cube.

• So, start with the basic cube
  [LIST]

• –> http://www.ideogram.nl/videos/blenderartists/pic1.png

• Create diagonals by adding new edges between the existing vertices

•    -->  http://www.ideogram.nl/videos/blenderartists/pic2.png
  

• remove the edges that belong to the cube

•   --> http://www.ideogram.nl/videos/blenderartists/pic4.png
  

• and create new faces between the edges of the tetrahedron.

•   --> http://www.ideogram.nl/videos/blenderartists/pic5.png
  

[/LIST]

[DolorSitAmet]

In a similar fashion, it should be possible to construct the dodecahedron from the icosahedron. In the same WikiPedia it is mentioned that

Dual polyhedra

A dual pair: cube and octahedron.

Every polyhedron has a dual (or “polar”) polyhedron with faces and vertices interchanged. The dual of every Platonic solid is another Platonic solid, so that we can arrange the five solids into dual pairs.

• The tetrahedron is self-dual (i.e. its dual is another tetrahedron).
• The cube and the octahedron form a dual pair.
• The dodecahedron and the icosahedron form a dual pair.

Now the problem is that I need to add a vertex to the exact centre of a triangle… If I can find a way to do that, I could construct a dodecahedron form a icosahedron…:rolleyes: :yes:

[DolorSitAmet]

Now I come to think of it: this is the way to create the octahedron:

1. Start with the default cube
2. select all faces --> subdivde
3. select the midpoints of 3 adjactend faces and press “f” --> Blender now creates a new face between these vertices
4. remove the 4 * 6 = 24 faces of the old cube

In the next picture, I’ve inserted one of the 8 faces of the octahedron into the cube:


Now, there’s still one Platonic body left

[RickyBlender]

in 2.5 there is already a script to do theses solids

have a look and see hwo it is done

i it it called regular solid

and there are many other solid type also

salutations

[NoeOM]

Many thanks for your help DolorSitAmet, but the add_mesh_solid.py script seems to be a much more reasonable solution.

The question is… where are scripts located in blender? How can I find and execute this script?

Thanks,

Noé.

[RickyBlender]

dowload the latest version of blender at graphical.org

and then go to the user preference panel select the addons panel
and unable the solid script

then go to the add menu at top of screen and select mesh and at bottom of the menu you should see the added solid script then select whichever solid you want

and that’s it it will do it in viewport !

hope it helps

[DolorSitAmet]

:spin: :rolleyes:

[loopduplicate]

Check the screenshot for clarity. Get a build from http://graphicall.org
Here’s my personal builds:

Non-optimized

GraphicAll.org

Optimized for SSE2

GraphicAll.org

Attachments

[NoeOM]

Great! I just needed to enable it on the user preferences panel, as suggested.

Thanks a lot everyone!

[ldo]

The octahedron is the dual of the cube, and can be easily produced from it using the Bevel function. Similarly, the dodecahedron is the dual of the icosahedron. The icosahedron can be produced as an “icosphere” with a subdivision level of 1.

The tetrahedron can be produced as a cone with 3 vertices, though it needs to be scaled to the right height in order for all the faces to become equilateral triangles. This is the only one that can’t seem to be done without typing a number.

More details here http://en.wikibooks.org/wiki/Blender_3D:_Noob_to_Pro/Platonic_Solids

[playfulgeometer]

Nifty stuff, I love to play with geometry !