When looking at pencil points there are all sorts of angles you could sharpen a pencil to.
I guess an angle of 180°, i.e. an unsharpened pencil is as low as you could go – unless you want an angle > 180°.
Here’s a photo of an unsharpened pencil, seen in Season 10 of Inspector Montalbano (Il commissario Montalbano), between the two eraser-tipped Noris pencils. You can see his other pencils in this blog post from 2012. Where they got an unsharpened Noris from is a mystery to me. Maybe they removed the pencil point of a factory sharpened pencil?
On the other hand you have pencil like the ones from Pencil Guide that seem to have an angle of 6.8° Thanks to Sola and Gunther I now think the angle might be 6.8°. (for comparison: the KUM Masterpiece has an angle of 15°). They look deadly.
If you create a point with an angle of 6.8° (cone angle 3.4°) on a pencil with a diameter of 8 mm you expose the wood at a length of approximately 67.6 mm. This length and the pencil’s length are in a ratio of approx. 1:1.618.
1:1.618 is the golden ration.
Pencil Guide calls itself a pencil sharpening service company, but they only sell sharpened pencils and don’t follow David Rees’ business model.
I would like to thank Jun-Haeng Lee for the information about Pencil Guide.
The images in this blog post have been taken from Pencil Guide and from episode A Delicate Matter of the RAI TV series Il commissario Montalbano. I believe that the use of the images shown in this blog post falls under “fair dealing” as described by the UK Copyright service.