# Blender 3D: Noob to Pro/Platonic Solids

The **Platonic solids** or **Platonic polyhedra** are the convex
polyhedra where all faces are copies of the same regular polygon, and
the same number of edges meet at every vertex. There are five of these
shapes: the tetrahedron (like a pyramid but with a triangular base):
cube, octahedron, dodecahedron and icosahedron.

Recent versions of Blender include an addon called "Regular Solids",
which lets you instantly generate these and a whole bunch of other
similar shapes. However, the following steps do not require any addons.

### The Tetrahedron

Bring up the Add Mesh menu (Shift+A), and select a Cone. Set the number
of Vertices to 3, leave Radius 1 at its default value of 1.000 and
Radius 2 at 0.000[^1]. Now, set the Depth to $\sqrt{2} \approx 1.414$.
To make sure that you have a regular tetrahedron, you can check the
lengths of the edges (in Edit Mode, press N to open the Properties panel
and locate the checkbox **Length** in the section **Edge Info**).

### The Cube

This happens to be a built-in shape in Blender. Just bring up the Add
Mesh menu, and select Cube. Done!

### The Octahedron

This shape is the *dual* of the cube---it has vertices where the cube
has faces, and faces where the cube has vertices. To make it, first
create a cube. Press  to switch to Edit
mode. All the vertices should already be selected. Press
 to bring up the Specials menu, and select
the Bevel function (or select it directly with
). As you move the mouse, you will
see each vertex of the cube turn into a triangular face; don't bother
getting the shape exactly right, simply press
 to finish the drag. Then, look in the
panel that should have appeared at the bottom of the Toolshelf on the
left of the 3D view (press  to toggle
its visibility); you should see an editable numeric field labelled
"Offset". Type the value 1.0 into this field, and that should exactly
form the octahedron shape.

Finally, bring up the Specials menu again, and this time select Remove
Doubles[^2].

### The Icosahedron

Bring up the Add Mesh menu, and select an Icosphere. Set the Subdivision
to 1. Simple!

### The Dodecahedron

This shape is the dual of the icosahedron. To create it, make an
icosahedron as above. Then do what you did to make an octahedron out of
a cube: press  to switch to Edit mode.
All the vertices should already be selected. Press
 to bring up the Specials menu, and select
the Bevel function. As with the octahedron, press
 to finish the drag. Then set the Offset
value to 0.30310889132, which comes from the formula
$\frac{a\sqrt{3}}{6}$, with $a$ being the edge length of the icosahedron
(1.05 if made by the method above)[^3].

Then, bring up the Specials menu again, and this time select Remove
Doubles[^4], you should see the message "Removed 40 vertices" briefly
flash up.

![](BlenderPlatonicSolids.png "BlenderPlatonicSolids.png")

### Exercise

What's the dual of the tetrahedron? Try applying the Bevel operation to
one of those; what do you end up with?

## External Link

Wikipedia article


[^1]: Blender 2.8\^ in the \"Adjust last operation\" menu in the lower
    left corner only available after the first creation

[^2]: Blender 2.8\^: Merge Vertices By Distance

[^3]: To understand why this formula works: understand how the dual is
    formed, how offset in Blender works and what the formula computes
    (http://www.treenshop.com/Treenshop/ArticlesPages/FiguresOfInterest_Article/The%20Equilateral%20Triangle.htm)

[^4]: Blender 2.8\^: Merge Vertices By Distance
