View Full Version : Cubes and beyond

06-18-2001, 04:49 PM
I have just made a 6" cube using a 45 degree cutter from 1/4" masonite. I would like to make a multi-sided object using a 60 degree cutter, but I dont know the math (or terminology)for this calculation, does anyone have this know-how?

6"cube file

2427 (1 k)

It has a few repeat cuts after the first pass.

06-18-2001, 06:40 PM
That's a pretty cool idea.

A 60 degree cutter should work for a "box" with triangular panels.

06-18-2001, 09:32 PM
Thats right, I will need less angle to get more sides.
Does anyone know what angles are available and what the corresponding number of sides I will get from those.


06-18-2001, 11:25 PM
If you look for "flowerpot" router bits, you will find they make them with all sorts of angles. This is so you can make a pot with 4 sides or a pot with 16 sides.

06-19-2001, 02:57 AM
Here is the math for 7 solids:

do a search for "POLYHEDRAL" to get more info.

A polyhedral is a multi sided solid, a cube has six faces square shaped, a tetrahedron has 4 faces triangular shaped, an octahedron has 8 faces triangular shaped, an icosahedron has 20 faces triangular shaped, a dodecahedron has 12 faces pentagon shaped. These are the 5 platonic solids. What you need is the dihedral angle and make your cuts 1/2 of the dihedral angle. For example a cube's dihedral angle (the angle between faces) is 90 degrees so you cut each edge at 45 degrees.

Here is a chart that summarizes some of the solids:

Tetrahedron / 70.53 Degrees
Cube / 90
Octahedron / 109.46
Dodecahedron / 116.56
Icosahedron / 138.18

Truncated Icosahedron (soccer ball)
made from 12 pentagons and 20 hexagons
The hex to hex dihedral is 138.18 degrees
The hex to pentagon dihedral is 142.61

Icosidodecahedron has 12 pentagons and 20 isosceles triangles
pentagon dihedral is 142.61
isosceles dihedral is also 142.61

From the above you can see that there are not too many standard bits that are exactly 1/2 the dihedral angle except for the cube. Solution is to grind your own bits to the correct angle or use a sliding compound miter saw to make the cuts.

I have built all of the above using strips instead of solid faces, the math is the same and the fabrication a slightly more difficult, to see them go to this website:
and then click on Phil's Polyhedral Pholly and then click on the photo for an enlarged view.

They took over 150 hours to build (without CNC)

Phil Laliberte

06-19-2001, 10:36 AM
Well that sums it up, thanks Phil.
Congratulations on your awards, you swept up.

Rob S.